Workshop on Discourse Networks & Risk Policy Konstanz, January 14-15, 2007 Risk in Networks: Network Influence & Selection in Minority Games M.A. Boudourides

Workshop onDiscourse Networks & Risk PolicyKonstanz, January 14-15, 2007

Risk in Networks: Network Influence & Selection in Minority

Games M.A. Boudourides

RISK IN SOCIAL NETWORKS:RISK IN SOCIAL NETWORKS:Network Influence & Selection Network Influence & Selection on Minority Games among on Minority Games among Competitive ChoicesCompetitive Choices

Moses A. BoudouridesMoses A. BoudouridesUniversity of Patras, Greece

[email protected]



GamesM.A. Boudourides

The DBO TheoryThe DBO TheoryDesires-Beliefs-Desires-Beliefs-Opportunities (Hedstrom’s Opportunities (Hedstrom’s social mechanism)social mechanism)




DBO in C.S. Peirce’s Scheme of DBO in C.S. Peirce’s Scheme of CategoriesCategories Firstness: DBO performed

individually (essential ontology). Secondness: DBO shaped in a

network (relational ontology). 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).




The Pragmatics of RiskThe Pragmatics of Risk Reality imposes constraints or even falsifies

intentions. Risk as an indicator of structural uncertainty and

ignorance on the real outcome of natural or social processes.

Risk provokes innovative desires: e.g., the role of marginal groups in Science & Technology.

Risk preempts beliefs: e.g., the precautionary principle.

Risk mitigates opportunities: e.g., institutional frames, policy discourses, movements impact.




Risk & Social SimulationRisk & Social Simulation Need of experimentation in policy making. Simulations provide a ‘test and develop’

background. Counterfactual scenarios expand intuition. Simulated strategies provide useful resources

to realistic and rational intentions. Network simulations formally schematize

social interaction. Social choice in risky situations is not only a

problem of aggregation but it should incorporate aspects of learning & adaptation.




Classic Minority Game NOT a game-theoretic problem but

rather an adaptive agent-based simulation.

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)]

In general: N agents (N is always odd), each of which can make only one of two moves: play “0" or play “1".

If most agents play 0, then those who play 1 win, and vice-versa.

Each player remembers whether 0 or 1 won on each of the last m turns.

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.




Books on Minority Games

Challet, D., Marsili, M., & Zhang, Y.-C., Minority Games: Interacting Agents in Financial Markets (Oxford, 2004)

Coolen, A,C.C., The Mathematical Theory of Interacting Agents: Statistical Mechanics of Interacting Agents (Oxford, 2005)




A Universal Phase A Universal Phase TransitionTransition




Our Context: COMPETITIVE Our Context: COMPETITIVE TECHNOLOGIESTECHNOLOGIES

A decision problem with two mutually exclusive choices (technologies to adopt):

Choice 0: Technology A – say a fossil-based energy technology.

Choice 1: Technology B – say a clean renewable energy technology.

Motivation: To maximize economic profit (spending less). Assumptions: When prices in technology A fall due to low demand, they

cost less than prices in technology B under high demand. When prices in technology A rise due to high demand,

they cost more than prices in technology B under low demand.




Our Context: NETWORK Our Context: NETWORK INFLUENCEINFLUENCE Agents are located on a square lattice with periodicity b.cs.

(More general social network topologies might be considered.) 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.

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:

If more than half of her neighbors choose one side, then she will chose the other with probability p i, 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.

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).




Our Context: NETWORK Our Context: NETWORK SELECTIONSELECTION Agents are influenced only by those of their neighbors who

perform best (in their history): Leaders and Followers. The Minority Game with network influence (by leaders to

followers) is played at each time step (with full susceptibility). Rating Links: If a leader’s influence is successful, then the

corresponding link gets one point (otherwise none). 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).

The initial location of agents is on a regular graph (such as a square lattice or a cyclical lattice with even degree).

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.




Results on Network InfluenceResults on Network Influence

N = 225 ( = 15 x 15 agents) m = 3 p = 0.30 iterations = 200




Results on Network Influence Results on Network Influence (continued)(continued)

N = 225

( = 15 x 15 agents),

m = 2, 3, 4

iterations = 10000

T = 5000 (iterations from 5001

to 10000)

Crowding-Crowding-AnticrowdingAnticrowdingEffectsEffects





PERSISTENT AGENTS

no strategy

never influenced but possibly influencing

0-Persistent, if always chooses 0 – percentage p0

1-Persistent, if always chooses 1 – percentage p1




Results on Network Influence Results on Network Influence (continued)(continued)N = 225 ( = 15 x 15 agents), m = 3

p = 0.30, p0 = p1 = 0.20iterations = 200





N = 225

( = 15 x 15 agents)

p = 0.30

iterations = 10000

T = 5000 (iterations from 5001

to 10000)




N = 225m = 3p = 0.3




N = 225m = 3p = 0.3p0 = p1 = 0.10




N = 225m = 3p = 0.3p0 = p1 = 0.20




Results on Network SelectionResults on Network Selection

0.0 0.5 1.0 1.5 2.0

-6-5

-4-3

-2-1

0

X1

X2




Future Research Future Research DirectionsDirections Multi-Type Minority Games Majority Games in Spatial Voting Heterogeneity effects Conflict partitions. Incorporation of actors’ non-relational

dispositions and non-contextual ‘intentional’ strategies.

Inverse problems with real data: Statistical models of hypothesis testing (e.g., ERG models).

Documents

Workshop on Discourse Networks & Risk Policy Konstanz, January 14-15, 2007 Risk in Networks: Network Influence & Selection in Minority Games M.A. Boudourides