This thesis investigates using interactive genetic algorithms to derive intelligent behavior for agents in a smart grid system. The thesis tests different variations of genetic algorithms in repeated matrix games against other learning algorithms like GIGA-WoLF and Q-learning. The results show the potential of using genetic algorithms, particularly when incorporating effective human input, to develop adaptive agent strategies in dynamic multi-agent environments like smart grids.

1. Applicability of Interactive Genetic Algorithms to
Multi-agent Systems: Experiments on Games Used
in Smart Grid Simulations.
by
Yomna Mahmoud Ibrahim Hassan
A Thesis Presented to the
Masdar Institute of Science and Technology
in Partial Fulfillment of the Requirements for the Degree of
Master of Science
in
Computing and Information Science
c 2011 Masdar Institute of Science and Technology
All rights reserved

2. AUTHOR’S DECLARATION
I understand that copyright in my thesis is transferred to Masdar Institute of Science
and Technology.
ACCEPTANCE DECLARATION
This thesis has been accepted and approved by Masdar Institute of Science and
Technology on August 01, 2011.
EXAMINATION COMMITTEE MEMBERS
Jacob Crandall, Advisor, Masdar Institute of Science and Technology
Davor Svetinovic, Masdar Institute of Science and Technology
Iyad Rahwan, Masdar Institute of Science and Technology
ii

3. Abstract
A common goal of many organizations over the next decades is to enhance the
efficiency of electrical power grids. This entails : (1) modifying the power grid
structure to be able to utilize the available resources in the best way possible, and
(2) introducing new energy sources that are able to benefit from the surrounding
circumstances. The trend toward the use of renewable energy sources requires the
development of power systems that are able to accommodate variability and intermittency in electricity generation. Therefore, these power grids, usually called
“smart grids,” must be dynamic enough to adapt smoothly to changes in the environment and human preferences.
In a smart grid, each decision maker can be represented as an intelligent agent
that consumes or produces electricity. Each agent interacts with other agents and
the surrounding environment. The goal of these agents may vary between maintaining the stability of electricity in the grid from the generation side and increasing users’ satisfaction with the electricity service from the consumers’ side (which
is our focus). This is done through the interaction between different agents to
schedule and divide the tasks of consumption and generation among each other,
depending on the need and the type of each agent.
In this thesis, we investigate the use of interactive genetic algorithms to derive
intelligent behavior that enables an agent on the consumer’s side to consume the
proper amount of electricity to satisfy human preferences. This behavior must take
iii

4. into account the existence of other agents within the system, which increases the
dynamicity of the system. In order to evaluate the effectiveness of the suggested
algorithms within a multi-agent settings, we test our algorithms in repeated matrix games when they associate with other copies of themselves, and against other
known multi-agent learning algorithms. We run different variations of the genetic
algorithm, with and without human input, in order to determine what are the factors
that affect the performance of the algorithm within a dynamic multi-agent system.
Our results show reasonable potential for using genetic algorithms in such circumstances, particularly when they utilize effective human input.
iv

5. This research was supported by the Government of Abu Dhabi to help fulfill the
vision of the late President Sheikh Zayed Bin Sultan Al Nayhan for sustainable
development and empowerment of the UAE and humankind.
v

6. Acknowledgments
I would first like to thank Masdar for giving us the opportunity to conduct our research, and increase the potential of a suitable environment to achieve a successful
research.
I would also like to express my gratitude towards my committee members, starting
with my advisor Professor Jacob Crandall, for his support, encouragement and continuous enthusiasm about our research for the past 2 years. Furthermore, I would
like to thank Dr. Davor Svetinovic and Dr. Iyad Rahwan for their feedback.
Last, but never least, I would like to thank my family and friends, for their
continuous support and their belief in me.
Yomna Mahmoud Ibrahim Hassan,
Masdar City, August 1, 2011.
vi

7. Contents
1
1
1.1
Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Motivation and Relevance to the Masdar Initiative . . . . . . . . .
2
1.3
Thesis statement . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.4
2
Introduction
Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . .
6
Literature Review
7
2.1
Electrical Power grids . . . . . . . . . . . . . . . . . . . . . . . .
8
2.1.1
Smart grids . . . . . . . . . . . . . . . . . . . . . . . . .
8
2.2
Multi-agent systems . . . . . . . . . . . . . . . . . . . . . . . . .
10
2.3
Matrix games . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
2.3.1
Types of matrix games . . . . . . . . . . . . . . . . . . .
12
2.3.2
Solution concepts . . . . . . . . . . . . . . . . . . . . . .
13
2.3.3
Repeated matrix games . . . . . . . . . . . . . . . . . . .
15
2.3.4
Stochastic games . . . . . . . . . . . . . . . . . . . . . .
17
Learning in repeated matrix games . . . . . . . . . . . . . . . . .
17
2.4
vi

8. 2.4.1
18
Evolutionary algorithms . . . . . . . . . . . . . . . . . . . . . .
19
Genetic algorithms . . . . . . . . . . . . . . . . . . . . .
19
Genetic algorithm structure . . . . . . . . . . . . . . . . .
20
Genetic algorithms in repeated matrix games . . . . . . . . . . .
27
2.6.1
Genetic algorithms in distributed systems . . . . . . . . .
29
2.6.2
Genetic algorithms in dynamic systems . . . . . . . . . .
29
Interactive learning . . . . . . . . . . . . . . . . . . . . . . . . .
31
2.7.1
Interactive learning in repeated matrix games . . . . . . .
32
2.7.2
3
Reinforcement learning . . . . . . . . . . . . . . . . . . .
2.5.2
2.8
18
2.5.1
2.7
No-regret learning . . . . . . . . . . . . . . . . . . . . .
2.4.3
2.6
18
2.4.2
2.5
Belief-based learning . . . . . . . . . . . . . . . . . . . .
Interactive genetic algorithms . . . . . . . . . . . . . . .
32
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
Experimental Setup
36
3.1
Games’ structure . . . . . . . . . . . . . . . . . . . . . . . . . .
36
3.1.1
Prisoner’s dilemma . . . . . . . . . . . . . . . . . . . . .
37
3.1.2
Chicken . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
3.1.3
Shapley’s game . . . . . . . . . . . . . . . . . . . . . . .
38
3.1.4
Cooperative games . . . . . . . . . . . . . . . . . . . . .
38
3.2
Knowledge and Information . . . . . . . . . . . . . . . . . . . .
39
3.3
Opponents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
3.3.1
GIGA-WolF . . . . . . . . . . . . . . . . . . . . . . . .
40
3.3.2
Q-learning . . . . . . . . . . . . . . . . . . . . . . . . .
41
3.4
Evaluation criteria . . . . . . . . . . . . . . . . . . . . . . . . . .
42
3.5
Performance of GIGA-WoLF and Q-learning . . . . . . . . . . .
43
3.5.1
Prisoner’s dilemma . . . . . . . . . . . . . . . . . . . . .
43
3.5.2
Chicken . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
vii

9. 3.5.3
4
44
3.5.4
3.6
Shapley’s game . . . . . . . . . . . . . . . . . . . . . . .
Cooperative games . . . . . . . . . . . . . . . . . . . . .
44
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
45
Learning using Genetic Algorithms
47
4.1
Algorithm structure . . . . . . . . . . . . . . . . . . . . . . . . .
48
4.1.1
Basic genetic algorithm . . . . . . . . . . . . . . . . . . .
51
4.1.2
Genetic algorithm with history propagation . . . . . . . .
52
4.1.3
Genetic algorithm with stopping condition
. . . . . . . .
52
4.1.4
Genetic algorithm with dynamic parameters’ setting . . .
52
4.1.5
Genetic algorithm with dynamic parameters’ setting and
stopping condition . . . . . . . . . . . . . . . . . . . . .
Genetic algorithms vs. GIGA-WoLF . . . . . . . . . . . .
55
Genetic algorithms Vs. Q-learning . . . . . . . . . . . . .
56
4.2.3
5
54
4.2.2
4.3
Results and analysis . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1
4.2
53
Genetic algorithms in self play . . . . . . . . . . . . . . .
59
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
Interactive genetic algorithms
63
5.1
Human input framework . . . . . . . . . . . . . . . . . . . . . .
64
5.1.1
Evaluate the population . . . . . . . . . . . . . . . . . . .
64
5.1.2
Select set of histories . . . . . . . . . . . . . . . . . . . .
66
5.1.3
Generate statistics for selected histories . . . . . . . . . .
67
5.1.4
Generating a new population from human input . . . . . .
68
Interactive genetic algorithms: Six variations . . . . . . . . . . .
69
5.2.1
Effect of input quality on the performance of GA . . . . .
69
Results and analysis . . . . . . . . . . . . . . . . . . . . . . . . .
71
5.3.1
73
5.2
5.3
Interactive genetic algorithms . . . . . . . . . . . . . . .
viii

10. 5.3.2
Modificiations on interactive genetic algorithms . . . . . .
5.3.3
78
The effect of human input quality on interactive genetic
algorithms . . . . . . . . . . . . . . . . . . . . . . . . .
5.4
6
83
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
89
90
6.1
N-player prisoner’s dilemma . . . . . . . . . . . . . . . . . . . .
90
6.2
Strategy representation . . . . . . . . . . . . . . . . . . . . . . .
92
6.3
Human input . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
6.4
Results and analysis . . . . . . . . . . . . . . . . . . . . . . . . .
94
6.5
7
IGA in N-player matrix games
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
97
Conclusions and Future work
99
7.1
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
7.2
Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
ix

11. List of Tables
2.1
Payoff matrix for the Prisoner’s dilemma. . . . . . . . . . . . . .
12
2.2
Payoff matrix for the Prisoner’s dilemma. . . . . . . . . . . . . .
17
3.1
Payoff matrix for the Prisoner’s dilemma. . . . . . . . . . . . . .
37
3.2
Payoff matrix for chicken game. . . . . . . . . . . . . . . . . . .
38
3.3
Payoff matrix of Shapley’s game. . . . . . . . . . . . . . . . . . .
38
3.4
Payoff matrix of a fully cooperative matrix game. . . . . . . . . .
39
4.1
Variables used within the algorithms . . . . . . . . . . . . . . . .
49
4.2
Payoff matrix for the Prisoner’s dilemma. . . . . . . . . . . . . .
56
4.3
Payoff of a fully cooperative matrix game. . . . . . . . . . . . . .
56
4.4
Payoff matrix for chicken game. . . . . . . . . . . . . . . . . . .
56
4.5
Payoff matrix of Shapley’s game. . . . . . . . . . . . . . . . . . .
57
5.1
Properties of the different variations of IGA algorithms. . . . . . .
70
5.2
Acceptable and unacceptable human inputs for the selected 2-agent
matrix games. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
70

12. List of Figures
2.1
A traditional Electrical Grid [8]. . . . . . . . . . . . . . . . . . .
9
2.2
A smart electrical grid [8]. . . . . . . . . . . . . . . . . . . . . .
10
2.3
Payoff space for the prisoner’s dilemma game [25]. . . . . . . . .
16
2.4
Roulette wheel selection mechanism [30]. . . . . . . . . . . . . .
22
2.5
Crossover in genetic algorithms. . . . . . . . . . . . . . . . . . .
23
2.6
Mutation in genetic algorithms. . . . . . . . . . . . . . . . . . . .
24
2.7
Basic structure of genetic algorithms. . . . . . . . . . . . . . . .
25
2.8
The interactive artificial learning process [27]. . . . . . . . . . . .
31
3.1
Payoffs of GIGA-Wolf and Q-Learning within selected games. . .
46
4.1
Chromosome structure . . . . . . . . . . . . . . . . . . . . . . .
50
4.2
Effect of variations on GA on final payoffs against GIGA-WoLF
(all games). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3
57
Effect of variations on GA on final payoffs against GIGA-WoLF in
prisoner’s dilemma. . . . . . . . . . . . . . . . . . . . . . . . . .
xi
58

13. 4.4
Effect of variations on GA on final payoffs against GIGA-WoLF in
cooperation game. . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5
Effect of variations on GA on final payoffs against GIGA-WoLF in
Chicken game. . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6
59
Effect of variations on GA on final payoffs against Q-learning in
prisoner’s dilemma. . . . . . . . . . . . . . . . . . . . . . . . . .
4.9
58
Effect of variations on GA on final payoffs against Q-learning (all
games). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.8
58
Effect of variations on GA on final payoffs against GIGA-WoLF in
Shapley’s game. . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.7
58
60
Effect of variations on GA on final payoffs against Q-learning in a
Cooperation game. . . . . . . . . . . . . . . . . . . . . . . . . .
60
4.10 Effect of variations on GA on final payoffs against Q-learning in
Chicken game. . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
4.11 Effect of variations on GA on final payoffs against Q-learning in
Shapley’s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
4.12 Sample of the chromosomes generated vs. Q-learning in prisoner’s
dilemma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
4.13 Effect of history propagation on GA against Q-learning in Prisoners dilemma. Values shows are the average payoff per generation.
61
4.14 Effect of variations on GA against Q-learning in cooperation game
(Average payoff per generation). . . . . . . . . . . . . . . . . . .
61
4.15 Effect of variations on GA on final payoffs in self play (all games)
61
4.16 Effect of variations on GA on final payoffs in prisoner’s dilemma .
62
4.17 Effect of variations on GA on final payoffs in a Cooperation game
62
4.18 Effect of variations on GA on final payoffs in Chicken game . . .
62
4.19 Effect of variations on GA on final payoffs in Shapley’s game . . .
62
xii

14. 5.1
Human input framework. . . . . . . . . . . . . . . . . . . . . . .
65
5.2
Designed graphical user interface. . . . . . . . . . . . . . . . . .
66
5.3
Evaluation metrices example . . . . . . . . . . . . . . . . . . . .
72
5.4
Effect of human input on basic IGA against GIGA-WoLF (all games). 73
5.5
Effect of basic human input on the performance (final payoff) of
GA vs. GIGA-WoLF in prisoner’s dilemma. . . . . . . . . . . . .
5.6
Effect of basic human input on the performance (final payoff) of
GA vs. GIGA-WoLF in a cooperation game. . . . . . . . . . . . .
5.7
74
Effect of basic human input on the performance (final payoff) of
GA vs. GIGA-WoLF in Shapley’s game. . . . . . . . . . . . . . .
5.9
74
Effect of basic human input on the performance (final payoff) of
GA vs. GIGA-WoLF in chicken game. . . . . . . . . . . . . . . .
5.8
74
74
Effect of basic human input on GA against GIGA-WoLF in Shapley’s (Average payoff per generation). . . . . . . . . . . . . . . .
75
5.10 Effect of basic human input on GA on final payoffs against Qlearning (all games). . . . . . . . . . . . . . . . . . . . . . . . .
75
5.11 A sample of the chromosomes generated from basic IGA vs. Qlearning in prisoner’s dilemma. . . . . . . . . . . . . . . . . . . .
76
5.12 Effect of basic human input on the performance (final payoff) of
GA vs. Q-learning in prisoner’s dilemma. . . . . . . . . . . . . .
76
5.13 Effect of basic human input on the performance (final payoff) of
GA vs. Q-learning in a cooperation game. . . . . . . . . . . . . .
76
5.14 Effect of basic human input on the performance (final payoff) of
GA vs. Q-learning in chicken game. . . . . . . . . . . . . . . . .
76
5.15 Effect of basic human input on the performance (final payoff) of
GA vs. Q-learning in shapley’s game. . . . . . . . . . . . . . . .
xiii
76

15. 5.16 Effect of basic human input on GA on final payoffs in self-play (all
games). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
5.17 Effect of basic human input on GA in self-play in chicken game
(Average payoff per generation). . . . . . . . . . . . . . . . . . .
77
5.18 Effect of basic human input on the performance (final payoff) of
GA in self-play in prisoner’s dilemma. . . . . . . . . . . . . . . .
78
5.19 Effect of basic human input on the performance (final payoff) of
GA in self-play in a cooperation game. . . . . . . . . . . . . . . .
78
5.20 Effect of basic human input on the performance (final payoff) of
GA in self-play in chicken game. . . . . . . . . . . . . . . . . . .
78
5.21 Effect of basic human input on the performance (final payoff) of
GA in self-play in shaply’s game. . . . . . . . . . . . . . . . . . .
78
5.22 Effect of variations on human input on GA against GIGA-WoLF
(all games). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
79
5.23 Effect of variations on IGA against GIGA-WoLF in prisoners dilemma
(Average payoff per generation). . . . . . . . . . . . . . . . . . .
79
5.24 Effect of variations on IGA on final payoffs vs. GIGA-WoLF in
prisoner’s dilemma. . . . . . . . . . . . . . . . . . . . . . . . . .
80
5.25 Effect of variations on IGA on final payoffs vs. GIGA-WoLF in a
cooperation game. . . . . . . . . . . . . . . . . . . . . . . . . . .
80
5.26 Effect of variations on IGA on final payoffs vs. GIGA-WoLF in
Chicken game. . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
5.27 Effect of variations on IGA on final payoffs vs. GIGA-WoLF in
Shapley’s game. . . . . . . . . . . . . . . . . . . . . . . . . . . .
80
5.28 Effect of variations on IGA on final payoffs vs. Q-learning (all
games). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xiv
81

16. 5.29 Effect of variations on IGA on final payoffs vs. Q-learning in prisoner’s dilemma. . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
5.30 Effect of variations on IGA on final payoffs vs. Q-learning in a
cooperation game. . . . . . . . . . . . . . . . . . . . . . . . . . .
82
5.31 Effect of variations on IGA on final payoffs vs. Q-learning in
chicken game. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
5.32 Effect of variations on IGA on final payoffs vs. Q-learning in Shapley’s game. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
82
5.33 Effect of variations on IGA on final payoffs in self-play (all games). 83
5.34 Effect of variations on IGA on final payoffs in self-play in prisoner’s dilemma. . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
5.35 Effect of variations on IGA on final payoffs in self-play in a cooperation game. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
5.36 Effect of variations on IGA on final payoffs in self-play in chicken
game. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
5.37 Effect of variations on IGA on final payoffs in self-play in shapley’s game. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
84
5.38 Human input quality and its effect on final payoffs of IGA against
GIGA-WoLF (all games). . . . . . . . . . . . . . . . . . . . . . .
85
5.39 Human input quality and its effect on final payoffs of IGA vs.
GIGA-WoLF in prisoner’s dilemma. . . . . . . . . . . . . . . . .
85
5.40 Human input quality and its effect on final payoffs of IGA vs.
GIGA-WoLF in a cooperation game. . . . . . . . . . . . . . . . .
85
5.41 Human input quality and its effect on final payoffs of IGA vs.
GIGA-WoLF in chicken game. . . . . . . . . . . . . . . . . . . .
85
5.42 Human input quality and its effect on final payoffs of IGA vs.
GIGA-WoLF in shapley’s game. . . . . . . . . . . . . . . . . . .
xv
85

