Social Decision Making and Rational Choice: Insight from Game Theory

1. Social Decision Making
&
Rational Choice
Insight from Game Theory
Hamed Abdi
PhD Student in Cognitive Science at ICBS

2. Decision Making
Decision Making is the process of identifying and
choosing alternatives based on the preferences
of the decision-maker.
Decision makers (or Agents) may be humans,
organizations, animals, robots or even genes.
Goals
Values
Norms
Beliefs
Desires
2

3. Decision Theory
Decision theory is concerned with the reasoning
underlying an agent’s choices.
Decision theory
An entity, usually an individual person, that is capable of deliberation and action
Normative
Descriptive
3
Logic
Reason

4. Decision Theory
Decision theory starting as early as the 17th
century with probabilistic theories of gambling
by Blaise Pascal and Pierre Fermat.
Consider an option that offers some n number
of quantifiable outcomes, {x1, … , xn} each with
some specified probability, {p1, … , pn},
respectively. The decision maker should
choose to maximize the expected value:
E[X] = σ1
𝑛
𝑝𝑗. 𝑥𝑗
4

5. St. Petersburg Paradox
5
𝐸 =
1
2
. 2 +
1
4
. 4 +
1
8
. 8 + … = ∞
Expected Utility Theory
Von Neumann–Morgenstern Utility

6. Rational Choice
Rational choice theory (RCT) is social physics or
sociophysics:
A search for universal mathematical laws to
explain social and economic phenomena in
terms of the behavior of their fundamental
particles, namely human decision makers.
6

7. 7
Rationality
Individual (single-agent behavior)
Maximized Reward
Ordinal
Utility
Certainty
Expected
Utility
Risk
subjective
expected
utility
Uncertainty
non-
expected
utility
Strategic
(small-group)
Game
Theory
Competitive
(large-group)
Arbitrage
Pricing
Theory

8. Properties of Environments
• Fully vs. Partially Observable
• Single agent vs. Multi agent
• Deterministic vs. Stochastic
• Episodic vs. Sequential (Markov)
• Static vs. Dynamic
• Discrete vs. Continuous
• Known vs. Unknown (Information)
• Symmetric vs. Asymmetric
8

9. Game Theory
Game Theory is the formal study of strategic
interaction. In a strategic setting the actions of
several agents are interdependent. Each agent’s
outcome depends not only on his actions, but
also on the actions of other agents.
Prediction Problem
9

10. Game Theory
Key elements of a game:
• Players: Who is interacting?
• Strategies: What are their options?
• Payoffs: What are their incentives?
• Information: What do they know?
• Rationality: How do they think?
10

11. Normal-Form Games
A normal form game is a triplet (N, S, u) with the
following properties:
• N: Finite set of players
• S: Set of pure strategy profiles
• u: Payoff function of players
11

12. Common Knowledge
All players know (N, S, u), and know that their
opponents know it, and know that their
opponents know that everyone knows, and so
on.
Rock-Paper-Scissors:
12
R P S
R 0,0 -1,1 1,-1
P 1,-1 0,0 -1,1
S -1,1 1,-1 0,0

13. Nash Equilibrium
A Nash equilibrium is a strategy profile with the
property that no player can benefit by deviating
from his corresponding strategy.
Nash equilibrium is a Conservative Decision.
13

14. Prisoner’s Dilemma Game
Simplest form (Symmetric) of the PDG is a game
described by the payoff matrix:
satisfying the following chain of inequalities:
T>R>P>S
14
Cooperate Defect
Cooperate R,R S,T
Defect T,S P,P

15. Prisoner’s Dilemma Game
Simplest form (Symmetric) of the PDG is a game
described by the payoff matrix:
satisfying the following chain of inequalities:
T>R>P>S
15
Cooperate Defect
Cooperate 2,2 0,5
Defect 5,0 1,1

16. Research Directions
• Social Reward (Punish)
• Competition, Cooperation, and Coordination
• Strategic Reasoning
Social Decision-Making: Insights from Game Theory and Neuroscience.
Alan G. Sanfey.
16

17. Ultimatum & Dictator (Trust) Game
17

18. Stag Hunt Game
The stag hunt is a game that describes a conflict
between safety and social cooperation.
Stag hunt is a game with two pure strategy Nash
equilibria. (Risk dominant & Payoff dominant)
18
Stag Hare
Stag 2,2 0,1
Hare 1,0 1,1

19. Other Games
Chicken Game
El Farol Bar Game (Problem)
Guess p of the Average
Public Goods Game
Signaling Game (Theory of Convention)
Pirate Game
19

20. Thanks for your attention
Any Question?