Boudourides: Risk in Social Networks: Network Influence & Selection on Minority Games among Competitive Choice

Workshop on
Discourse Networks & Risk Policy
Konstanz, January 14-15, 2007
Risk in Networks:
Network Influence & Selection in
Minority Games
M.A. Boudourides
RISK IN SOCIAL NETWORKS:
Network Influence & Selection on
Minority Games among Competitive
Choices
Moses A. Boudourides
University of Patras, Greece
mboudour@upatras.gr

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
The DBO Theory
Desires-Beliefs-Opportunities
(Hedstrom’s social mechanism)

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
DBO in C.S. Peirce’s Scheme of Categories
n  Firstness: DBO performed
individually (essential ontology).
n  Secondness: DBO shaped in a
network (relational ontology).
n  Thirdness: DBO shaped in a
network but mediated or
regulated through an exogenous
‘third’-type reference like a
normative or utilitarian principle
or interpretive signification
(semantic ontology).

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
The Pragmatics of Risk
n  Reality imposes constraints or even falsifies
intentions.
n  Risk as an indicator of structural uncertainty and
ignorance on the real outcome of natural or social
processes.
n  Risk provokes innovative desires: e.g., the role of
marginal groups in Science & Technology.
n  Risk preempts beliefs: e.g., the precautionary
principle.
n  Risk mitigates opportunities: e.g., institutional
frames, policy discourses, movements impact.

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
Risk & Social Simulation
n  Need of experimentation in policy making.
n  Simulations provide a ‘test and develop’
background.
n  Counterfactual scenarios expand intuition.
n  Simulated strategies provide useful resources
to realistic and rational intentions.
n  Network simulations formally schematize
social interaction.
n  Social choice in risky situations is not only a
problem of aggregation but it should
incorporate aspects of learning & adaptation.

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
Classic Minority Game
n  NOT a game-theoretic problem but
rather an adaptive agent-based
simulation.
n  El Farol bar attendance problem: Go
to bar (1) or stay at home (0)? [W. B.
Arthur, Increasing Returns and Path
Dependence in the Economy,
Economics, Cognition and Society
(Univ. of Michigan Press, 1994)]
n  In general: N agents (N is always odd),
each of which can make only one of two
moves: play “0" or play “1".
n  If most agents play 0, then those who
play 1 win, and vice-versa.
n  Each player remembers whether 0 or 1
won on each of the last m turns.
n  Strategies are rules mapping histories to
actions; each agent has s of them.
Agents keep track of how many times
each of their strategies would have won,
and uses the strategy with the best
record over the time it can remember.
Ties between strategies are broken
randomly or pseudo-randomly.

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
Books on Minority Games
n  Challet, D., Marsili, M., & Zhang, Y.-
C., Minority Games: Interacting
Agents in Financial Markets (Oxford,
2004)
n  Coolen, A,C.C., The Mathematical
Theory of Interacting Agents:
Statistical Mechanics of Interacting
Agents (Oxford, 2005)

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
A Universal Phase Transition

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
Our Context: COMPETITIVE TECHNOLOGIES
n  A decision problem with two mutually exclusive choices
(technologies to adopt):
n  Choice 0: Technology A – say a fossil-based energy
technology.
n  Choice 1: Technology B – say a clean renewable energy
technology.
n  Motivation: To maximize economic profit (spending less).
n  Assumptions:
n  When prices in technology A fall due to low demand, they
cost less than prices in technology B under high demand.
n  When prices in technology A rise due to high demand,
they cost more than prices in technology B under low
demand.

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
Our Context: NETWORK INFLUENCE
n  Agents are located on a square lattice with periodicity b.cs.
(More general social network topologies might be
considered.)
n  At each time step, the agents follow the usual rules of the
Minority Game, but they are given the extra opportunity to
modify their bets by social/network influence, after knowing
what their nearest neighbors will do in the same step.
n  For each agent i, there is a susceptibility coefficient pi !
[0,1] to be influenced by her neighbors in such a way that she
tries to be in the local minority:
n  If more than half of her neighbors choose one side, then she
will chose the other with probability pi, regardless of what her
best strategy says; but if half of the neighbors choose each
side, then she will decide in agreement with her best strategy.
n  Once all the agents have made their choice, they make their
moves simultaneously (Cellular Automata rules but
Interacting Particle Systems rules might be applied too).

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
Our Context: NETWORK SELECTION
n  Agents are influenced only by those of their neighbors who
perform best (in their history): Leaders and Followers.
n  The Minority Game with network influence (by leaders to
followers) is played at each time step (with full susceptibility).
n  Rating Links: If a leader’s influence is successful, then the
corresponding link gets one point (otherwise none).
n  Selecting/Deselecting Links: At certain time steps, for each
agent, the link with the lowest point is severed (randomly if
more than one such links) and a new link is created with the
closest successful agent who is not a neighbor (again
randomly if more than one such agents).
n  The initial location of agents is on a regular graph (such as a
square lattice or a cyclical lattice with even degree).
n  After a large number of iterations with intermittent selections/
deselections of links, the resulting network topology turns out
to be that of a scale-free network.

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
Results on Network Influence
N = 225 ( = 15 x 15 agents)
m = 3
p = 0.30
iterations = 200

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
Results on Network Influence (continued)
N = 225
( = 15 x 15 agents),
m = 2, 3, 4
iterations = 10000
T = 5000
(iterations from 5001
to 10000)
Crowding-
Anticrowding
Effects

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
PERSISTENT AGENTS
q  no strategy
q  never influenced but possibly influencing
n  0-Persistent, if always chooses 0 – percentage p0
n  1-Persistent, if always chooses 1 – percentage p1

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
N = 225 ( = 15 x 15 agents), m = 3
p = 0.30, p0 = p1 = 0.20
iterations = 200

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
N = 225
( = 15 x 15 agents)
p = 0.30
iterations = 10000
T = 5000
(iterations from 5001
to 10000)

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
N = 225
m = 3
p = 0.3

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
N = 225
m = 3
p = 0.3
p0 = p1
= 0.10

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
N = 225
m = 3
p = 0.3
p0 = p1
= 0.20

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
Results on Network Selection
0.0 0.5 1.0 1.5 2.0
-6-5-4-3-2-10
X1
X2

Workshop on
Risk in Networks:
Minority Games
M.A. Boudourides
Future Research Directions
n  Multi-Type Minority Games
n  Majority Games in Spatial Voting
n  Heterogeneity effects
n  Conflict partitions.
n  Incorporation of actors’ non-relational
dispositions and non-contextual ‘intentional’
strategies.
n  Inverse problems with real data: Statistical
models of hypothesis testing (e.g., ERG
models).

Boudourides: Risk in Social Networks: Network Influence & Selection on Minority Games among Competitive Choice

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