17. 5.43 Human input quality and its effect on IGA vs. GIGA-WoLF in
prisoners dilemma (Average payoff per generation). . . . . . . . .
86
5.44 Effect of human input quality and its effect on IGA against GIGAWoLF in cooperation (Average payoff per generation). . . . . . .
86
5.45 Human input quality and its effect on final payoffs of IGA vs. Qlearning (all games). . . . . . . . . . . . . . . . . . . . . . . . .
86
5.46 Human input quality and its effect on final payoffs of IGA vs. Qlearning in prisoners dillema (per generation). . . . . . . . . . . .
87
5.47 Human input quality and its effect on final payoffs of IGA vs. Qlearning in prisoner’s dilemma. . . . . . . . . . . . . . . . . . . .
87
5.48 Human input quality and its effect on final payoffs of IGA vs. Qlearning in a cooperation game. . . . . . . . . . . . . . . . . . . .
87
5.49 Human input quality and its effect on final payoffs of IGA vs. Qlearning in chicken game. . . . . . . . . . . . . . . . . . . . . . .
87
5.50 Human input quality and its effect on final payoffs of IGA vs. Qlearning in shapley’s game. . . . . . . . . . . . . . . . . . . . . .
87
5.51 Human input quality and its effect on final payoffs of IGA in selfplay (all games). . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
5.52 Human input quality and its effect on final payoffs of IGA in selfplay in prisoner’s dilemma. . . . . . . . . . . . . . . . . . . . . .
88
5.53 Human input quality and its effect on final payoffs of IGA in selfplay in a cooperation game. . . . . . . . . . . . . . . . . . . . . .
88
5.54 Human input quality and its effect on final payoffs of IGA in selfplay in chicken game. . . . . . . . . . . . . . . . . . . . . . . . .
88
5.55 Human input quality and its effect on final payoffs of IGA in selfplay in shapley’s game. . . . . . . . . . . . . . . . . . . . . . . .
6.1
88
Payoff matrix of the 3-player prisoner’s dilemma. . . . . . . . . .
91
xvi

18. 6.2
Relationship between the fraction of cooperators and the utility received by a game participant. . . . . . . . . . . . . . . . . . . . .
92
6.3
Final payoffs of selected opponents in 3-player prisoner’s dilemma.
93
6.4
Effect of human input on the performance of GA in the 3-player
prisoner’s dilemma in self-play. . . . . . . . . . . . . . . . . . . .
6.5
95
Effect of human input on the performance of GA in the 3-player
prisoner’s dilemma with 1-player as GIGA-WoLF and 1-player in
self-play. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.6
Effect of human input on the performance of GA in 3-player prisoner’s dilemma with 2-players as GIGA-WoLF. . . . . . . . . . .
6.7
95
96
Effect of human input on the performance of GA in 3-player prisoner’s dilemma with 1-player as Q-learning and 1-player in self-play. 96
6.8
Effect of human input on the performance of GA in 3-player prisoner’s dilemma with 2-players as Q-learning. . . . . . . . . . . .
6.9
97
Effect of human input on the performance of GA in 3-player prisoner’s dilemma with 1-player as Q-learning and 1-player as GIGAWoLF. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xvii
97

19. List of Algorithms
3.1
GIGA-WolF . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
3.2
Q-learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
4.1
Basic genetic algorithm . . . . . . . . . . . . . . . . . . . . . . .
51
4.2
Genetic algorithm with history propagation . . . . . . . . . . . .
52
4.3
Genetic algorithm with stopping condition . . . . . . . . . . . . .
53
4.4
Genetic algorithm with dynamic parameters’ setting . . . . . . . .
54
4.5
Genetic algorithm with dynamic parameters’ setting and stopping
condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xviii
55

20. CHAPTER
1
Introduction
1.1
Problem Definition
In multi-agent systems (MAS), intelligent agents interact with each other seeking
to maximize their own welfare. In many instances, these agents need to learn overtime in order to become more successful. One of the main issues within MAS is
the ability of each agent in the system to learn effectively and co-exist with heterogeneous agents within the system. MAS is considered one of the most prominent
fields of research because its structure describes many of sreal life problems.
Extensive research has been performed in an effort to design a learning algorithm applicable to work in MAS [10, 53, 91]. However, proposed solutions
typically suffer from at least one of the following problems:
1. Inability to adapt with the increase of dynamic situations within the system.
2. Settlement into myopic, non-evolving solutions.
1

21. CHAPTER 1. INTRODUCTION
2
3. Requirement of extensive learning time in order to reach an acceptable solution.
Power systems are widely used as an example of MAS [51, 106]. In such systems, each consumer can be considered as an agent. Each agent in this multi-agent
system must learn an intelligent behavior in order to maximize its own personal
gain. In this case, the gain from the consumer’s perspective is the ability to satisfy
the user’s consumption and preferences.
1.2
Motivation and Relevance to the Masdar Initiative
Electricity consumption has increased drastically in the past decade as a result of
an enormous increase in population and technology. In the UAE for instance, there
has been a sudden increase in the usage of high-tech appliances and ability to add
more electrical devices than ever before [70]. This increase in consumption, while
still relying on the old electrical grid as a mean of distributing electricity, leads
to high losses in electricity. This is partially due to the variation in consumption
among different sectors, where each sector consumes electricity based on different schedules. Another recent development in modern power systems is the entry
of renewable energy sources on a large scale. The use of these energy sources,
which generate an intermittent and less predictable supply, is expected to continue
to increase over the next few decades to reduce the consumption of less environmentally friendly energy resources. To effectively handle these forms of electricity
generation and increased electricity usage, a more intelligent distribution structure
must be implemented. This intelligent solution is referred to in the literature as the
“smart grid” [16].
Electricity dispatch, in which electricity supply must be matched with electricity demand, is a common problem in electrical grids. Research and industrial

22. CHAPTER 1. INTRODUCTION
3
work has been dedicated to design systems that are capable of taking information
from generators and consumers to determine how to effectively distribute electricity. These types of systems are called “electricity management systems” [105].
Traditional management systems typically use a centralized structure, and rely
on a market operator to manage electricity distribution [99]. This central agent
determines the distribution of electricity either by applying a constant scheduling
mechanism or by running an off-line predication mechanism to model and predict
supply and demand [59]. However, management systems relying on a central single
operator do not match the structure of how an electricity market operate. Normally,
electricity markets rely on different entities (including the generators, distributors
and consumers) to make a decision. As such; electricity markets are better modeled by distributed interactions between consumers and distributors. Furthermore,
traditional management systems have other drawbacks, such as:
1. The extensive computational power required at the decision center, which
results in slow response times and an inability to keep up with real-time
updates [37].
2. The system’s inability to respond adequately to an event not covered by the
system occurs. This is the result of the static structure of the scheduling
mechanism running in the system, and its inability to adapt to regulatory
changes in the environment in a real-time manner [37].
3. The algorithm running at the center of the system must be completely redesigned if the configuration has to be changed (addition or removal of an
element or an agent) [37].
4. The centralized model’s focus concentrates solely on the overall response of
the power grid, making it difficult to model real-time interactions between
different entities [59].

23. CHAPTER 1. INTRODUCTION
4
However, the realization of a distributed power system requires the development of additional capabilities to manage electricity transmission efficiently without relying on a central agent. By moving into a multi-agent perspective, where
we rely on different decision makers, we must determine how charges can be distributed amongst generation companies, how to take transmission constraints into
account, and which regulation mechanisms are suitable for such a system [99].
Additionally, informational and motivational aspects of the agents, such as beliefs,
desires, intentions and commitments, must be investigated [13]. Furthermore, with
variations in workloads and energy sources, it is hard to define a single policy that
will perform well in all cases [32]. This leads us to a requirement for making
the agents more intelligent and adaptable. To achieve this, agents need to evolve
their own behavior with respect to scheduling their consumption according to these
changes, without the need to redesign their decision making structure. This can be
potentially achieved by applying game theory and machine learning concepts.
Previous work has been done in order to investigate the use of evolutionary
algorithms (EA) within the area of electricity management [67]. These algorithms
have been shown to be successful under specific conditions [81, 20, 83]. Unfortunately, under other conditions, EA tend to perform poorly. One such situation
occurs when there is a very large solution space defined by two or more interacting subspaces. One solution to this challenge is to run EAs on a multi-agent distributed structure of the system, and use the interaction between agents as means of
decreasing the search space by dividing it among different agents, and make each
agent benefit from others’ experience [102]. This introduces the concept of “multiobjective fitness function”, where EA work on multiple fitness functions for each
agent. The ideal solution, in most cases, does not exist because of the contradictory
nature of objective functions, so compromises have to be made.
A second challenge of the use of EA for distributed power systems is a chal-

24. CHAPTER 1. INTRODUCTION
5
lenge that exists in most of the existing learning algorithms, which is the inability
to adapt quickly to the changes in the environment and user preferences. EAs are
expected to work best if the market is not volatile.
Research has been done to try to overcome these problems in evolutionary algorithms, mainly in single agent systems. One suggested solution was to utilize
human input through “Interactive evolutionary algorithms” [33, 6]. In these algorithms, human input is used by the algorithm to decrease the amount of time needed
to reach a stable and efficient policy for the system. To ensure that the policy follows human preferences, and that it is robust enough to cope with variations in
the system. The latest of our knowledge, the idea of using interactive evolutionary
algorithms in multi-agent systems has not be studied to date.
Therefore, our objective is to find a learning algorithm that can be used by
individual entities in power systems to effectively acquire and manage energy resources to satisfy user preferences. This learning algorithm should be able to adapt
to the behavior of other learning entities, changes in the environment and changes
in user preferences.
1.3
Thesis statement
In this research, we study the performance of genetic algorithms (GAs) as a learning methodology for an agent within a multi-agent system. We discuss the effect of
integrating human input into GAs (known as interactive genetic algorithms) within
a multi-agent system. By conducting different experiments, we try to identify how
human input can be integrated into GAs, and test the applicability of interactive
genetic algorithms (IGAs) in repeated matrix games. The matrix games we use in
our experiments cover different possibilities and variations of the agents’ payoffs
in order to examine the effect of this variation on the algorithms’ performance.

25. CHAPTER 1. INTRODUCTION
6
We run different variations of our algorithms against different learning opponents,
including itself, Q-learning [100] and GIGA-WoLF [10].
1.4
Thesis Overview
Through this thesis, we will give a detailed analysis of related work done on the
aforementioned problem. We will begin by giving a literature review on related
topics through chapter 2 such as: multi-agent systems, genetic algorithms, and
interactive genetic algorithms. In chapter 3, we move forward to an overview of
the problem and our experimental setup. We show different variations of GAs
implemented through our experiments in chapter 4, and we study the effect of each
of these variations on the final performance of the system.
The next part of our thesis discusses and evaluates a potential framework for integrating human input into GAs. In chapter 5, we experiment the suggested framework within the repeated matrix games and evaluate their performance against the
previously selected learning opponents. In order to evaluate the scalability of our
algorithms, in chapter 6, we apply the GA with and without human input in a 3player environment. We show how GA perform in such an environment and if
there are certain features that are not able to propagate to large-scale enviornments.
This study will help us gain an understanding of how our algorithms will perform
within more complex systems.
Finally, we will give a detailed discussion of the results (Chapter ??). This discussion helps in deriving the conclusions presented in chapter 7. We then suggest
potential future research to be based on this thesis.

26. CHAPTER
2
Literature Review
In this section, we present an overview of different fields related to our research.
We also discuss related work and explain how this work came to help in our experiments. We will start by giving an overview about electrical power grids in section
2.1. Then, we will connect it to multi-agent systems, and explain the structure of
a standard MAS problem. We then move along to the specific MAS branch of
problems that we study in this thesis, which are repeated matrix games.
After giving the required background about the problem structure, we start giving background about the solution methodology we are using. We give an overview
about evolutionary algorithms in general (which includes genetic algorithms), after
which we explain the history and structure of genetic algorithms. We then examine
the work done in the field of learning in multi-agent systems, and start relating the
work done within genetic algorithms and learning in multi-agent systems. This relation is materialized through different topics including genetic algorithms within
dynamic systems, genetic algorithms for developing strategies in matrix games and
7

27. CHAPTER 2. LITERATURE REVIEW
8
finally, our main topic, interactive genetic algorithms.
2.1
Electrical Power grids
An electrical power grid is a network of interconnected entities, in which electricity generators are connected to consumers through a set of transmission lines and
distributors (Figure 2.1). Existing electrical grids mainly rely on classic control
systems. The structure of these systems is based on the following: The generator
generates a certain amount of electricity (depending on its capacity), which is then
distributed to the consumers through the distributers. This main structure faces
many difficulties, mainly when it tries to deal with variable types of generators,
distributors and consumers.
In real life systems, this variety is to be expected. In the generators’ case,
renewable energy sources have become extensively used for power generation, especially within the past decade. This leads to intermittency in the supply that is
usually hard to model [48]. Within the consumers’ case, although various research
is targeted towards modeling electricity demand and consumption patterns [43, 24],
demand is not always deemed predictable. This unpredictability leads to many constraints regarding distribution (which is also called a demand-supply problem), and
requires additional research to visualize more work that can efficiently enhance the
generation, distribution and consumption cycles through more intelligent means.
2.1.1
Smart grids
In order to enhance the efficiency of electricity generation, distribution and consumption within the power grid, a logical solution is the merger of intelligent automation systems into the electrical power grid to form the “smart grid” [37].
A smart grid (see Figure 2.2) delivers electricity from suppliers to consumers

28. CHAPTER 2. LITERATURE REVIEW
9
Figure 2.1: A traditional Electrical Grid [8].
using two-way digital communications to control appliances at consumers’ homes.
This could save energy, reduce costs and increase reliability and transparency if the
risks inherent in executing massive information technology projects are avoided.
Smart grids are being promoted by many governments as a way of addressing energy independence, global warming and emergency resilience issues [37].
In our research, we consider the management of electricity from the consumer
side, where an “agent” here represents a consumer, which tries to satisfy its needs
in the presence of external circumstances.

29. CHAPTER 2. LITERATURE REVIEW
10
Figure 2.2: A smart electrical grid [8].
2.2
Multi-agent systems
A multi-agent system (MAS) is a system composed of multiple interacting intelligent agents. Many of the real world problems, including electricity grids’ demandresponse problems, can be easily visualized as a MAS [78, 106]. In power systems,
each entity (distributors, consumers, and generators), is represented as an agent.
Each agent may have an individual goal to reach while interacting with other entities (agents).
Various research has been in done in the field to solve the electrical supplydemand problem using multi-agent simulations [97, 80]. As we are testing a
new technique in this thesis, we wanted to base our work on research trends that
have been used before in the field of simulating electrical power grids. One of
these trends is considering our MAS as a simple matrix game (more details in
the following section). This decision was based on the fact that various electrical grids, electricity scheduling and electricity market simulators use matrix
games [61, 73, 62, 5]. The supplier’s goal in these games is to supply power to

30. CHAPTER 2. LITERATURE REVIEW
11
the consumers with the best price possible, while maintaining stability in the grid.
On the other hand, the consumer agents must satisfy their needs while minimizing
their costs (depending on the consumers’ preferences). All of these goals should
be satisfied keeping in mind the existence of other agents and external influences.
In order to achieve its goal, each agent follows a “strategy,” which is either fixed or
adaptable with time.
As a result of this extensive usage as a representation of an electricity market
problem, we choose to evaluate our algorithms within repeated matrix games. In
the following section we give more details about matrix games and their structure.
2.3
Matrix games
Matrix games are a subset of what are called “stochastic games.” In these games,
each player takes an action, which produces a reward. In a matrix game (also called
“normal form game”), the payoffs (rewards) towards the players action space is defined in the form of a matrix. This action space represents the set of possible actions
that each player can perform within this game. Depending on the rewards they get,
the players decide the “strategy” they are going to follow, where the strategy represents the decision of which action to play over time [42].
For clarification, consider the game represented in Table 2.1. In this matrix
game, we have two players, player1 and player2. Player 1 (row player) can play
either action A or B (so its strategy space is {A,B}). Likewise, Player 2 (column
player) can play either action a or b. From this we can conclude that the set of
possible joint actions is {(A, a), (A, b), (B, a), (B, b)}. Each cell within the matrix
shown in the figure represents the reward for each player when this joint action
occurs. In the matrix given as example, the payoff to the row player (player 1) is
listed first, followed by the payoff to the column player (player 2). For example, if

31. CHAPTER 2. LITERATURE REVIEW
A
B
a
-1,2
0,0
12
b
3,2
2,-1
Table 2.1: Payoff matrix for the Prisoner’s dilemma.
the row player plays B and the column player plays a (which is the joint action (B,
a)), then the row player receives a payoff of 2, while the column player receives a
payoff of -1.
A strategy for an agent (player) i is a distribution πi over its action set Ai .
Similarly, it can be defined as the probability that a player will move from one state
to another. A strategy can be either a pure strategy (where the probability of playing
one of the actions is 1, while the probability of playing any of the other actions is
0), or a mixed strategy, where each action is played with a certain probability over
time. The joint strategy played by the n agents is π=(π1 , π2 ,...,πn ) and, thus, ri (π)
is the expected payoff for agent i when the joint strategy π is played.
Depending on the action taken, a player’s situation changes overtime. The
situation of the player can be represented in what is called a “state” [11]. In this
example, this situation where each player takes a certain payoff in the presence of
a certain joint-action pair represents the state.
2.3.1
Types of matrix games
Matrix games can be divided into different types using different criteria. In this
section, we discuss the main criteria that affected how we selected the games used
for the experiments. Details about the exact games used in the experiments are
mentioned in the next chapter.

