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

1. RISK IN SOCIAL NETWORKS:Network Influence & Selection on Minority Games among Competitive Choices Moses A. Boudourides University of Patras, Greece mboudour@upatras.gr

2. The DBO TheoryDesires-Beliefs-Opportunities (Hedstrom’s social mechanism)

3. DBO in C.S. Peirce’s Scheme of Categories • 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).

4. The 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.

5. Risk & 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.

6. 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.

7. 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)

8. A Universal Phase Transition

9. Our Context: COMPETITIVE TECHNOLOGIES • 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.

10. Our Context: NETWORK INFLUENCE • 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 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. • 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).

11. Our Context: NETWORK SELECTION • 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.

12. Results on Network Influence N = 225 ( = 15 x 15 agents) m = 3 p = 0.30 iterations = 200

13. 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

14. Results on Network Influence (continued) 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

15. Results on Network Influence (continued) N = 225 ( = 15 x 15 agents), m = 3 p = 0.30, p0 = p1 = 0.20 iterations = 200

16. Results on Network Influence (continued) N = 225 ( = 15 x 15 agents) p = 0.30 iterations = 10000 T = 5000 (iterations from 5001 to 10000)

17. N = 225 m = 3 p = 0.3

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

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

20. Results on Network Selection

21. Future Research Directions • 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).