32. CHAPTER 2. LITERATURE REVIEW
13
Cooperative vs. non-cooperative games
A cooperative game represents a situation in which cooperation amongst the players is the most beneficial to them. Therefore, these games mainly require an efficient arrangement between players to reach the cooperative behavior. An example
of these games is a coordination game [17].
On the other hand, non-cooperative games are not defined as games in which
players do not cooperate, but as games in which any cooperation must be selfenforcing. Most of realistic problems fall under the non-cooperative games.
Symmetric vs. asymmetric games
A symmetric game is a game where the payoffs for playing a particular strategy
depend only on the other strategies employed, not on who is playing them. If the
order of the players can be changed without changing the payoff to the strategies,
then a game is symmetric. On the other hand, in asymmetric games, the action set
for each player is different than the others. For simplicity, we focus in this research
on symmetric games.
2.3.2
Solution concepts
In matrix games, there are concepts through which we can identify strategies for
the players, which, if played, can lead to a state known as equilibrium. These
concepts can be useful in evaluating the performance of the strategy played. We
will give an overview about some of these concepts, which are directly related to
our research.
Best response
A best response is a strategy that produces the most favorable outcome for a player,
given the other players’ strategies [36]. Therefore the strategy πi ∗ is a best response

33. CHAPTER 2. LITERATURE REVIEW
14
for agent i if ri (πi ∗, π−i ) ≥ ri (πi , π−i ) for all possible πi .
Nash equilibrium
A Nash equilibrium, is a set of strategies, one for each player, that has the property
that no player can unilaterally change his strategy and get a better payoff. The Nash
equilibrium (NE) has had the most impact on the design and evaluation of multiagent learning algorithms to date. The concept of a Nash equilibrium is based on
the best response. When all agents play best responses to the strategies of other
agents, the result is an NE. Nash showed that every game has at least one NE [74].
However, there is no known algorithm for calculating NEs in polynomial time [77].
If we consider that all players are self-interested, each of them would tend to
play the best response to the strategies of other agents, if they know them, therefore
resulting in an NE. Many games have an infinite number of NEs. In the case of
repeated games, these NEs are called NEs of the repeated game(rNEs), which we
will discuss shortly. Therefore, the main goal of an intelligent learning agent is
not just to play best-response to the surrounding agents, but also to influence other
agents to play according to what is profitable to the agent as much as possible.
Maximin
Maximin is a decision rule used in different fields for minimizing the worst possible
loss while maximizing the potential gain. Alternatively, it can be thought of as
maximizing the minimum gain. The maximin theorem states [75]:
For every two-person, zero-sum game with finite strategies, there exists a value V and a mixed strategy for each player, such that (a) Given
player 2’s strategy, the best payoff possible for player 1 is V, and (b)
Given player 1’s strategy, the best payoff possible for player 2 is V [75].

34. CHAPTER 2. LITERATURE REVIEW
15
Equivalently, Player 1’s strategy guarantees him a payoff of V regardless of Player
2’s strategy, and similarly Player 2 can guarantee himself a payoff of -V. The name
minimax arises because each player minimizes the maximum payoff possible for
the other since the game is zero-sum, he also maximizes his own minimum payoff.
Pareto efficiency
Named after Vilfredo Pareto, Pareto efficiency (optimality) is a measure of efficiency. An outcome of a game is Pareto efficient if there is no other outcome that
makes every player at least as well off and at least one player strictly better off.
That is, if an outcome is Pareto optimal, there does not exist another outcome that
does not provide at least one other player a lower payoff.
2.3.3
Repeated matrix games
A repeated matrix game, from the name, is a matrix game that is played repeatedly.
The joint action taken by the agents identifies the payoff (reward) in each round
(or stage) of the game, which can help the player in taking the decision of which
action can be taken next through learning. The task of a learning agent in a repeated
matrix game is to learn to play a strategy πi such that its average payoff over time
(denoted ri for agent i) is maximized. Let ri be given by:
¯
¯
ri =
¯
1 T
∑ ri (πit , π−it )
T t=1
(2.1)
where πi is the strategy played by agent i at time t, π−i is the joint strategy played
by all the agents except agent i, and 1 ≤ T ≤ ∞ is the number of episodes in the
game. In our work, we consider simultaneous action games, where in each round,
both agents play an action (without knowing the action of the other agents within
the same round).

35. CHAPTER 2. LITERATURE REVIEW
16
Figure 2.3: Payoff space for the prisoner’s dilemma game [25].
In order to evaluate the strategies played, and see different equilibria, the concept of the one-shot Nash equilibrium does not fully represent the equilibrium in
repeated games. Therefore, in order to define the concept of NE within a repeated
game, we discuss what is called the folk theorem [90].
Consider the case in the prisoners’ dilemma, shown in Figure 2.3, which shows
the joint payoffs of the two players. The x-axis shows the payoffs of the row player
and the y-axis shows the payoffs of the column player. The combination of the
shaded regions (light and dark) in the figure represents what is called the “ConvexHull”, which is all the possible joint-action pairs possible within the game. As
can be noticed, on average, the player guarantees itself a higher stable payoff by
playing defect; neither of the players has incentive to receive an average payoff
(over time) less than 0. Therefore, the darkly shaded region in the figure shows the
set of expected joint payoffs that the agents may possibly accept as average payoffs
within each step of the game.
The folk theorem states that any joint payoffs in the convex hull can be sus-

36. CHAPTER 2. LITERATURE REVIEW
Cooperate
Defect
Cooperate
3,3
5,0
17
Defect
0,5
1,1
Table 2.2: Payoff matrix for the Prisoner’s dilemma.
tained by an rNE, provided that the discount rates of the players are close to
unity (i.e., players believe that play will continue with high probability after each
episode). This theorem helps us understand the fact that, in repeated games, it is
possible to have an infinite number of NE.
2.3.4
Stochastic games
In real life situations, the more detailed stochastic games (where we have different
possible games to transit from one action-state pair to another) can be considered
more informative and suitable for modeling. However, research has been done [26]
in experimenting if learning algorithms that work within repeated matrix games
can be extended into repeated stochastic games or not. This extension was found
to give suitable results within the prisoner’s dilemma and its stochastic version
(for 2-agent games), which gives us the motivation needed in pursuing the current
experimentation within matrix games.
2.4
Learning in repeated matrix games
In this section, we give an overview of the related work in multi-agent learning,
especially algorithms that were used within matrix games. Because of the existence of various multi-agent learning algorithms found in the literature, we restrict
our attention to those that have had the most impact on the multi-agent learning
community as well as to those that seem to be particularly connected to the work
presented in this thesis. We divided the learning algorithms that we review into
three different (although related) categories: belief-based learning, reinforcement

37. CHAPTER 2. LITERATURE REVIEW
18
learning, and no-regret learning [26].
2.4.1
Belief-based learning
Belief-based learning is based on the idea of constructing a model of the opponent’s
behavior. These models usually rely on previous interactions with the opponent.
Using this model, we try to find the best response with respect to this model. One
of the most known belief-based learning algorithms is fictitious play [15].
2.4.2
No-regret learning
A no-regret algorithm compares its performance with the “best action” available
within its set. Regret in this case is defined as the difference between the rewards
obtained by the agent and the rewards the agent might have obtained if it followed
a certain combination of its history of actions. In the long run, an algorithm with
no-regret plays such that it has little or no regret for not having played any other
strategy. GIGA-WoLF [10] is one example of a no-regret algorithm. We describe
GIGA-WoLF in greater detail within the next chapter.
2.4.3
Reinforcement learning
Reinforcement learning (RL) methods involve learning what to do so as to maximize (future) payoffs. RL agents use trial and error to learn which strategies produce the highest payoffs. The main idea of reinforcement learning is that through
time, the learner tries to take an action that maximizes a certain reward. Reinforcement learning is widely used within matrix game environments [91, 52]. There are
several known learning algorithms that can be identified as reinforcement learning,
including: Q-learning [100] and evolutionary algorithms [70].

38. CHAPTER 2. LITERATURE REVIEW
2.5
19
Evolutionary algorithms
Evolutionary algorithms are a popular form of reinforcement learning. Evolutionary algorithms (EAs) are population-based metaheuristic optimization algorithms
that use biology-inspired mechanisms like mutation, crossover, natural selection,
and survival of the fittest in order to refine a set of solution candidates iteratively.
Each iteration of an EA involves a competitive selection designed to remove poor
solutions from the population. The solutions with high ”fitness” are recombined
with other solutions by swapping parts of a solution with another.
Solutions are also mutated by making a small change to a single element of
the solution. Recombination and mutation are used to generate new solutions that
are biased towards solutions that are most fit [58]. This process is repeated until
the solution population converges to the solution with a high fitness value. In general, evolutionary algorithms are considered an effective optimization method [2].
Survival of the fittest concept, together with the evolutionary process, guarantees a
better adaptation of the population [58].
2.5.1
Genetic algorithms
A Genetic Algorithm (GA) [45] is a type of evolutionary algorithm. GAs are based
on a biological metaphor, in which learning is a competition among a population of
evolving candidate problem solutions. A fitness function evaluates each solution to
decide whether it will contribute to the next generation of solutions. Then, through
operations analogous to gene transfer in sexual reproduction, the algorithm creates
a new population of candidate solutions [65, 44].
The main feature of GAs is that they encode the problem within binary string
individuals. In addition to other encoding techniques. Another feature of GAs is
their simplicity as a concept, and their parallel search nature, which makes it possible to easily modify GAs so they can be adapted to a distributed environment [18].

39. CHAPTER 2. LITERATURE REVIEW
2.5.2
20
Genetic algorithm structure
In this section we give a description of how GAs work. In order to get a better understanding of the algorithms, we define certain terminology that we use
throughout subsequent sections.
Fitness Fitness is the value of the objective function for a certain solution.
The goal of the algorithm is either to minimize or maximize this value, depending
on the objective function.
Genome “Chromosome”
A genome, or frequently called a chromosome, is
the representation of a solution (strategy in the case of matrix games) that is to be
taken at a certain point of time. The GA generates various chromosomes, each
of which is assigned a certain fitness according to its performance. Using this
fitness, the known evolutionary functions are implemented in order to create new
population (generation) of chromosomes.
Gene Genes are the units that form a certain genome (chromosome). The
evolutionary functions such as mutation and crossover are mainly performed on
the genes within the chromosomes.
Solution space The solution space defines the set of all possible chromosomes (solutions) within a certain system. Through the evolutionary functions, we
try to cover as much as possible of the solution space for proper evaluation, without
trying all possible solutions one by one, as in the case of brute-search, in order to
save time.
After giving the proper definitions, we are going to describe how GAs work. In
the following sections, we will discuss the main components that vary among different GAs according to the application. These components include: chromosome

40. CHAPTER 2. LITERATURE REVIEW
21
representation, selection process (fitness calculation and representation), mutation
process, and crossover process.
Chromosome structure
As previously mentioned, one important feature of GAs is their focus on fixedlength characters’ strings, although variable-length strings and other structures
have been used. Within matrix games, these character strings represent the binary
encoding of a certain strategy [3, 31]. But others have used non-binary encoding,
depending on their application [86].
It should be noted, however, that there are special cases in which we consider
the use of a binary encoding perfectly acceptable. In a prisoner’s dilemma, for example, agents have to make decisions that are intrinsically binary, namely decisions
between cooperation and defection. The use of a binary encoding of strategies then
seems like a very natural choice that is unlikely to cause undesirable artifacts [4].
Fitness functions and selection
The fitness function is a representation of the quality of each solution (chromosome). This representation varies from one application to another. According to
the fitness value, we select the fittest chromosomes and then perform crossover
and mutation functions on these chromosomes to generate the new chromosomes.
These techniques include: roulette wheel selection, rank base selection, elitism and
tournament based selection.
In the following section, we discuss each method. We exclude going over
tournament based selection, as it requires experimenting and testing the solution
through the selection process, which is not be suitable to our application since it is
an off- line training technique for the algorithm.

41. CHAPTER 2. LITERATURE REVIEW
22
Figure 2.4: Roulette wheel selection mechanism [30].
Roulette wheel selection
Parents are selected according to their fitness. The
better the chromosomes, the more chances they have to be selected. In order to
get a better understanding, imagine a roulette wheel where all chromosomes in the
population are distributed on a wheel. Each chromosome gains its share of the
wheel size according to its fitness (Figure 2.4). A marble is thrown to select the
chromosome on this wheel. The fittest chromosome has a higher opportunity of
being selected.
Rank based selection Roullete wheel selection has problems when the fitnesses vary widely. For example, if the best chromosome’s fitness is 90 percent of
all the roulette wheel then the other chromosomes will have very few chances to
be selected. Rank selection first ranks the population and then every chromosome
receives fitness from this ranking. The worst will have a fitness of 1, the second
worst will have a fitness of 2, and this continues till we reach the best chromosome. The best chromosome will have a fitness of N (where N is the number of

42. CHAPTER 2. LITERATURE REVIEW
23
Figure 2.5: Crossover in genetic algorithms.
chromosomes in the population).
Elitism The idea of elitism has already been introduced. When creating new
population by crossover and mutation, we have a big chance that we will lose the
best chromosome. Elitism selection starts by copying a certain percentage of the
best chromosomes to the new population. The rest of the population is then created
by applying mutation and crossover on the selected elite. Elitism can very rapidly
increase the performance of a GA because it prevents the algorithm from forgetting
the best found solution.
Crossover and Mutation
Crossover and mutation are the main functions of any genetic algorithm after selection. They are the functions responsible for the creation of new chromosomes
out of the existing chromosomes.
In the crossover phase, all of the selected chromosomes are paired up, and
with a probability called “crossover probability,” they are mixed together so that a
certain part of one of the parents is replaced by a part of the same length from the
other parent chromosome (Figure 2.5). The crossover is accomplished by randomly

43. CHAPTER 2. LITERATURE REVIEW
24
Figure 2.6: Mutation in genetic algorithms.
choosing a site along the length of the chromosome, and exchanging the genes of
the two chromosomes for each gene past this crossover site.
After the crossover, each of the genes of the chromosomes (except for the elite
chromosome) is mutated to any one of the codes with a probability defined as
the “mutation probability” (Figure 2.6). With the crossover and mutations completed, the chromosomes are once again evaluated for another round of selection
and reproduction. Setting the parameters concerned with crossover and mutation
is mainly dependent on the application at hand and the chromosome structure [45].
Algorithm summary
Genetic algorithms are based on the fundamental algorithm structure as shown in
Figure 2.7. First, an initial population of N individuals, which evolves at each generation, is created. Generally, we can say that a generation of solutions is obtained
from the previous generation through the following procedure: solutions are randomly selected from the current population. Pairs of selected individuals are then
submitted to the crossover operation with a given crossover probability Pc . Each
descendant is then submitted to a mutation operation with a mutation probability
Pm , which is usually very small. The chromosome’s ability to solve the problem
is determined by its fitness function; the final step in the generation process is the
substitution of individuals of the current population with low performance by the

44. CHAPTER 2. LITERATURE REVIEW
25
Figure 2.7: Basic structure of genetic algorithms.
new descendants. The algorithm stops after a predefined number, Gen, of generations has been created. An alternative stopping mechanism is a limit on computing
time [101].
Advantages and Applications of genetic algorithms
GAs represent one of the most renowned optimization search techniques, especially with the presence of high potential, non-linear search spaces. GAs have been
used to solve different single agent problems [70]. As the computational requirements increase, it became more applicable to distribute different methods within
the GA to different agents, where all agents in this case have the same goal. As
a summary, we can say that GAs are most efficient and appropriate for situations
such as the following:

45. CHAPTER 2. LITERATURE REVIEW
26
• The search space is large, complex, or not easily understood
• There is no programmatic method that can be used to narrow the search space
• Traditional optimization methods, such as dynamic programming, are not
sufficient
Genetic algorithms may be utilized in solving a wide range of problems across
multiple fields such as science, business, engineering, and medicine. The following
provides a few examples:
• Optimization: production scheduling, call routing for call centers, routing
for transportation, determining electrical circuit layouts
• Machine learning: designing neural networks, designing and controlling
robots
• Business applications: utilized in financial trading, credit evaluation, budget
allocation, fraud detection
Genetic algorithms are important in machine learning for various reasons:
1. They can work on discrete spaces, where generally gradient methods cannot
be applied.
2. They can be used to search parameters for other machine learning models
such as fuzzy sets and neural networks.
3. They can be used in situations where the only information we have is a
measurement of performance, and here it competes with temporal difference
techniques, such as Q-learning [86].
4. They converge to a near optimal solution after exploring only a small fraction
of the search space [98, 49].

46. CHAPTER 2. LITERATURE REVIEW
27
5. They can be easily hybridized and customized depending on the application.
6. They may also be advantageous in situations when needs to find a near optimal solution [87].
While the great advantage of GA is the fact that they find a solution through
evolution, this is also the biggest disadvantage. Evolution is inductive in nature,
so it does not evolve towards a good solution, but it evolves away from bad circumstances [84]. This can cause a species to evolve into an evolutionary dead end.
This disadvantage can be clearly seen within more dynamic system, where stabilzing within a dead-end can stop the algorithm from satisfying a dynamic learning
process.
2.6
Genetic algorithms in repeated matrix games
GAs have also been used within matrix games. Mainly, they have been used in
this context as either a method for computing the Nash equilibrium of a certain
game [22, 2, 54], or for generating the “optimal” chromosomes (strategies) to be
played within a certain game [4]. These applications have been either solved by a
single genetic algorithm running through the game parameters to reach an optimal
solution [34], or by using what is called a “co-evolutionary” technique, which basically involves the usage of two genetic algorithms (both having the same goal),
in order to reach the optimal solution in a more trusted and efficient manner [52].
Note here that co-evolution is considered as an “offline” learning technique,
as it require testing all the current chromosomes within the population against all
other chromosomes. This is not the same case while playing online, where the
chromosome is tested against only the current associate it was set up to play against
(not the whole population), which gives it less opportunity of exploration in front
of different criteria.

47. CHAPTER 2. LITERATURE REVIEW
28
GAs have been used before in formation of strategies in dynamic Prisoner’s
Dilemma games. For example, Axelrod has used genetic algorithms in order to find
the most desirable strategies to be used in the prisoner’s dilemma [4]. Axelrod’s
stimulus-response players were modeled as strings, where each character within
the string corresponds to a possible state (one possible history) and decodes to the
player’s action in the next period. The longer the steps in memory to be taken into
consideration, the longer the string representing the chromosome will be. This is
as a result of the increase in the possible number of states. In addition, moving to a
game with more than two possible moves of will lengthen the string. Increasing the
number of players will also increase the number of states. Formally, the number of
states is given by am×p , where there are a actions and p players, and each player
keeps m periods of time in its history [44].
Another example was the usage of GA within a simple formulation of a buyerseller dilemma [92]. The GA implements a mixed strategy for the seller as an
individual member of the population. Each population member is therefore a vector of probabilities for each action that all add up to 1.0. Within this experiment,
they discussed the performance of GA in contrast of other RL techniques. The difference in performance between the GA agents and RL agents is primarily because
GA agents are population based. Since RL agents deal with only one strategy, they
are faster in adapting it in response to the feedback received from the environment.
In contrast, the GA agents are population based. It takes the GA population
as a whole longer to respond to the feedback received. For the same reason, the
GA agents are expected to exhibit less variance, and hence better convergence
properties. This was a good start in using genetic algorithm as a learning technique
instead of optimization. However, it still needed more work regarding working
against simple learning agents, for example without full state representation, and
without more specific domain knowledge. The authors of this work also raised the

48. CHAPTER 2. LITERATURE REVIEW
29
question of how human input can contribute as potential future work [92].
In order to get a better understanding about how GAs may perform in more
complicated situations, we now discuss within the following sections the performance of GAs within similar fields, such as distributed and dynamic systems.
2.6.1
Genetic algorithms in distributed systems
In distributed systems, the primary form of GAs that has been used was co-evolutionary
algorithms [56, 52, 107]. In this case, each GA agent represents one possible solution, and with the existence of other GA agents, they try to verify which solution
will possibly be optimal. In another context, where each GA agent evolves its own
set of solutions, all the agents are centralized with the same objective function (all
the agents cooperate and communicate in order to reach the same goal) [47, 69].
As we can see in all of these situations, the GA agent is not completely independent
of other existing agents’ objective.
2.6.2
Genetic algorithms in dynamic systems
The goal of a GA within a dynamic system changes from finding an “optimal”
answer to tracking a certain goal (and enhancing the overall performance). Most
real world, artificial systems and societies change due to changes in a number of
external factors in the environments, agents learning new knowledge, or changes
in the make up of the population. When the environment changes over time, resulting in modifications of the fitness function from one cycle to another, we say that
we are in the presence of a dynamic environment [93]. Several researchers have
addressed related issues in previous work. Examples include evolutionary models
and co-evolutionary models where the population is changing over time, and studies in the viscosity of populations [68, 103]. Different from classical GA the goal
of such system is to maximize the average result instead of determining the best

49. CHAPTER 2. LITERATURE REVIEW
30
optimal solution, where you track the performance of different solutions over time
instead of reaching a certain optimal target.
Brank [12] surveys the strategies for making evolutionary algorithms, which
include GAs, suitable for dynamic problems. The author grouped the different
techniques into three categories:
• React to changes, where as soon as a change in the environment has been
detected explicit actions are taken
• Maintain diversity throughout the run, where convergence is avoided all the
time and it is hoped that a spread-out population can adapt to modifications
more easily [55]
• Maintain an additional memory through generations (memory-based approaches),
where the evolutionary algorithm is supplied with memory to be able to recall useful information from past generations
Many methods have been presented to make genetic algorithms applicable in dynamic environments. First, researchers have modeled change in the environment
by introducing noise into the system whereby agents actions are mis-implemented
or mis-interpreted by other agents[29]. Another idea has been to localize the search
within a certain part of the search space. This can be either done through intelligent initialization of the population [85], or as done within the “memetic algorithm” [79], by evaluating close and similar neighbors of the chromosomes on trial
in addition to the chromosomes already tested. This is where we get part of our
motivation within interactive learning. This idea motivated our feedback of generating populations based on feedback from users(evaluating close neighbors helps
me evaluate existing ones).
The aforementioned methods either do not consider the existence of other heterogeneous learning entities in the system, or learn only under certain identified

50. CHAPTER 2. LITERATURE REVIEW
31
constraints [1]. However, experimental results are promising and show interesting
properties of the adaptive behavior of GA techniques.
2.7
Interactive learning
Another factor to consider to potentially enhance the performance of genetic algorithms is to gather human input in real time to teach the algorithm. Within
any learning algorithm, this can be done by merging the learning algorithm with
human-machine interaction, resulting in what is called in the literature “interactive artificial learning.” Using human input as a part of the learning procedure can
provide a more concrete reward mechanism, which can increase the convergence
speed [96, 27]. These learning methods occur in either the “act,” “observe” or “update” step of an interactive artificial learning mechanism [27]. Experiments have
been performed to evaluate potential effects of human input on the learning curve
in multi-agent environments. Results show a significant improvement in learning,
depending on the quality of the human input [27, 28].
Figure 2.8: The interactive artificial learning process [27].

51. CHAPTER 2. LITERATURE REVIEW
2.7.1
32
Interactive learning in repeated matrix games
Within the repeated games environment. Experiments have been performed in
order to analyze the effect of the human input on the performance of the learning algorithms [27]. The algorithms used in these experiments use “learning by
demonstration” (LbD). Results showed that LbD does help learning agents to learn
non-myopic equilibrium in repeated stochastic games when human demonstrations
are well-informed. On the other hand, when human demonstrations are less informed, these agents do not always learn behavior that produces (more successful)
non-myopic equilibria. However, it appears that well-formed variations of LbD algorithms that distinguish between informed and uninformed demonstrations could
learn non-myopic equilibrium.
When humans play iterated prisoners’ dilemma games, their performance depends on many factors [32, 41, 59]. Thus, it can be concluded that a similar trend
applies to LbD algorithms, and that there is a chance that LbD algorithms could
potentially provide information about the game and associates that would provide
a context that facilitates better demonstrations.
2.7.2
Interactive genetic algorithms
An interactive genetic algorithm (IGA) is defined as a genetic algorithm that uses
human evaluation. These algorithms belong to a more general category of interactive evolutionary computation. The main application of these techniques include
domains where it is hard or impossible to design a computational fitness function,
including evolving images, music, various artistic designs and forms to fit a user’s
aesthetic preferences.
In an in interactive genetic algorithm (IGA), the algorithm interacts with the
human in attempt to quickly learn effective behavior and to better consider human
preferences. Previous work on IGA in distributed tasks has shown that human

52. CHAPTER 2. LITERATURE REVIEW
33
input can allow genetic algorithms to learn more effectively [33, 38]. However,
such successes required heavy user interaction, which causes human fatigue [33].
Previous work in interactive evolutionary learning in single-agent systems has
analyzed methods for decreasing the amount of necessary human interaction in
interactive genetic learning. These methods either apply bootstrapping techniques,
which rely on estimations of the reward in between iterations instead of a direct
reward from the user [60, 66], or they divide the set of policies to be evaluated into
clusters, where the user only evaluates the center of the cluster and not all policies
[82].
Another suggestion for reducing human fatigue, which is applicable only in
multi-agent systems, is by using input from other agents (and potentially other
agents’ experiences), as one’s own experience [39].
Interaction between a human and the algorithm may occur in different stages
of GA and in different ways. The most common way is to make a human part of
the fitness evaluation for the population. This can be done by either ranking available solutions [94], or directly assigning the fitness function value to the available
policies in the population. Other work, which targets reducing human fatigue as
mentioned above, had the human evaluate only selected representatives of the population [82, 88, 60]. Also human input has been investigated in the mutation stage,
where the human first selects the best policy from his point of view, and suggests a
mutation operation to enhance its performance [33].
Babbar-Sebens et al. [28] realized a problem with IGA, which was how an algorithm can overcome the temporal changes in human input. This situation not only
leads the genetic algorithm to prematurely converge, but it can also reduce diversity
in the genetic algorithm population. This occurs when solutions that initially have
poor human rankings are not able to survive the GA’s selection process. Loss of
these solutions early in the search process could be detrimental to the performance

53. CHAPTER 2. LITERATURE REVIEW
34
of the genetic algorithm, if these solutions have the potential to perform better
when preferences change later. That is why they suggested the use of case-based
memory per population of policies. This memory acts as a continuous memory of
the population and its fitnesses to give a more continuous and non-myopic view of
evaluating the performance of the chromosomes through the generations (instead
of having the evaluations be based on a single generation biases) [6].
IGAs have also been used to define robot behavior in known environments. A
child (representing the human factor) trains the genetic algorithm through feedback on the evolved population. This training happens by selecting the top three
preferred routes to be taken by the robot [66]. Usually IGA are used in more visual
problems, where we can easily make the user rank or evaluate chromosomes in
certain domains such as music and design [40, 14, 89]. It also has been used in
resource allocation problems (which usually are more static) [94, 7].
The last related example was the interaction of a human with a GA within a
board game, where GA plays against another GA or against a human. The GA
here works on a limited set of (easy to reach) solutions that describe a behavior for
the whole game (not move by move). The human in this case sets the parameters in
the beginning of the game, including the number of generations and the mutation
rate [21].
Interactive genetic algorithms in multi-agent systems
Research that studied interactive genetic algorithms in multi-agent systems was
mainly focused on dividing the IGA functions (including human interaction, mutation, crossover) into separate agents [57, 51]. In this case, the IGA is not fully
independent of the other modules, where all modules interact with each other to
reach a common objective.

54. CHAPTER 2. LITERATURE REVIEW
2.8
35
Summary
Past work has derived intelligent behavior in repeated games using various methodolgies. However, existing solutions have various problems, including:
• They require too much input from the user.
• They force certain constraints on users which decrease their comfort level.
• They do not learn fast enough for real time systems, and are not able to deal
with environments or goals that change over time.
• They cannot be used in distributed systems.
• They do not consider how human input can be incorporated in the system.
From this, we conclude that there is a need of a solution that is able to target
these drawbacks.

55. CHAPTER
3
Experimental Setup
In this chapter, we will present the experimental setup used to test our hypothesis.
Since our goal is to test the performance of interactive genetic algorithms (IGAs)
within a multi-agent system setting, we designed an experiment that will allow us
to do that. In order to test the efficiency of the algorithm, we run it against itself and
other learning algorithms in a variety of matrix games. The two renowned learning
algorithms we use are GIGA-Wolf [10] and Q-learning [100].
3.1
Games’ structure
In this section, we give an overview of the matrix games’ we use to evaluate our
algorithms. The expectations from the players within the games differ from one
game to another. Therefore, we expect a different response from each learning
algorithm.
36

56. CHAPTER 3. EXPERIMENTAL SETUP
Cooperate
Defect
Cooperate
3,3
5,0
37
Defect
0,5
1,1
Table 3.1: Payoff matrix for the Prisoner’s dilemma.
3.1.1
Prisoner’s dilemma
The prisoner’s dilemma is perhaps the most studied social dilemma [4], [3], as it
appears to model many real life situations. In the prisoner’s dilemma (Table 3.1),
defection is each agent’s dominant action. However, both agents can increase their
payoffs simultaneously by influencing the other agent to cooperate. To do so, an
agent must (usually) be willing to cooperate (at least to some degree) in the longrun. An n-agent, m-action version of this game has also been studied [95].
As we can see from the matrix in Table 3.1, if we consider the reward of each
player for each joint-action pair, the following rule should apply within a prisoner’s
dilemma matrix: rdc ≥ rcc ≥ rdd ≥ rcd . Here, i represents my action, j represents
the opponent’s action, and ri j represents my reward at the joint action pair (i, j).
However, it is more desirable than mutual defection for both players to choose the
first actions (C,C) and obtain rcc .
3.1.2
Chicken
The game of Chicken is a game of conflicting interests. Chicken models the Cuban
Missile Crisis [19], among other real-life situations. The game has two one-shot
NEs ((C, d) and (D, c)). However, in the case of a repeated game, agents may
be unwilling to receive a payoff of 2 continuously when much more profitable
solutions are available. Thus, in such cases, compromises can be reached, such as
the Nash bargaining solution (Swerve, Swerve) (Table 3.2). Therefore, the game is
similar to the prisoner’s dilemma game (Table 3.1) in that an “agreeable” mutual
solution is available. This solution, however, is unstable since both players are

57. CHAPTER 3. EXPERIMENTAL SETUP
Swerve
6,6
7,4
Swerve
Straight
38
Straight
4,7
2,2
Table 3.2: Payoff matrix for chicken game.
A
B
C
a
0,0
1,0
0,1
b
0,1
0,0
1,0
c
1,0
0,1
0,0
Table 3.3: Payoff matrix of Shapley’s game.
individually tempted to stray from it.
3.1.3
Shapley’s game
Shapley’s game [36] is a 3-action game. It is a variation from the rock-paperscissors game. Shapley’s game has often been used to show that various learning
algorithms do not converge. The game has a unique one-shot NE in which all
agents play randomly. The NE of this game gives a payoff of 1/3 to each agent
(in a 2-agent formulation). However, the players can reach a compromise in which
both receive an average payoff of 1/2. This situation can be reached if both players
alternate between receiving a payoff of 1 and receiving a payoffs of 0. The payoff
matrix for this game is shown in Table 3.3.
3.1.4
Cooperative games
As mentioned in the previous chapter, cooperative games are exactly opposite to
competitive games (which are part of non-cooperative games). In these games, all
agents share common goals, some of which may be more profitable than others.
Table 3.4 shows the payoff matrix of a fully cooperative game.

58. CHAPTER 3. EXPERIMENTAL SETUP
A
B
a
4,4
0,0
39
b
0,0
2,2
Table 3.4: Payoff matrix of a fully cooperative matrix game.
3.2
Knowledge and Information
In matrix games, the more information any learning algorithm has about the game
and its associates, the more efficiently it can learn. Some of the information is
usually hidden within the learning process, and the algorithm has to deal with only
the information available. The following list shows the possible variations in the
level of knowledge of the agent. This will help us have a better understanding of
how our algorithm, and its opponents view the surrounding world.
• The agent’s own action. The agent has to basically know its actions in order
to know how to act in the first place.
• The agent’s own payoffs. The agent may know the reward it has taken at a
certain point of time, or how the actions are rewarded over time.
• Associates’ actions. The agent can either know directly which action was
taken by an associate, or be able to predict it over time.
• Associates’ payoffs. The agent can know what outcomes can be used to
motivate or threaten the other associates to be able to act accordingly.
• Associates’ internal structure. The agent may have a knowledge of how the
opponent reacts to certain situations. This knowledge usually is gained by
attempts to model the associates over time.
In our experiment, we assume that the algorithm has a complete knowledge
about its own payoffs and actions as well as the opponent’s history of actions (from
previous plays). No knowledge of the opponents internal structure is assumed.

59. CHAPTER 3. EXPERIMENTAL SETUP
40
Algorithm 3.1 GIGA-WolF
xt is the strategy according to which I play my action
zt is the “baseline” strategy
loop
xt+1 ← xt + ηt ∗ rt
ˆ
zt+1 ← zt + ηt ∗ rt /3
δt+1 ← min( zt+1 − zt / zt+1 − xt+1 )
ˆ
xt+1 = xt+1 + δt+1 ∗ (zt+1 − xt+1 )
ˆ
ˆ
end loop
3.3
Opponents
The following section overviews the learning algorithms that we selected as opponents in our experiments.
3.3.1
GIGA-WolF
GIGA-WoLF [10] (Generalized Infinitesimal Gradiet Ascent-Win or Learn Fast) is
a gradient ascent algorithm. It is also a model-free algorithm like Q-learning. The
idea of the algorithm is that it compares its strategy to a baseline strategy. It learns
quickly if the strategy is performing worse than the baseline strategy. On the other
hand, if the strategy is performing better than the baseline strategy, it learns at a
slower rate. Algorithm 3.1 shows the basic update structure of the algorithm.
As we can see, this algorithm consists of two main components. The first
component is the “GIGA” component. The idea of “GIGA” is that after each play
the agent updates its strategy in the direction of the gradient of its value function.
The “WoLF” component was introduced later [11]. The idea is to use two different
strategy update steps, one which is updated with a faster learning rate than the other.
To distinguish between those situations, the player keeps track of two policies.
Each policy is concerned with assigning the probabilities of taking a certain action
under this specific situation.
GIGA-WoLF is a no-regret algorithm. No-regret learning converges to NEs

60. CHAPTER 3. EXPERIMENTAL SETUP
41
Algorithm 3.2 Q-learning
for each state-action pair (s, a) do
Q(s, a) ← 0
end for
loop
Depending on exploration rate ε, select an action a and execute it
Receive immediate reward r
Observe the new state s
Update the table entry for Q(s, a) as follows:
Q(s, a) ← (1 − α) ∗ Q(s, a) + α ∗ (r + γ ∗ maxa Q(s , a ))
s←s
end loop
in dominance-solvable, constant-sum, and 2-action general-sum games, but do not
necessarily converge in Shapleys Game [50].
3.3.2
Q-learning
Q-learning [100] is a reinforcement learning technique that is widely used in artificial intelligence research [35], [72], [9]. It can be also viewed as a dynamic
programing technique, in which it iteratively tries to learn its ”to-go” payoff(called
a Q-value) over time. Its main idea can be summarized as follows: an agent tries
an action at a particular state, and evaluates its consequences in terms of the immediate reward or penalty it receives and its estimate of the value of the next state. By
trying all actions in all states repeatedly, it learns which are best overall, judged by
the long-term discounted reward. Algorithm 3.2 shows the main structure of the
algorithm.
For all states and action pairs, Q(s, a) converges to the true value under the
optimal policy when (i) the environment has the Markov property, (ii) the agent
visits all states and takes all actions infinitely often, and (iii) the learning rate α
is decreased properly. However, if the agent always chooses the actions greedily
during learning, Q-values may converge to a local optimum because the agent may
not visit all states sufficiently. To avoid this, the agent usually uses a stochastic

61. CHAPTER 3. EXPERIMENTAL SETUP
42
methods (like ε-greedy) to choose actions. The ε-greedy method chooses an action that has the maximum Q-value with probability (1-ε) or a random action with
probability ε [72].
The Q-learning algorithm we are using in our experiments has the following
settings:
• Discount factor γ = 0.95.
• State is represented by the previous joint action of the agent and its associates.
• Exploration rate ε = 1.0/(10.0 + (t/1000.0)), where t represents the number
of rounds played.
3.4
Evaluation criteria
In order to evaluate the performance of our algorithms, we will mainly focus on
two main points:
1. The average fitness of population per generation: This will help us to evaluate the performance of the algorithm regarding convergence and the ability
of the algorithm to learn over time.
2. The final payoff achieved: By knowing and studying the final payoff, we
know the final performance of the algorithm in comparison to other algorithms.
These evaluation criteria are averaged over 10 runs of each algorithm against
the selected opponent in order to eliminate the effect of randomness. We show the
variations within the final payoffs over all the conducted runs in order to verify
the stability of the performance of the algorithm within a specific game against a
specific opponent.

62. CHAPTER 3. EXPERIMENTAL SETUP
3.5
43
Performance of GIGA-WoLF and Q-learning
In order to get a better understanding of the behavior of the algorithms in the selected games, we compared the performance of the algorithms against each other
and in self-play with available reports from previous work [10], [104], [71]. Figure 3.1 shows our results. These results represent the average of the average of
final payoffs of both learners over 10 runs within each game. Each run consists of
running both learning algorithms against each other for 100,000 steps. In addition,
the figure shows the standard deviation of the payoffs from the average (to show if
it converges consistently to the same rewards or not).
3.5.1
Prisoner’s dilemma
In the prisoner’s dilemma, we expected the agents to learn mutual defection when
GIGA-WoLF plays against Q-learning. This is due to the fact that we are working
with a no-regret algorithm, which learns within few iterations to defect. On the
other hand, the Q-learner learns slower than the GIGA-Wolf, so it takes it a larger
number of iterations for the Q-learner to learn to defect against GIGA-WoLF. The
Q-learner we used uses a high value for γ as it was shown from previous work
that it increases the probability of cooperation if the other learners are willing to
cooperate [71].
3.5.2
Chicken
When GIGA-WoLF and Q-learning interact in Chicken, they did not stabilize to
a fixed outcome among the 10 simulations we ran. Depending on the state action
pairs experimented by the Q-learner in the beginning of a simulation, GIGA-WoLF
acts accordingly. Thus, if the Q-learner started by attempting to swerve in the beginning, the GIGA-WoLF will go straight. But in most of the cases, GIGA-WoLF

63. CHAPTER 3. EXPERIMENTAL SETUP
44
will go with the safe option (if Q-learner tried to go straight in the beginning), and
it will swerve for the rest of the game.
Both Q-learning and GIGA-WoLF are not able to reach the compromise situation of (swerve, swerve) in self-play. One agent always “bullies” the other into
swerving, while the other goes straight.
3.5.3
Shapley’s game
Previous work [9], [50] shows that GIGA-WoLF’s policy does not converge in
Shapley’s game. This fact is apparent in both self-play and against Q-learning. As
a result, players receive an average payoff near the NE value in this game. The
best performance for Q-learning is in self play, as it is often able to learn over time
to reach the solution of iterating between “winning” and “loosing”. But again, in
some cases it is still unable to reach this satisfactory solution.
3.5.4
Cooperative games
Within cooperative games, GIGA-WoLF will find it easy to maintain one of the
actions over time, giving it the ability to reach cooperation quickly in self-play.
This property helps the Q-learner to easily discover the state-action pair that has
the maximum Q-value (as both of the agents in this case have the same goal). As
a result, our Q-learners learn mutual cooperation. On the other hand, Q-learning is
not able to maintain the highest payoff possible from cooperation in self-play. The
reason is although each agent tries to stabilize at one of the actions (to reach its
steady-state), the exploration mechhanism within the algorithm sometimes make it
hard for both agents to maintain a certain action pair.

64. CHAPTER 3. EXPERIMENTAL SETUP
3.6
45
Summary
From the results presented within this chapter, we find that, although both Qlearning and GIGA-WoLF perform well under certain situations, there are situations in which the algorithms do not learn effectively. Furthermore, these algorithms sometimes take a long time to converge. This motivates us to work on
deducing new algorithms that are able to adapt within such dynamic systems. In
the following chapter, we start discussing the structure of the suggested algorithm
and potential variations that could enhance it.

65. CHAPTER 3. EXPERIMENTAL SETUP
46
Final payoffs of GIGA−WoLF and Q−learning in Prisoners dilemma
3
Average payoff (10 runs, each run 100,000 steps)
GIGA−WoLF
Q−learning
2.5
2
1.5
1
0.5
Vs. GIGA−WoLF
Vs. Q−learning
Opponents (Vs.)
Final payoffs of GIGA−WoLF and Q−learning in Cooperation game
GIGA−WoLF
Q−learning
4.5
Average payoff (10 runs, each run 100,000 steps)
4
3.5
3
2.5
2
1.5
1
0.5
0
Vs. GIGA−WoLF
Vs. Q−learning
Opponents (Vs.)
Final payoffs of GIGA−WoLF and Q−learning in Chicken game
7.5
GIGA−WoLF
Q−learning
Average payoff (10 runs, each run 100,000 steps)
7
6.5
6
5.5
5
4.5
4
3.5
Vs. GIGA−WoLF
Vs. Q−learning
Opponents (Vs.)
Final payoffs of GIGA−WoLF and Q−learning in Shapleys game
0.55
GIGA−WoLF
Q−learning
Average payoff (10 runs, each run 100,000 steps)
0.5
0.45
0.4
0.35
0.3
0.25
0.2
Vs. GIGA−WoLF
Vs. Q−learning
Opponents (Vs.)
Figure 3.1: Payoffs of GIGA-Wolf and Q-Learning within selected games.

66. CHAPTER
4
Learning using Genetic Algorithms
In this chapter, we discuss the performance of a basic genetic algorithm (GA) algorithm in repeated matrix games. In addition, we present several suggested modifications to this basic algorithm and show how they may affect the performance of
the GA. We first describe the basic GA structure, and the modifications we apply to
it. We then demonstrate the performance of these algorithms against GIGA-WoLF,
Q-Learning and in self-play.
We initially define a set of parameters that are used within our algorithms, we
tried to maximize the number of steps taken in order to get a better understanding
of the learning trends. These parameters include: the total number of steps (Ns )
and the number of generations (NG ), both determine the time range through which
the agent can learn through playing against another agents. We set NG = 100 generations and Ns = 100,000 (for easier manipulation of the calculations required).
Once we know NG and Ns , we get a trade-off between the number of chromosomes within a population (Nc ), and the number of steps that each chromosome
47

67. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
48
plays against the opponent (Nsc ). Equation 4.1 shows the resulting trade-off.
NG =
Ns
Nsc × NG
(4.1)
Therefore, by setting the total number of steps (Ns ) to 100,00, and by fixing the
number of generations to 100 (in order to have an acceptable number of generations
through which we compare our results), we get that Nsc × Nc =1000.
Through initial experimentations, we set Nsc to different values including 50,
100, and 200, which caused Nc to be 20, 10, and 5 respectively. This analysis
shows us that decreasing the number of chromosomes within a population reduces
randomization, which can cause the population lean towards a local-optima in certain situations. At the same time, by increasing the members in the population,
although it will allow us more exploration, evaluating the population consumes
more time. That is why we settled for a population of 20 chromosomes, which
appears to be reasonable in our settings.
In the following section, we will describe the main structure of the algorithm
to get a better understanding of how we incorporate these modifications, as well as
comprehend the results and analysis.
4.1
Algorithm structure
We analyze a GA typically used in similar problems [3], with slight modifications
to the selection function. Before we start, we introduce some of the variables
used within our work. Table 4.1 shows the common parameters used within the
algorithms.
As mentioned within the literature review, GA starts with the initialization of a
new population of chromosomes (Pop). Each chromosome C represents the strategy followed by the player in response to the current history (his) of both the player

68. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
49
and its opponent. An example of the structure of the chromosome within the prisoner’s dilemma game can be seen in Figure 4.1.
AIn this structure, each bit in the chromosome represents the action to be taken
for a particular history (specificed by the position) of joint action. In our case, we
used the last three actions taken by both the agent and its opponent, as has been
done in some past work [3]. In order to determine which action to take according to
a set of history steps (his), we convert the number his from the base Na to decimal
base in order to identify the bit location of the step to be taken. This conversion is
made as follows:
3
A p = ∑ (Na )i × hisi
i=1
Representation
Pm
Pc
Pe
C
f
P
Ch
Ap
Bp
Avp
Bavp
Nc
NG
Na
Ns
Ns c
Pop
his
Ovf
g
Entrop
Variable
Mutation Rate
Crossover Rate
Elitism Rate
Chromosome (Strategy)
Fitness
Parent
Child
Position of the gene to determine action to be taken
Best Chromosome in Previous Generation
Average fitness of chromosomes in current generation
Best average payoff over generations
Number of chromosomes per generation
Number of generations
Number of actions available for each player
Total number of chromosomes
Number of steps per chromosome
Current population
Current history of actions
Overall fitness of chromosome
Gene within a chromosome (bit)
Entropy of a gene
Table 4.1: Variables used within the algorithms
(4.2)

69. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
50
Figure 4.1: Chromosome structure
Using this equation, we can identify the position of the action to be taken in
response to a certain history within the chromosome. For example, if my history
was CCCCDC (which represents that my moves in the past three stages were Cooperate, except the last stage was defect, while the opponent cooperated all the
time). This history can be encoded as a binary number 000010, which we convert
to decimal base. This means that the bit g at position Ap=2 within the chromosome
shows the action to be taken given this history. Take note that the binary encoded
history can be set in other bases depending on the number of actions available. For
example in a 3-action game, we will be working with history encoded in the ternary
numeric base.
After the initialization of the population (in this experiment we have 20 chromosomes within the population), we start running these random chromosomes
against the opponent player to “evaluate” them. Our evaluation here is based on
averaging the reward taken by each chromosome within each step against the opponent. Each chromosome plays for 50 steps against the opponent. The reward is
then averaged to compute the fitness of the chromosome.
Following the evaluation, we sort the population according to fitness f. Here
our selection process starts, with the higher fitness at the top. We keep the elite
(top) chromosomes, whose number is defined by the elitism rate Pe for the following generation, and apply mutation and crossover on the best two chromosomes.
The same sequence is repeated again with the new population Ch until a stopping

70. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
51
condition is satisfied or the game ends.
In our algorithm, we used the traditional default parameter values (mutation,
crossover ,and elitism rates), which was commonly used in previous research [3], [64].
These values are set as: Pm = 0.01, Pc = 0.5, and Pe = 0.3, with the crossover point
at the middle of the chromosome.
In the following sections, we present the different variations of the genetic
algorithms applied to the basic GA. We also discuss our findings, which lead us to
the idea of integrating the human input to the genetic algorithm.
4.1.1
Basic genetic algorithm
The basic structure of the genetic algorithm that has been previously explained is
detailed in Algorithm 4.1. We can see that the algorithm starts with going through
each chromosome of the population. It computes the fitness function by playing
against the opponent. After passing through all the chromosomes, we sort them in
the population using the fitness values. We then apply the elitism, crossover and
mutation functions to generate the new population. We repeat the process until we
reach the designated number of generations.
Algorithm 4.1 Basic genetic algorithm
for i = 1 to Gen do
Run population Pop against opponent
for each C in population Pop do
Set f
end for
Sort the population depending on value f
Run elitism using Pe , crossover using Pc and mutate using Pm
end for

71. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
52
Algorithm 4.2 Genetic algorithm with history propagation
for i = 1 to Gen do
Run population Pop against opponent
for each C in population Pop do
Set f
Ov f ← ( f + Ov f )/2
end for
Sort the population depending on value Ov f
Run elitism using Pe , crossover using Pc and mutate using Pm
end for
4.1.2
Genetic algorithm with history propagation
Normally, GA sorts the chromosomes within its population based on the fitness
acquired within the current generation. Over time, this may lead the algorithm
to reach a short-sighted solution (as it goes through a local minima that it cannot
escape). To avoid this, the fitness of the chromosomes used over multiple generations is propagated from one generation to the next using what is called the overall
fitness (Ov f ). This variation of the algorithm is outlined in Algorithm 4.2.
4.1.3
Genetic algorithm with stopping condition
The previously explained GA is unstable as we cannot set the stopping condition
to be the number of generations. To achieve more stability, we tested another GA
with a stopping condition. If the fitness remains stable for a certain number of
generations (in our experiments, we set it to 3), the GA seizes to evolve. The
condition is described in algorithm 4.3.
4.1.4
Genetic algorithm with dynamic parameters’ setting
One commonly used method in the literature is to dynamically set different parameters within the GA, specifically the mutation and elitism rates based on the
performance of the chromosomes. If the fitness is increasing from one generation

72. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
53
Algorithm 4.3 Genetic algorithm with stopping condition
for i = 1 to Gen do
Run population Pop against opponent
for each C in population Pop do
Set f
Ov f ← f + Ov f
end for
Sort the population depending on value Ov f
if Ov f of Bp = Ov f of P then
Break from the loop
end if
Run elitism using Pe , crossover using Pc and mutate using Pm
end for
to another, we decrease the mutation rate in an attempt to stabilize the algorithm
at its current fitness. If the average fitness of the population is deteriorating, we
increase the mutation rate in order to try to generate a more fit population (see
Algorithm 4.4).
4.1.5
Genetic algorithm with dynamic parameters’ setting and stopping condition
This variation combines a good exploration methodology with a stopping condition. The structure of this combined variation is shown in Algorithm 4.5.

73. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
54
Algorithm 4.4 Genetic algorithm with dynamic parameters’ setting
for i = 1 to Gen do
Run population Pop against opponent
for each C in population Pop do
Set f
end for
Sort the population depending on value Ov f
if Avp ≥ Bavp then
Decrease mutation rate to 0.01
Bavp ← Avp
else
if Avp ≤ Bavp then
if Bavp − Avp ≥ 20% then
if Bavp − Avp ≥ 40% then
Increase the mutation rate to 0.4
else
Increase the mutation rate to 0.2
end if
else
Keep mutation rate the same
end if
i ← i+k
end if
end if
Run elitism using Pe , crossover using Pc and mutate using Pm
end for
4.2
Results and analysis
In this section, we present the results from the conducted experiments. As previously mentioned in chapter 3, we run our experiments on four different games:
1. Prisoner’s dilemma (Table 4.2).
2. Cooperation game (Table 4.3).
3. Chicken game (Table 4.4).
4. Shapley’s game (Table 4.5).

74. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
55
Algorithm 4.5 Genetic algorithm with dynamic parameters’ setting and stopping
condition
for i = 1 to Gen do
Run population Pop against opponent
for each C in population Pop do
Set f
end for
Sort the population depending on value Ov f
if Ov f of Bp = Ov f of P then
Break from the loop
end if
if Avp ≥ Bavp then
Decrease mutation rate to 0.01
Bavp ← Avp
else
if Avp ≤ Bavp then
if Bavp − Avp ≥ 20% then
if Bavp − Avp ≥ 40% then
Increase the mutation rate to 0.4
else
Increase the mutation rate to 0.2
end if
else
Keep mutation rate the same
end if
i ← i+k
end if
end if
Run elitism using Pe , crossover using Pc and mutate using Pm
end for
In presenting these results, we compare the performance of the algorithmic
variations discussed in the previous section.
4.2.1
Genetic algorithms vs. GIGA-WoLF
Our first set of results show the performance of the different variations of GA
against the opponent GIGA-WoLF. Overall, we can see from Figure 4.2 that the
performance of the Dynamic GA with mutation excels in comparison to the other
variations of GA with a smaller variation, which ensures stability. Figures 4.3, 4.4,

75. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
Cooperate
Defect
Cooperate
3,3
5,0
56
Defect
0,5
1,1
Table 4.2: Payoff matrix for the Prisoner’s dilemma.
A
B
a
4,4
0,0
b
0,0
2,2
Table 4.3: Payoff of a fully cooperative matrix game.
and 4.5 show that the same properties are valid if we consider each game seperately. We see that stopping condition on its own, although it provides stability, is
not able to overcome the local-optima in some situations (as no extensive exploration of the strategy space occurs). Thus, dynamic mutation in addition to the
stopping condition enhances the exploration most effectively.
From Figure 4.6, we can see a slight improvement in the performance in Shapley’s game when we add the propagation of history, where both versions of the GA
(with and without propagation) achieve a payoff that is near the Nash value(0.33).
However, in contradiction with the general trend of results, even though the modifications slightly enhanced the final payoff achieved, none of the algorithms converges. This is shown due to the wide margin within the final payoffs). In this case,
pure dynamic GA (without the stopping condition) performs better.
4.2.2
Genetic algorithms Vs. Q-learning
Figure 4.7 shows the average final payoffs of the various GAs against Q-learning
across all games. The figure shows that the algorithms perfoming the best are the
Swerve
Straight
Swerve
6,6
7,4
Straight
4,7
2,2
Table 4.4: Payoff matrix for chicken game.

76. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
A
B
C
a
0,0
1,0
0,1
b
0,1
0,0
1,0
57
c
1,0
0,1
0,0
Table 4.5: Payoff matrix of Shapley’s game.
GA vs. GIGA−WoLF (all games)
3.1
3
Average final payoff
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
Basic
W/ prop.
W/ stop.
Dynamic
Dynamic W/ stop.
Figure 4.2: Effect of variations on GA on final payoffs against GIGA-WoLF (all
games).
basic GA (without propagation) and the Dynamic GA with mutation. In figure 4.8,
we can see that some variations (such as history propagation) were able to reach
higher payoffs in certain circumstances.
However, we analyzed a few samples of resulting populations’ chromosomes of
both basic GA and dynamic GA with mutation in prisoner’s dilemma (Figure 4.12),
as well the margin of variation in the final payoffs. We saw that while the basic GA
results into a random population (not conforming to a certain pattern of strategies),
the Dynamic GA was able within certain iterations to conform to a cooperation
policy with Q-learning. We can also see from Figure 4.13, which shows the average
payoff awarded to the algorithm over time, that GA with propagation of history
shows a better learning trend in the end.
In contrast to what we expected, history propagation slightly decreased the
performance of the algorithm (wider margin of variation in figure 4.9). In chicken
(Figure 4.10), we can see that GA is unable to adapt to a bullying strategy in this

77. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
GA vs. GIGA−WoLF in prisoners dilemma
GA vs. GIGA−WoLF in Cooperation game
4
0.9
3.5
Average final payoff
1
Average final payoff
58
0.8
0.7
0.6
3
2.5
2
0.5
Basic
W/ prop.
W/ stop.
Dynamic
Dynamic W/ stop.
Figure 4.3: Effect of variations on GA
on final payoffs against GIGA-WoLF in
prisoner’s dilemma.
Basic
W/ prop.
W/ stop.
Dynamic
Dynamic W/ stop.
Figure 4.4: Effect of variations on GA on
final payoffs against GIGA-WoLF in cooperation game.
GA vs. GIGA−WoLF in Chicken game
GA vs. GIGA−WoLF in Shapleys game
7
0.45
0.4
Average final payoff
Average final payoff
6.5
6
5.5
5
0.35
0.3
0.25
0.2
0.15
0.1
4.5
0.05
0
Basic
W/ prop.
W/ stop.
Dynamic
Dynamic W/ stop.
Figure 4.5: Effect of variations on GA
on final payoffs against GIGA-WoLF in
Chicken game.
Basic
W/ prop.
W/ stop.
Dynamic
Dynamic W/ stop.
Figure 4.6: Effect of variations on GA
on final payoffs against GIGA-WoLF in
Shapley’s game.
case. Best performances can actually be seen in case of the basic GA and the
dynamic GA. This is a very unexpected result given that dynamicity confuses slowlearning algorithms such as Q-learning, making it more difficult to adapt.
In Shapley’s game (Figure 4.11), the GA with the highest performance was the
one with the propagation of history. What was expected and viewed from the results is the fact that algorithms with stopping conditions (not continuously learning
and mutating with a higher rate) are ones that performed the worst. This confirms
the need of an adaptable mutation rate in order to enhance the performance of the
algorithm. However, by implementing the dynamic mutation technique, we can
see in figures an improvement in the performance (Figure 4.14). It was noticed
that using the stopping condition on its own (without implementing the dynamic

78. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
59
GA vs. Q−learning (all games)
3.2
Average final payoff
3
2.8
2.6
2.4
2.2
2
Basic
W/ prop.
W/ stop.
Dynamic
Dynamic W/ stop.
Figure 4.7: Effect of variations on GA on final payoffs against Q-learning (all
games).
mutation) lead to the stability at an ucceptable local minima.
4.2.3
Genetic algorithms in self play
From Figure 4.15 shows that the dynamic GA with a stopping condition has a better
overall performance than its counterparts, both in terms of the average final payoff
and the margin of the final payoff.
However, this is not universally true in specific games(Figure 4.16-4.19), different variations do not affect the performance of the algorithms substantially in
the prisoner’s dilemma. With analyzing the set of policies achieved, we find that
almost in all self-play cases, the algorithms learn to alternate between defection
and cooperation.
None of the variations were able to achieve continuous cooperation int the
cooperation game(Figure 4.17). The best performer was the GA with the Dynamic
GA with stopping condition. On the other hand, none of the GA variations were
able to stabilize at a satisfactory payoff except for the dynamic GA with stopping
condition in both Chicken and Shapley’s (Figures 4.18 and 4.19). The variation
with only a stopping position gave an unacceptable performance. This may be due
the fact that it converged prematurely.

79. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
60
GA vs. Q−learning in Cooperation game
GA vs. Q−learning in prisoners dilemma
4
3.8
2
Average final payoff
Average final payoff
3.6
1.8
1.6
1.4
3.4
3.2
3
2.8
2.6
2.4
1.2
2.2
2
1
Basic
W/ prop.
W/ stop.
Dynamic
Basic
Dynamic W/ stop.
Figure 4.8: Effect of variations on GA on
final payoffs against Q-learning in prisoner’s dilemma.
W/ prop.
W/ stop.
Dynamic
Dynamic W/ stop.
Figure 4.9: Effect of variations on GA on
final payoffs against Q-learning in a Cooperation game.
GA vs. Q−learning in Chicken game
GA vs. Q−learning in Shapleys game
7
0.38
0.36
Average final payoff
Average final payoff
6.5
6
5.5
5
4.5
0.34
0.32
0.3
0.28
0.26
0.24
0.22
0.2
4
Basic
W/ prop.
W/ stop.
Dynamic
Dynamic W/ stop.
Figure 4.10: Effect of variations on GA
on final payoffs against Q-learning in
Chicken game.
Basic
W/ prop.
W/ stop.
Dynamic
Dynamic W/ stop.
Figure 4.11: Effect of variations on GA
on final payoffs against Q-learning in
Shapley’s.
Figure 4.12: Sample of the chromosomes generated vs. Q-learning in prisoner’s
dilemma.

80. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
61
GA vs. Q−learning in prisoners dilemma game
2.5
Average payoff per generation
Without history propagation
With history propagation
2
1.5
1
0.5
0
10
20
30
40
50
60
70
80
90
100
Numberof generations
Figure 4.13: Effect of history propagation on GA against Q-learning in Prisoners
dilemma. Values shows are the average payoff per generation.
GA vs. Q−learning in cooperation game
Average payoff per generation
4
3.5
3
2.5
2
With history propagation
With Stopping condition
Dynamic GA
Dynamic GA with stopping condition
1.5
1
0
20
40
60
80
100
Numberof generations
Figure 4.14: Effect of variations on GA against Q-learning in cooperation game
(Average payoff per generation).
GA in self−play (all games)
Average final payoff
3.5
3
2.5
2
Basic
W/ prop.
W/ stop.
Dynamic
Dynamic W/ stop.
Figure 4.15: Effect of variations on GA on final payoffs in self play (all games)

81. CHAPTER 4. LEARNING USING GENETIC ALGORITHMS
4.3
62
Conclusions
From the results, we can deduce that our final variation (GA with history propagation and stopping condition) performed the best on average. We also concluded
that a dynamic mutation rate (varying from time to time) is very effective in order
to enhance the performance of the GA. Also, we can see a variation in the performance of GA and its variations from one iteration to another (shown by the wide
margin within the final payoffs in some cases). This shows us that, as we are using
a random initial population, the population at the beginning of the game affects the
performance of the GA drastically.
GA in self−play in prisoners dilemma
GA in self−play in Cooperation game
3.5
Average final payoff
4
3
Average final payoff
3.5
2.5
2
3
2.5
2
1.5
1.5
1
Basic
W/ prop.
W/ stop.
Dynamic
Dynamic W/ stop.
Figure 4.16: Effect of variations on GA
on final payoffs in prisoner’s dilemma
Basic
W/ prop.
W/ stop.
Dynamic
Dynamic W/ stop.
Figure 4.17: Effect of variations on GA
on final payoffs in a Cooperation game
GA in self−play in Chicken game
GA in self−play in Shapleys game
1
0.9
6.5
Average final payoff
Average final payoff
0.8
6
5.5
5
0.7
0.6
0.5
0.4
0.3
0.2
4.5
0.1
0
Basic
W/ prop.
W/ stop.
Dynamic
Dynamic W/ stop.
Figure 4.18: Effect of variations on GA
on final payoffs in Chicken game
Basic
W/ prop.
W/ stop.
Dynamic
Dynamic W/ stop.
Figure 4.19: Effect of variations on GA
on final payoffs in Shapley’s game

82. CHAPTER
5
Interactive genetic algorithms
Through this chapter, we propose a method for using human input to improve the
performance for a GA in repeated matrix games. Furthermore, we will show the
results of running the resulting algorithm against the same set of opponents within
the same set of games as in the previous experiments.
As we have studied and analyzed in the previous chapter, slight changes within
the population structure, either initially or throughout the learning process, can
have a huge effect on the performance of the learning procedure within this learning
algorithm. We suggest the usage of human input as a changing factor in these
environments. So called interactive genetic algorithms are very widely used in
various applications, usually when it is easy for the user to visualize and evaluate
the performance. In this chapter, we describe and evaluate different variations of
the interactive GA in repeated matrix games.
As mentioned in the literature review, interactive genetic algorithms (IGA) are
the focus of a lot of current research, especially when systems include more qual63

83. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
64
itative criteria of judgement that require potential human interference. Currently,
the main focus of interactive genetic algorithms is within more visual applications,
where the user can show his “qualitative” satisfaction with the performance of the
algorithm. Such evaluations can be used as a fitness function.
Motivated by this idea, we designed a framework through which human can
receive and give feedback about the performance of the GA. This feedback should
provide, through minimal interactions, the necessary information in order to enhance the algorithm’s performance and adapt it quickly to any changes in the surrounding the environment.
We deduced from the results of the previous chapter two characteristics that
affect the performance of GAs within repeated matrix games: population initialization and mutation and variable mutation rates.
Our framework focuses primarily on using human input to improve the population. However, we also ran some experiments to show the possible benefit for of
the human to vary the algorithm’s mutation rate dynamically.
5.1
Human input framework
The human input framework is outlined in Figure 5.1. This framework should
enable the user to both give and recieve feedback from the algorithm throughout
the game. We also show a graphical user interface for interaction purposes in
figure 5.2. Within the following sections, we describe the detailed structure of the
framework. We do so by discussinng the main steps of our framework in turn.
5.1.1
Evaluate the population
Our main concern is how to allow the user to effectively change the chromosome
population. Initially, the population is generated randomly initially. After the initial

84. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
1-Evaluate
the
population
65
Evaluate the generated chromosomes (strategies) against the opponent to calculate the
experimental fitness
If cycle for human input
started
2- Select set
of histories
3-Generate
statistics for
selected
histories
4-Generate
new
population
using human
input
NO
Calculate entropy for every bit (representing the action at a
certain history combination) through the whole population
depending on the action and fitness value
Select the r bits with the highest entropy
After going
through all
chromosomes
within the
population
For each of the selected r bits, show to the human the action taken by the
algorithm within the previous generation for the corresponding history, in
addition to statistics about the action fitness
Take suggested input for the selected bits and match them with the action
taken within the previous generation for the corresponding history
For each chromosome, if there is at least one match between
human feedback and action previously taken for all bits
NO
Add the chromosome to
the new population
Yes
NO
For each bit ,If bit is one
of the r bits with highest
entropies
Yes
If variance < v
Replace value of
bit with a random
value
Leave value of bit
as it is
After going through all bits in chromosome
Figure 5.1: Human input framework.

85. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
Selected history
patterns (using
entropy)
Environment
information
(payoff matrix)
Human input (algorithm
parameters)
User input (suggestions
of actions for selected
history patterns)
Learning rate (average payoff
per generation)
66
Feedback from
algorithm regarding
previous population
State of algorithm (Busy/
Current number of stages
played)
Figure 5.2: Designed graphical user interface.
population plays against the opponent, it will be evaluated, sorted, mutated and
crossovered (the same sequence as in the normal GA).
5.1.2
Select set of histories
Since it is considered extensive work for the user to evaluate and alter each aspect
of the strategy, we select a particular part of the strategy for the user to evaluate.
To do this, we go through all the chromosomes, and we select the bits that have the
highest entropy Entrop within the chromosomes. We chose the entropy property,
as we want to select the bits within the population that have the the most variation,
and therefore represents the indecisiveness of the population. While calculating
the entropy, we give more value (weight) with higher fitness as follows:

86. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
Entropy = log(−p) × p
67
(5.1)
Where p represents the probability of occurence of a certain action Pa following a
certain history pattern, multiplied by a factor of the fitness of the chromosome f
within which this action occured divided by the total fitness of the whole population
FitnessTotal . The following equation shows how probability p is computed:
p = Pa ×
5.1.3
f
FitnessTotal
2
(5.2)
Generate statistics for selected histories
After calculating the entropy and deciding on which bits (history patterns) correspond to uncertain behavior, we calculate for each chromosome the average, minimum and maximum fitness of the chromosomes that contain a certain value for an
action at this bit g.
The human takes feedback about the performance of the population from the
algorithm regarding the population as a set of statistics about the performance of
the algorithm in the previous generation. These statistics include:
1. Selected history patterns: History patterns with highest entropy Entrop is
calculated based on the action taken) over the population.
2. Percentage of the population that performs a certain action in response to the
selected history patterns.
3. Average fitness of chromosomes that perform a certain action in response to
the selected history patterns.
4. Average fitness of the previous population.

87. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
5.1.4
68
Generating a new population from human input
In response to the statistics presented, the human suggests a strategy for the particular history presented to him. The GA uses this information to generate its
population for the subsequent generation. This is done by matching the suggested
strategies to the strategies expressed in the chromosomes of the previous population. For each chromosome, if there is a match between the strategy used by the
chromosome for at least one of the selected history patterns and the strategy suggested by the human input for that history pattern, we move the chromosome as it
is to the following population.
In chromosomes in which no matches occur, we can either replace the strategies in the chromosome used at the selected history patterns with the strategies
suggested by the human within this situation or replace the strategies with random
generated strategies. In order to choose whether we follow the human’s suggestion
or randomly replace the existing action, we depend on what we define as variance
v. The calculation of variance gives us an idea about the inner statistics within a
certain population, and whether their are major gaps in fitness between higher and
lower fitness chromosomes.
In case we have a (relatively) low variation in the fitness between the best and
the worst chromosomes, we follow the human input as there is a good probability
that the human suggestions enhances the performance the overall performance of
the population. Otherwise, we replace the non-matching actions randomly in order
to give space for more exploration and to not be completely reliable on the human
input (as no guarantee about its quality). Variance is declared using the following
equation:
v=
∑
chromosomes
( f − mean)
(5.3)

88. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
69
where f is the fitness of the chromosome and mean is the mean of the fitnesses
of all the chromosomes within the population. If variance is not implemented, we
will use the human suggested strategy as replacement by default (instead of random
replacement. The purpose of variance is to try to enhance the exploration of the
algorithm outside the suggestions of the human input.
After generating the new population, we repeat the process by evaluating this
population against the opponent. The process of feedback and input can be repeated with a certain defined rate. Here, we chose that it is to be repeated every
four generations so we can experiment the effect on a constant rate.
5.2
Interactive genetic algorithms: Six variations
We evaluated six variations of our IGA algorithm. These variations differ in the
implementation of certain factors including:
1. Using different (larger) mutation rates in the dynamic mutation (we multiplied the rates normally used by 2).
2. Using variance that depends only the current fitness of the chromosomes.
3. Using variance that depends on propagating fitness of the chromosomes.
4. Using stopping condition that depends only the current fitness of the chromosomes( default is that it depends on propagating fitness of the chromosomes).
Table 5.1 summarizes the algorithms we implemented, including which of the variations exist in each algorithm.
5.2.1
Effect of input quality on the performance of GA
In order to intensify our study of the effect of the human input on the GA performance, we considered how the quality of the human input may affect the perfor-

89. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
Variation
Larger mutation
Basic IGA
IGA2
IGA3
IGA4
IGA5
IGA6
Variance
Variance W/prop.
70
Stop. cond.
W/o prop.
√
√
√
√
√
√
√
Table 5.1: Properties of the different variations of IGA algorithms.
Game
Prisoner’s Dilemma
Cooperation Game
Chicken Game
Shapley’s Game
Acceptable human input
TIT-FOR-TAT
Always play A
Always straight and TFT
Random
Unacceptable human input
Inverse TIT-FOR-TAT
Always play B
Always swerve
Pure strategy
Table 5.2: Acceptable and unacceptable human inputs for the selected 2-agent
matrix games.
mance of the GA. For each game, we identified what we call “Acceptable” and
“Unacceptable” human input. This helps us to better understand how the qualities
of human input changes the performance of GA. In Table 5.2, we summarize the
possible qualities of human input for each of the games used in our simulations.
Note that in our selections of what is considered as “acceptable” and “unacceptable” input, we faced the dilemma of having different criteria of quality that varies
depending on the opponent faced. Therefore, the performance of a certain type of
human input is situational (depending on the opponent faced). We tried to identify well performing human input through analyzing the population generated by
running the algorithms from the previous chapter. We will notice that in some situations, human input did not perform as expected. More details on that will be
expressed in the results section.
In order to get a better understanding of the table, we will explain the set of
strategies mentioned. In the case of the prisoner’s dilemma, previous research has
shown that TFT is a robust strategy [4]. TFT behaves as follows: Start with coop-

90. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
71
eration. Subsequently, copy the opponents’ action from the previous time step. For
the “Unacceptable” input in the prisoners’ dilemma, we inversed the TIT-FOR-TAT
strategy (defect if opponent cooperates and cooperate if the opponent defects). This
human input should be misleading enough to be considered an “Unacceptable” human input.
In the cooperation game, we assume that an acceptable strategy would be to
always play A, while While always playing B would be less desirable. Moving on
to the chicken game. From the previous chapter, we found that almost all of our opponents (except in self-play), can be easily manipulated to swerve if our algorithm
persist on going straight, therefore we chose one of our acceptable inputs as going
straight. We also added a TFT strategy as an acceptable human input in order to
see if mutual swerving can be achieved, and also to show how the performance of
each human input is dependent on the opponent faced. Unacceptable human input
was defined as always swerving.
Finally we discuss the human input quality in case of Shapley’s game. In this
case, we assumed that a random strategy might be suitable to be considered acceptable as a result of the analysis from the population generated in previous experiments (from the previous chapter), because it maximizes the minimum payoff.
However it does not lead to amutually benificial solution. We chose the unacceptable strategy to be a pure strategy, which we chose to be taking the first possible
action (Playing action A).
5.3
Results and analysis
We now present the results from our experiments using the same settings as in the
experiments reported in the previous chapter. We first show the effect of basic
human input on the performance of GA. We then discuss the effect of different

91. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
72
variations on the human input on the performance of IGA. Finally, we show the
impact of the human input quality on the performance of IGA.
In the results, we rely on two evaluation criteria in order to compare the performance of the algorithms. These metrices include:
• Average final payoff: This represents the average of the final payoffs awarded
to the algorithm over the 10 conducted iterations.
• Consistency: This represents how consistent are the final payoffs over several iterations. This can be viewed from the figures as the range between
the maximum and the minimum payoff value reach over the 10 iterations,
excluding the outliers. An example is shown in figure 5.3.
• Convergence: This term is used when a figure shows average payoff of populations overtime. A better convergenceshows that the average payoff stabilizes at a good value over time.
Figure 5.3: Evaluation metrices example

92. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
73
IGA vs. GIGA−WoLF (all games)
3.1
Average final payoff
3.05
3
2.95
2.9
2.85
2.8
Without human input
With human input
Figure 5.4: Effect of human input on basic IGA against GIGA-WoLF (all games).
5.3.1
Interactive genetic algorithms
We first discuss the effect of implementing the basic IGA. In these results, we show
the change in performance when we use an acceptable human input on the dynamic
GA with mutation (final algorithm reached in last chapter). As done previously,
we will show the results for the algorithm against each opponent within each of the
selected games. Note that in case of Chicken, we will display the results regarding
two types of human input (TFT and bullying). The human input to be used within
the following sections will be the one with the highest overall performance for each
algorithm seperately.
Interactive genetic algorithms vs. GIGA-WoLF
In the previous chapter, we showed that, against GIGA-WoLF, the dynamic GA
with stopping condition was able to stablizie within a few generations in some of
the games. On the other hand, it sometimes was unable to explore the whole solutiona space, leading to a more “local” solution. Overall, we can see from Figure 5.4
that human input has not contributed to a major enhancement against GIGA-WoLF
except in the cooperation game (Figure 5.6) and Chicken (Figure 5.7). The selected
input in that case was bullying (showing stability).

93. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
IGA vs. GIGA−WoLF in prisoners dilemma
74
IGA vs. GIGA−WoLF in Cooperation game
3.99
3.98
Average final payoff
Average final payoff
0.995
0.99
0.985
0.98
0.975
3.97
3.96
3.95
3.94
3.93
0.97
3.92
Without human input
With human input
Figure 5.5: Effect of basic human input
on the performance (final payoff) of GA
vs. GIGA-WoLF in prisoner’s dilemma.
Without human input
With human input
Figure 5.6: Effect of basic human input
on the performance (final payoff) of GA
vs. GIGA-WoLF in a cooperation game.
IGA vs. GIGA−WoLF in Shapleys game
0.4
IGA vs. GIGA−WoLF in Chicken game
0.38
7
Average final payoff
0.36
Average final payoff
6.8
6.6
6.4
0.34
0.32
0.3
0.28
0.26
0.24
6.2
0.22
0.2
6
Without human input
Without human input
With human input
With human input (TFT) With human input (Bully)
Figure 5.7: Effect of basic human input
on the performance (final payoff) of GA
vs. GIGA-WoLF in chicken game.
Figure 5.8: Effect of basic human input
on the performance (final payoff) of GA
vs. GIGA-WoLF in Shapley’s game.
Interactive genetic algorithms vs. Q-learning
In the previous chapter, we observed that the average performance against Qlearning in some of the games (especially prisoner’s dilemma) needed vast improvements. In addition, we noticed that most of the populations generated were
not converging to an acceptable set of chromosomes. In this section, we will show
the difference in performance with and without human input.
From the previous results and from Figure 5.10, we observe that, on average,
acceptable human input has a positive effect on the GA. Although IGA is not consistent, but maximum and minimum payoff achieved still have higher values for
IGA than GA.

94. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
75
IGA vs. GIGA−WoLF in Shapleys game
0.5
Without human input
With human input
Average payoff per generation
0.45
0.4
0.35
0.3
0.25
0.2
0
10
20
30
40
50
60
70
80
90
100
Numberof generations
Figure 5.9: Effect of basic human input on GA against GIGA-WoLF in Shapley’s
(Average payoff per generation).
IGA vs. Q−learning (all games)
3.2
Average final payoff
3.1
3
2.9
2.8
2.7
2.6
2.5
2.4
2.3
Without human input
With human input
Figure 5.10: Effect of basic human input on GA on final payoffs against Q-learning
(all games).
We can also see a drastic improvement in figure 5.12 between the performance
of GA with and without the human input. This can be reasoned as the human input
motivates a stronger reputation from the GA side, and accordingly the Q-learner is
able to adapt quicker, and in some situation is able to reach cooperation as shown in
the sample population in Figure 5.11. In Chicken (Figure 5.14), we can see that as
a result of having the Q-learner settle to swerving, a human input that encourages
bullying is able to take the straight action much easier. That is why in this situation
we chose the bullying input as our acceptable input.
Figure 5.13 shows the performance in the cooperation game. Using human

95. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
76
Figure 5.11: A sample of the chromosomes generated from basic IGA vs. Qlearning in prisoner’s dilemma.
input actually decreases the performance, which is shown through having low consistency in the final payoffs. This shows an instability in the output population of
the GA. This can be attributed back to the fact that the human input in some case
has a slower effect than what is needed to motivate Q-learning to learn the right
action, and leads to confusion in taking the decision instead.
IGA vs. Q−learning in Cooperation game
IGA vs. Q−learning in prisoners dilemma
3
3.8
2.8
Average final payoff
Average final payoff
2.6
2.4
2.2
2
1.8
1.6
3.6
3.4
3.2
3
1.4
1.2
2.8
Without human input
Without human input
With human input
Figure 5.12: Effect of basic human input
on the performance (final payoff) of GA
vs. Q-learning in prisoner’s dilemma.
Figure 5.13: Effect of basic human input
on the performance (final payoff) of GA
vs. Q-learning in a cooperation game.
IGA vs. Q−learning in Chicken game
IGA vs. Q−learning in Shapleys game
0.38
5.8
0.36
Average final payoff
6
Average final payoff
With human input
5.6
5.4
5.2
5
4.8
4.6
0.34
0.32
0.3
0.28
0.26
0.24
0.22
4.4
Without human input
With human input (TFT) With human input (Bully)
Figure 5.14: Effect of basic human input
on the performance (final payoff) of GA
vs. Q-learning in chicken game.
Without human input
With human input
Figure 5.15: Effect of basic human input
on the performance (final payoff) of GA
vs. Q-learning in shapley’s game.

96. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
77
IGA in self−play (all games)
Average final payoff
3.3
3.2
3.1
3
2.9
2.8
Without human input
With human input
Figure 5.16: Effect of basic human input on GA on final payoffs in self-play (all
games).
IGA in self−play in Chicken game
7
Without human input
With TFT human input
With Bully human input
Average payoff per generation
6.5
6
5.5
5
4.5
4
3.5
0
10
20
30
40
50
60
70
80
90
100
Number of generations
Figure 5.17: Effect of basic human input on GA in self-play in chicken game
(Average payoff per generation).
Interactive genetic algorithms in self-play
In self-play, the results with the dynamic GA with stopping condition was not
satisfactory in cooperation games. Additionally, the population generated while
playing the prisoner’s dilemma did not converge as desired. However, across all
the games (Figure 5.16), human input produced a higher (though not statistically
different) performance.
In prisoner’s dilemma (Figure 5.18), we can see that although the human input
is more consistent, the final payoffs from the IGA has a slightly worse performance
on average. This was not expected, especially in the case of self-play, as both

97. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
IGA in self−play in prisoners dilemma
78
IGA in self−play in Cooperation game
4
2.9
2.8
3.8
Average final payoff
Average final payoff
2.7
2.6
2.5
2.4
2.3
2.2
3.6
3.4
3.2
2.1
3
2
1.9
2.8
Without human input
With human input
Figure 5.18: Effect of basic human input
on the performance (final payoff) of GA
in self-play in prisoner’s dilemma.
Without human input
With human input
Figure 5.19: Effect of basic human input
on the performance (final payoff) of GA
in self-play in a cooperation game.
IGA in self−play in Chicken game
IGA in self−play in Shapleys game
1
0.9
6.5
Average final payoff
Average final payoff
0.8
6
5.5
0.7
0.6
0.5
0.4
0.3
0.2
5
0.1
0
Without human input
With human input (TFT) With human input (Bully)
Figure 5.20: Effect of basic human input
on the performance (final payoff) of GA
in self-play in chicken game.
Without human input
With human input
Figure 5.21: Effect of basic human input
on the performance (final payoff) of GA
in self-play in shaply’s game.
algorithms are directed by the same TFT human input. Even though, the algorithms
are able to reach cooperation in some iterations. We can also see a slightly worse
performance using our chosen human input in Shapley’s (Figure 5.21).
Figure 5.19 shows how the average of the final payoffs rewarded to the algorithm is better and consistent. The algorithm reaches near perfect coordination
between the agents. From Figures 5.20 and 5.17, we chose our acceptable input to
be also the one that motivates always bullying.
5.3.2
Modificiations on interactive genetic algorithms
In this section, we display the results concerning the different variations implemented on GA that we explained earlier. We show how these variation may effect

98. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
79
IGA variations vs. GIGA−WoLF (all games)
3.1
Average final payoff
3.05
3
2.95
2.9
2.85
2.8
2.75
Basic IGA
IGA 2
IGA 3
IGA 4
IGA 5
IGA 6
Figure 5.22: Effect of variations on human input on GA against GIGA-WoLF (all
games).
IGA variations vs. GIGA−WoLF in prisoners dilemma
Average payoff per generation
1.1
1
0.9
0.8
Basic IGA
IGA 2
IGA 3
IGA 4
IGA 5
IGA 6
0.7
0.6
0.5
0
20
40
60
80
100
Numberof generations
Figure 5.23: Effect of variations on IGA against GIGA-WoLF in prisoners
dilemma (Average payoff per generation).
the human interaction potential. This gives us an idea about different parameters
that the human can adjust according to his knowledge of the environment in order
to enhance the performance of the algorithm.
Against GIGA-WoLF
We can see in Figure 5.22 that overall the basic GA has the highest performance,
followed by IGA6, which is more consistent. From the results displayed in Figure 5.23, we can see that applying different mutation rates (IGA2) improves the
performance immensly in the prisoner’s dilemma. We can see also that using a

99. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
80
IGA variations vs. GIGA−WoLF in Cooperation game
IGA variations vs. GIGA−WoLF in prisoners dilemma
4
1
3.9
Average final payoff
Average final payoff
0.95
0.9
0.85
0.8
0.75
3.8
3.7
3.6
3.5
3.4
3.3
0.7
3.2
0.65
3.1
Basic IGA
IGA 2
IGA 3
IGA 4
IGA 5
IGA 6
Figure 5.24: Effect of variations on IGA
on final payoffs vs. GIGA-WoLF in prisoner’s dilemma.
Basic IGA
IGA 2
IGA 3
IGA 4
IGA 5
IGA 6
Figure 5.25: Effect of variations on IGA
on final payoffs vs. GIGA-WoLF in a cooperation game.
IGA variations vs. GIGA−WoLF in Chicken game
IGA variations vs. GIGA−WoLF in Shapleys game
7
0.4
0.35
6.6
Average final payoff
Average final payoff
6.8
6.4
6.2
6
5.8
0.3
0.25
0.2
0.15
0.1
Basic IGA
IGA 2
IGA 3
IGA 4
IGA 5
IGA 6
0.05
Basic IGA
Figure 5.26: Effect of variations on IGA
on final payoffs vs. GIGA-WoLF in
Chicken game.
IGA 2
IGA 3
IGA 4
IGA 5
IGA 6
Figure 5.27: Effect of variations on IGA
on final payoffs vs. GIGA-WoLF in
Shapley’s game.
propagating variance (IGA4) negatively impacts the performance of the algorithm.
This is expected due to the fact that propagating variance eliminates an important
factor for speeding up the learning progress, which is how we merge both the consideration of the history, as well as the current payoff within the generation.
Figure 5.24 shows us that IGA3 (propagating history without a propagating
variance) has the highest performance, also it shows a good convergence trend.
Both are expected for the same reason mentioned earlier concerning the variance.
Against Q-learning
Here, we compare the various forms of IGA against Q-learning. Overall, basic IGA
had a better average performance than the other variations (figure 5.28). IGA6 has

100. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
81
IGA variations vs. Q−learning (all games)
3.4
Average final payoff
3.2
3
2.8
2.6
2.4
2.2
2
1.8
1.6
Basic IGA
IGA 2
IGA 3
IGA 4
IGA 5
IGA 6
Figure 5.28: Effect of variations on IGA on final payoffs vs. Q-learning (all
games).
the least variance in comparsion to other modifications.
The basic IGA is excelling in comparison to the other modifications (as shown
in figure 5.29) in the prisoner’s dilemma, same in shapley’s game (Figure 5.32).
We can see that the original set of mutation rates chosen for the algorithm is more
suitable in this case. In addition, adding the variance factor, which makes the
algorithm take into consideration the within generation variance did not improve
the performance considering the average final payoffs. However, under certain
circumstances, it was able to decrease the margin of the final payoffs achieved,
which means more stability in terms of convergence over different sets of iterations.
In Chicken (Figure 5.31), the performance agrees with this trend.
Figure 5.30 shows that IGA2 performs better than basic GA in a cooperation
game. We can also see that basic IGA, IGA3 and IGA4 perform better than others.
Therefore algorithms with propagation of history tends to perform better.
Changing the set of mutation rates also improved the performance in Shapley’s
(Figure 5.27). It also reduces the variance in the cooperation game (Figure 5.25).
It can be noticed that IGA2 has a an outlier that learns to coordinate with the
opponent, but at the action having the lower payoff. This proves that the set of
mutation rates suggested are not suitable for all games and all opponents.

101. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
82
IGA variations vs. Q−learning in Cooperation game
IGA variations vs. Q−learning in prisoners dilemma
3
3.8
Average final payoff
Average final payoff
2.8
2.6
2.4
2.2
2
1.8
3.6
3.4
3.2
3
1.6
1.4
2.8
1.2
Basic IGA
IGA 2
IGA 3
IGA 4
IGA 5
Basic IGA
IGA 6
Figure 5.29: Effect of variations on IGA
on final payoffs vs. Q-learning in prisoner’s dilemma.
IGA 2
IGA 3
IGA 4
IGA 5
IGA 6
Figure 5.30: Effect of variations on IGA
on final payoffs vs. Q-learning in a cooperation game.
IGA variations vs. Q−learning in Chicken game
IGA variations vs. Q−learning in Shapleys game
7
0.4
6.5
0.35
Average final payoff
Average final payoff
6
5.5
5
4.5
4
3.5
0.3
0.25
0.2
0.15
0.1
3
0.05
2.5
0
2
Basic IGA
IGA 2
IGA 3
IGA 4
IGA 5
IGA 6
Figure 5.31: Effect of variations on IGA
on final payoffs vs. Q-learning in chicken
game.
Basic IGA
IGA 2
IGA 3
IGA 4
IGA 5
IGA 6
Figure 5.32: Effect of variations on IGA
on final payoffs vs. Q-learning in Shapley’s game.
Self-play
Overall, basic IGA seems to behave slightly better than its counterparts(Figure 5.33).
As in the case when played against Q-learning incooperation game, IGA2 performed the best in the cooperation game (Figure 5.35).
In prisoner’s dilemma, Figure 5.34 shows that IGA6 is more consistent and has
the highest average payoff. This is the first time that IGA6 was considered as one
of the best performers within prisoner’s dilemma. This can be returned due to the
fact that IGA6 does not consider history propagation, which agrees with our results
from the previous chapter, where we showed that history propagation in self-play
affects the performance negatively.

102. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
83
IGA variations in self−play (all games)
3.6
Average final payoff
3.4
3.2
3
2.8
2.6
2.4
2.2
Basic IGA
IGA 2
IGA 3
IGA 4
IGA 5
IGA 6
Figure 5.33: Effect of variations on IGA on final payoffs in self-play (all games).
5.3.3
The effect of human input quality on interactive genetic algorithms
Against Giga-Wolf
We can see that, overall games, the performance with acceptable human input is
much better than unacceptable human input (Figure 5.38). An improvement in
convergence in various games is seen in Figures 5.43 and 5.44.
Recall that our model of an acceptable human input for the game chicken was to
motivate bullying. Figure 5.41 shows that both input types produce similar average
payoffs, but the unacceptable input is more consistent. An explaination to this
would be that experimenting ”swerving” with GIGA-WoLF in the beginning, made
the algorithm realize that it is potentially a not convenient solution if the other
algorithm was ”bullying”. The algorithm with acceptable input was even able to
motivate the GIGA-WoLF to swerve with it (mutual swerving) at one point of the
time.
Against Q-learning
On average, it is prefered to use acceptable human input (Figure 5.45). An unacceptable input gives an inconsistent reputation and confuses Q-learning. Therefore

103. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
84
IGA variations in self−play in Cooperation game
IGA variations in self−play in prisoners dilemma
4
3
Average final payoff
Average final payoff
3.8
2.5
2
3.6
3.4
3.2
3
2.8
1.5
Basic IGA
IGA 2
IGA 3
IGA 4
IGA 5
Basic IGA
IGA 6
Figure 5.34: Effect of variations on IGA
on final payoffs in self-play in prisoner’s
dilemma.
IGA 2
IGA 3
IGA 4
IGA 5
IGA 6
Figure 5.35: Effect of variations on IGA
on final payoffs in self-play in a cooperation game.
IGA variations in self−play in Chicken game
IGA variations in self−play in Shapleys game
0.45
7
Average final payoff
Average final payoff
0.4
6
5
4
0.35
0.3
0.25
0.2
3
0.15
2
Basic IGA
IGA 2
IGA 3
IGA 4
IGA 5
IGA 6
Figure 5.36: Effect of variations on IGA
on final payoffs in self-play in chicken
game.
Basic IGA
IGA 2
IGA 3
IGA 4
IGA 5
IGA 6
Figure 5.37: Effect of variations on IGA
on final payoffs in self-play in shapley’s
game.
the algorithm is unable to achieve mutual cooperation, or even exploit Q-learning.
This agrees with the results within individual games (Figures 5.46- 5.50).
Self play
As was the case in previous results, overall performance in self play is much better
with acceptable (figure 5.51). Figure 5.54 shows yet another unexplainable result in
chicken, although the algorithm is encouraged to bully using the acceptable human
input, it is able to reach the swerving solution with more consistency.

104. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
85
IGA input quality vs. GIGA−WoLF (all games)
3.08
Average final payoff
3.06
3.04
3.02
3
2.98
2.96
2.94
2.92
2.9
2.88
Acceptable human input
Unacceptable human input
Figure 5.38: Human input quality and its effect on final payoffs of IGA against
GIGA-WoLF (all games).
IGA input quality vs. GIGA−WoLF in prisoners dilemma
IGA input quality vs. GIGA−WoLF in Cooperation game
4
1
3.95
3.9
Average final payoff
Average final payoff
0.95
0.9
0.85
0.8
3.85
3.8
3.75
3.7
3.65
3.6
3.55
0.75
3.5
Acceptable human input
Unacceptable human input
Figure 5.39: Human input quality and its
effect on final payoffs of IGA vs. GIGAWoLF in prisoner’s dilemma.
Acceptable human input
Figure 5.40: Human input quality and its
effect on final payoffs of IGA vs. GIGAWoLF in a cooperation game.
IGA input quality vs. GIGA−WoLF in Chicken game
IGA input quality vs. GIGA−WoLF in Shapleys game
7
0.4
6.95
0.35
6.9
Average final payoff
Average final payoff
Unacceptable human input
6.85
6.8
6.75
6.7
0.3
0.25
0.2
0.15
0.1
6.65
0.05
6.6
Acceptable human input
Unacceptable human input
Figure 5.41: Human input quality and its
effect on final payoffs of IGA vs. GIGAWoLF in chicken game.
Acceptable human input
Unacceptable human input
Figure 5.42: Human input quality and its
effect on final payoffs of IGA vs. GIGAWoLF in shapley’s game.

105. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
86
IGA input quality vs. GIGA−Wolf in prisoners dilemma
Average payoff per generation
1.1
1
0.9
0.8
0.7
Acceptable human input
Unacceptable human input
0.6
0.5
0
20
40
60
80
100
Number of generations
Figure 5.43: Human input quality and its effect on IGA vs. GIGA-WoLF in prisoners dilemma (Average payoff per generation).
IGA input quality vs. GIGA−Wolf in Cooperation game
Average payoff per generation
4
3.5
3
2.5
Acceptable human input
Unacceptable human input
2
1.5
0
20
40
60
80
100
Number of generations
Figure 5.44: Effect of human input quality and its effect on IGA against GIGAWoLF in cooperation (Average payoff per generation).
IGA input quality vs. Q−learning (all games)
3.2
Average final payoff
3
2.8
2.6
2.4
2.2
2
Acceptable human input
Unacceptable human input
Figure 5.45: Human input quality and its effect on final payoffs of IGA vs. Qlearning (all games).

106. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
87
IGA input quality vs. GIGA−Wolf in prisoners dilemma
Average payoff per generation
3
2.5
2
1.5
1
Acceptable human input
Unacceptable human input
0.5
0
0
20
40
60
80
100
Number of generations
Figure 5.46: Human input quality and its effect on final payoffs of IGA vs. Qlearning in prisoners dillema (per generation).
IGA input quality vs. Q−learning in prisoners dilemma
IGA input quality vs. Q−learning in Cooperation game
4
3
3.8
2.8
Average final payoff
Average final payoff
3.6
2.6
2.4
2.2
2
1.8
1.6
3.4
3.2
3
2.8
2.6
2.4
2.2
1.4
2
1.2
Acceptable human input
Unacceptable human input
Figure 5.47: Human input quality and its
effect on final payoffs of IGA vs. Qlearning in prisoner’s dilemma.
Acceptable human input
Unacceptable human input
Figure 5.48: Human input quality and its
effect on final payoffs of IGA vs. Qlearning in a cooperation game.
IGA input quality vs. Q−learning in Chicken game
IGA input quality vs. Q−learning in Shapleys game
0.4
6
0.35
Average final payoff
Average final payoff
5.5
5
4.5
4
0.3
0.25
0.2
0.15
0.1
3.5
0.05
3
0
Acceptable human input
Unacceptable human input
Figure 5.49: Human input quality and its
effect on final payoffs of IGA vs. Qlearning in chicken game.
Acceptable human input
Unacceptable human input
Figure 5.50: Human input quality and its
effect on final payoffs of IGA vs. Qlearning in shapley’s game.

107. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
88
IGA input quality in self−play (all games)
3.2
3.1
Average final payoff
3
2.9
2.8
2.7
2.6
2.5
2.4
2.3
2.2
Acceptable human input
Unacceptable human input
Figure 5.51: Human input quality and its effect on final payoffs of IGA in self-play
(all games).
IGA input quality in self−play in prisoners dilemma
IGA input quality in self−play in Cooperation game
4
3.8
2.6
Average final payoff
Average final payoff
2.8
2.4
2.2
3.6
3.4
3.2
3
2.8
2
2.6
1.8
Acceptable human input
2.4
Unacceptable human input
Figure 5.52: Human input quality and its
effect on final payoffs of IGA in self-play
in prisoner’s dilemma.
Acceptable human input
Unacceptable human input
Figure 5.53: Human input quality and its
effect on final payoffs of IGA in self-play
in a cooperation game.
IGA input quality in self−play in Chicken game
IGA input quality in self−play in Shapleys game
0.4
7
6.5
0.38
Average final payoff
Average final payoff
6
5.5
5
4.5
4
3.5
0.36
0.34
0.32
0.3
0.28
3
0.26
2.5
2
Acceptable human input
Unacceptable human input
Figure 5.54: Human input quality and its
effect on final payoffs of IGA in self-play
in chicken game.
0.24
Acceptable human input
Unacceptable human input
Figure 5.55: Human input quality and its
effect on final payoffs of IGA in self-play
in shapley’s game.

108. CHAPTER 5. INTERACTIVE GENETIC ALGORITHMS
5.4
89
Conclusions
In this chapter, we described a framework for using human input to enhance the
performance of GAs. Through this framework, we tested different variations of
how human input can be handles, as well as experimented with different quality
cases of simulated human input. These experiments was in order to show how
variation in human input affects the performance of GA. From these results we
reached several conclusions, which can be summarized as following:
• Human input, even though it may not enhance the final payoff in all the
situations, it shows consistency per several iterations.
• Variations of IGA performed differently within different games and against
different opponents. Fitness that propagates through generations (propagation of history) is not always the best option. Further investigation about
balancing how previous and current payoffs affects the evaluation of the
chromosomes can be taken into consideration as future work.
• Human input quality is variable over different games and opponents. In our
simulations, our knowledge of the games and the opponents contributed into
the effectiveness of the human input. This shows that an expert human will
enhance the performance of an IGA more than a novice.
In the next chapter, we discuss the usage of basic IGA on a larger scale version
of the prisoner’s dilemma in order to discuss how well IGA performance propagates.

109. CHAPTER
6
IGA in N-player matrix games
To better explore the effectiveness of our methodology in more complex systems,
we repeated our experiments in a three-player prisoner’s dilemma game. In doing
so, we compare the performance of GA with dynamic mutation and a stopping
condition versus basic IGA. We also analyze the effect of the quality of human
input on IGA in this game. We first describe the N-player prisoner’s dilemma.
Note that out focus is on the iterative N-player prisoner’s dilemma (NIPD) and not
the one-shot game.
6.1
N-player prisoner’s dilemma
N-player dilemmas provide a formal representation of many real world social dilemmas [23], including power markets [63]. In the n-player prisoner’s dilemma, also
known as the Tragedy of the Common (Hardin, 1968), a land (the commons) is
freely available for farmers to use for grazing cattle. For any individual farmer,
90

110. CHAPTER 6. IGA IN N-PLAYER MATRIX GAMES
91
Figure 6.1: Payoff matrix of the 3-player prisoner’s dilemma.
it is advantageous to use this resource rather than their own land. However, if all
farmers adopt the same reasoning, the commons will be over-used and soon will be
of no use to any of the participants, resulting in an outcome that is undesirable for
all farmers. The payoff matrix for a three-player variation of this game is shown in
Figure 6.1.
In this game, there is a linear relationship between the fraction of cooperators
and the utility received by a game participant (Figure 6.2). Importantly, the payoff
received for a defection is higher than for a cooperation. The utility for defection
dominates the payoff for cooperation in all cases.
Yao and Darwen [6] were among the first to use an evolutionary approach for
the NIPD. In their initial work, they showed that when the number of players in an
NIPD game increases, it becomes more difficult for cooperation to emerge. This is
mainly due to the fact that a player is unable to clearly distinguish who the defectors and who the cooperators are. In the iterative prisoner’s dilemma (IPD) game,
a player can easily reciprocate against a defector in a one-to-one situation, and
therefore discourage defection. However, in the NIPD, retaliation against a defector means punishment to everyone else in the game, including the cooperators.

111. CHAPTER 6. IGA IN N-PLAYER MATRIX GAMES
92
Figure 6.2: Relationship between the fraction of cooperators and the utility received by a game participant.
6.2
Strategy representation
We have decided to adopt the representation of strategies developed by Yao and
Darwen [6] as it is simpler and easier to implement than other techniques. Under
this representation, a history of l rounds for an agent can be represented as the
combination of the following:
• l bits to represent the agent’s l previous actions.
• l * log2 N bits to represent the number of cooperators in the previous l rounds
among the agent’s N − 1 group members, where N is the group size.
In our representation of the chromosome, ‘1’ indicates a defection and ‘0’ a cooperation. In our implementation, we have limited the number of previous actions
in memory to three (i.e. l = 3). In the case of a society of N=4 agents, the history
for an agent would therefore be 3 + 3 * log2 4 = 9 bits long based on the above
representation scheme. For example, an agent in our NIPD model could have a
history as follows: 110 11 01 10. Here, the first three bits from the left are the
agent’s previous three actions. From this we can see that the agent defected in the

112. CHAPTER 6. IGA IN N-PLAYER MATRIX GAMES
93
Figure 6.3: Final payoffs of selected opponents in 3-player prisoner’s dilemma.
last two rounds and cooperated the round before that. The two-bit sets after the
first three bits represent the number of cooperators in the last three rounds from
the agent’s group members. This agent’s history indicates that there were 3, 1 and
2 cooperators in the agent’s group in the last three rounds. In order to see if our
experiments agree with performance of previous work, we studied the performance
of GIGA-WoLF and Q-Learning in 3-player prisoner’s dilemma (Figure 6.3). This
agrees with results presented in previous work, especially when related to the performance of Q-Learning [9], [46], [76].
6.3
Human input
In this game, we define acceptable human input as follows: If all agents cooperated
in the previous round, then cooperate; otherwise defect. On the other hand, the unacceptable input defects if the other two players cooperated in the previous round;
otherwise, it cooperates. This definition of acceptable and unacceptable was deter-

113. CHAPTER 6. IGA IN N-PLAYER MATRIX GAMES
94
mined as a first hypothesis, though it is not successful under certain conditions.
6.4
Results and analysis
Figure 6.4 shows a very vast potential for cooperation in different variations of the
GA in self-play. We can see that human input that encourages cooperation can lead
to direct cooperation. In case of an input that encourages defection, the algorithms
maybe able to learn fast enough to reach cooperation, but under certain instances,
mutual defection may prevail (as the algorithms follow the suggestions from the
human input).
Figure 6.5 shows the results in the situation where we have two GA agents in
the presence of GIGA-WoLF as the third agent. We observe no major differences
in terms of the final payoffs.
In the three variations of GA, the algorithms were not able to conform to cooperation (except within certain iterations), which is why the final payoff represented
leans towards the defection case. This can be due to the fact that the algorithms
use a more complex structure to represent the world. Thus, it may need a longer of
period of time in order to learn to cooperate (but this hypothesis was not verified
over a longer period of time). Instead, it converges to what may seem easier (defection). The human input (acceptable, which encourages cooperation), can lead
to a successful cooperation, but at the same time, it may encourage other agents to
retaliate (which happens most of the time).
Figure 6.6 conforms with what we expected in the case in which IGA interacts
with two GIGA-WoLF agents. The “unaccpetable” human input performed the
worse, as GIGA-WoLF learns to defect as fast as possible. Thus, unacceptable
human input suggests cooperation in this case, which leads to a slower convergence
to defection from the GA side.

114. CHAPTER 6. IGA IN N-PLAYER MATRIX GAMES
95
IGA in complete self−play
6
Average final payoff
5.5
5
4.5
4
3.5
3
2.5
2
1.5
No human input
Acceptable human input Unacceptable human input
Figure 6.4: Effect of human input on the performance of GA in the 3-player prisoner’s dilemma in self-play.
IGA vs. 1−player IGA and 1−player GIGA−WoLF
4.5
Average final payoff
4
3.5
3
2.5
2
1.5
1
0.5
No human input
Acceptable human input Unacceptable human input
Figure 6.5: Effect of human input on the performance of GA in the 3-player prisoner’s dilemma with 1-player as GIGA-WoLF and 1-player in self-play.
In case of the presence of a Q-learning agent (Figure 6.7), we notice a more
consistency within the final payoffs achieved. It is noticeable as well that the GA
with its different variations is able to converge easily with the existence of Qlearning. GA is sometimes even able to easily exploit the Q-learning agent, which
mainly occurs in the presence of a human input that encourages defection under
certain situations “unacceptable human input”. We can see also a major improvement in the performance of GA in figure 6.8, which shows the results in the presence of two Q-learning agents. This shows that GA with acceptable human input
establishes a reputation strong enough to lead Q-learning agents to cooperate.

115. CHAPTER 6. IGA IN N-PLAYER MATRIX GAMES
96
IGA vs. 2−players GIGA−WoLF
1.99
Average final payoff
1.98
1.97
1.96
1.95
1.94
1.93
1.92
1.91
1.9
No human input
Acceptable human input Unacceptable human input
Figure 6.6: Effect of human input on the performance of GA in 3-player prisoner’s
dilemma with 2-players as GIGA-WoLF.
IGA vs. 1−player IGA and 1−player Q−learning
5.6
Average final payoff
5.5
5.4
5.3
5.2
5.1
5
4.9
4.8
No human input
Acceptable human input Unacceptable human input
Figure 6.7: Effect of human input on the performance of GA in 3-player prisoner’s
dilemma with 1-player as Q-learning and 1-player in self-play.
A situation that is quiet interesting is when we have three heterogeneous agents
(one representing GA, Q-learning and GIGA-WoLF). Cooperation is not the ideal
method in case of the presence of GIGA-WoLF as an agent in the game (Figure 6.9). If our algrithm is directed to defect (“Unacceptable human input”), GIGAWoLF and GA can exploit Q-learning (in certain situations), gaining higher payoff
than going to cooperation.

116. CHAPTER 6. IGA IN N-PLAYER MATRIX GAMES
97
IGA vs. 2−players Q−learning
Average final payoff
6
5.5
5
4.5
4
No human input
Acceptable human input Unacceptable human input
Figure 6.8: Effect of human input on the performance of GA in 3-player prisoner’s
dilemma with 2-players as Q-learning.
IGA vs. 1−player GIGA−WoLF and 1−player Q−learning
5
Average final payoff
4.5
4
3.5
3
2.5
2
1.5
No human input
Acceptable human input Unacceptable human input
Figure 6.9: Effect of human input on the performance of GA in 3-player prisoner’s
dilemma with 1-player as Q-learning and 1-player as GIGA-WoLF.
6.5
Conclusions
A trend that was noticed and applies for almost for all the results within the following section can be summarized within the following:
• A more complex human input simulator (or in reality a more experienced
human) is required for more complex environments (Figures 6.3- 6.9).
• GA can adapt within larger environments (even without human interaction)
in comparison to other tested opponents.

117. CHAPTER 6. IGA IN N-PLAYER MATRIX GAMES
98
• The existence of a wider variety of opponents may lead to degradation in
performance, especially with the presence of non-suitable human input.

118. CHAPTER
7
Conclusions and Future work
7.1
Conclusions
In this thesis, we discussed and presented the results regarding the usage of interactive genetic algorithms as a learning mechanism in repeated games. We conducted
several sets of experiments in order to discover the applicability of using genetic algorithms within multi-agent systems (more specifically in repeated matrix games),
and how human input may affect its performance. Our evaluation was mainly based
on the analysis of the final payoffs rewarded, the learning rate (average payoff per
generation) and the population generated through the learning process. Our experiments were done on four different type of two-player matrix games, and a 3-player
version of the prisoner’s dilemma. The experiments were conducted in the presence of several opponents. These opponents included GIGA-WoLF, Q-Learning
and also the presence of an identical algorithm.
We evaluated a number of variations of GAs, including:
99

119. CHAPTER 7. CONCLUSIONS AND FUTURE WORK
100
• Modifying the existing fitness function to be based on propagating history
from previous generations.
• Using a stopping condition in which the algorithm stops evolving when the
fitness of the highest fitness chromosome stops changing.
• Updating the mutation rate over time based on the performance of a population within a generation (dynamic mutation).
• Merging the stopping condition with dynamic mutation.
Our results showed that the use of history propagation decreases the randomness in the population generated, and therefore decreases the variations in the average payoff the algorithm achieves per generation. This can be very is particularly
visible in self play, where, although the algorithm does not always achieve better payoffs, the average payoff per generation and the chromosome population are
more consistent.
We also studied the effect of having both the stopping condition and the dynamic mutation. Our results shows that, with the exception of Chicken, the use of
the stopping condition can drive the algorithm to converge pre-maturely to a local
optimal point. Dynamic mutation, however, helps the algorithm maintain a certain
amount of exploration, though in certain cases, such as against GIGA-WoLF, dynamic mutation without a stopping condition can lead to instability in the learning
trend of the algorithm.
After studying the different variations that have been previously suggested in
order to enhance the performance of the genetic algorithm in dynamic environments, we analyzed the idea of how human input can benefit and improve the performance of genetic algorithms in repeated matrix games.
In the beginning, we implemented a framework that allows the human to give
feedback to the dynamic GA with stopping condition (which we chose as our base-

120. CHAPTER 7. CONCLUSIONS AND FUTURE WORK
101
line). Through this framework, we desired to enhance the performance of the algorithm while requiring minimal human interaction.
Our results showed that human input provided to the GA using our framework
led to an improvement in the GAs perforamcne in a number of games, inlcuding prisoner’s dilemma and the cooperation game, given effective human input.
Furthermore, the simulated human input we used improved the GAs performance
against opponents with a slower learning rate (such as Q-learning), as it motivates
the opponents by conveying a better reputation.
In other games, such as Chicken, we had to experiment to know what can represent an effective human input. This turned out to be the inverse of what we
expected. We expected that a bullying input would enhance its performance. However, in contrast to our expectations, having a “swerve” input enhances the performance effectively. A reason for this can be that the human input helps to “deceive”
the opponent into swerving, then it bullies it by the end, but no major enhancement
in the performance can be noticed in this case.
In addition to the previous experiments, we tested the effect of different handling techniques of the human input and how they effect the performance of the
GA against its opponents. The different techniques in handling the human input
can be summarized as following:
• The basic handling technique, were we discover the bits with the highest
entropy within the population, then request the human feedback regarding
the history related to these bits.
• The basic handling technique with modified mutation rates. This study shows
us the effect of varying the mutation rate and how it can affect the results.
The results shows us that specific changes in the mutation rates used can enhance the performance in certain situations. This helps us conclude that a

121. CHAPTER 7. CONCLUSIONS AND FUTURE WORK
102
human user can potentially be used to specify the mutation rate (according
to the human’s knowledge of the environment) to enhance the performance
of IGA.
• Incorporating what we call variance in order to take into consideration the
performance of each chromosome with respect to the overall population.
This helps us to overcome actions that leads to a decrease in fitness in chromosomes with lower fitness values within the population.
Results showed a vast difference in the performance of the algorithms where
some of the algorithms perform better in certain situations, but not in others. Overall, the basic IGA had the highest performance. This led us to follow the basic
handling technique in our three-player experiment.
Finally we studied the performance of GAs in a three-player environment. This
study was conducted to determine how well our framework (and GAs in general)
perform on a larger scale. These experiments, were performed in the 3-player prisoner’s dilemma world, showed that GAs performance depends on the opponents,
and the quality of human input. Also, we showed that a GA with dynamic mutation
and stopping condition performs well in this game.
From the previous discussions, we can conclude the following:
• GAs are an effective learning technique in static systems.
• GAs, when improved through implementing a dynamic mutation technique
(where mutation rate changes depending on previous performance), can adapt
well enough in dynamic systems, except in the presence of other intelligent
agents of slower learning rate, such as Q-learning.
• Effective human input improves the performance of GAs in multi-agent (dynamic systems in general). Unacceptable input on the otherhand decreases

122. CHAPTER 7. CONCLUSIONS AND FUTURE WORK
103
the performance, though the IGA can still learn acceptable strategies. In
general, the more effective human input is, the better the performance of the
algorithm.
• The studied forms of GAs and IGAs maintains its effectiveness in environments with higher numbers of players.
These results confirm our initial hypothesis that we derived through our literature review, which enforces the idea that GAs, can be used as a dynamic learning
technique. Also they motivate us to experiment more complex means of handling
the human input, as well as studying GAs in more complex multi-agent systems.
7.2
Future work
During the course of this research, we discovered a number of areas that deserve
further investigation. This research area is vast and may cover other potential ideas.
However, we highlight the areas of potential future work related to the topics discussed:
1. Test the effectiveness of interactive genetic algorithms in more complex environments against a wider range of opponents.
2. Experiment with other techniques used for improving the adaptability of genetic algorithms within dynamic systems, including:
(a) Maintaining multiple interactive populations through the generations,
and then maintaining the population that exhibits the best performance.
The population is then compared to every new population generated
through any of the following generations in order to choose the strategies with the best performance from one of these populations [55].

123. CHAPTER 7. CONCLUSIONS AND FUTURE WORK
104
(b) Varying the size of the population depending on the rate of exploration
we want to exhibit within the algorithm over time [82].
3. Develop more complex techniques to overcome the effect of unacceptable
human input without degrading the performance of the algorithm.
4. Explore the effectiveness of human input with various interaction rates. This
is in order to reach the most effective rate of interaction.
5. Study the use of actual human input on GAs and discuss their effectiveness
using participants with various backgrounds.

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