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How Cooperation Arises in Evolving Social Networks

This study explores how cooperation emerges within evolving social networks using an agent-based model based on the Prisoner's Dilemma. Each agent adopts a cooperation strategy, interacting with neighbors and updating link weights based on payoffs from these interactions. The model reveals that networks with a probability of breaking ties tend to converge towards cooperation. Factors influencing the speed of convergence include tie-breaking probabilities, network size, and link density. Implications suggest that social punishment can effectively promote cooperation in intelligent agents.

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How Cooperation Arises in Evolving Social Networks

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  1. How Cooperation Arises in Evolving Social Networks An Agent-Based Model by Ariana Strandburg-Peshkin

  2. The Prisoner’s Dilemma

  3. Networks

  4. Evolving Networks Network Structure Network Dynamics

  5. The Model Each agent has… A strategy - probability of cooperating (0 - 1) Links to other agents (“neighbors”) Agent 1 Payoffs C D C Agent 2 Payoffs Agents in a network play prisoners’ dilemma with all their “neighbors” D

  6. An Agent’s Universe Strategy Payoff Weight Strategy Payoff Weight Weight Strategy Payoff Strategy Payoff

  7. Each Iteration… Play all neighbors, sum up total payoff, and update link weights Find most successful neighbor Replenish ties broken Break ties with worst enemy Move toward most successful strategy

  8. Results Break ties --> Cooperate No breaking ties --> Defect

  9. Why? Links Strategy

  10. Speed of Convergence • Parameters Explored: • Probability of Breaking Ties • Network Size (# agents) • Network Density (# links)

  11. Results - Summary • Networks with any probability of breaking ties eventually converge on cooperation • The speed of convergence depends on: • Probability of breaking ties (> = faster) • Size of network (> = slower) • # of Links (> = slower)

  12. Implications / Limitations • Social “punishment” (by breaking ties) is effective in promoting cooperation • Model requires that agents be intelligent and knowledgeable about one another • Keep track of neighbors / weights • Know neighbors’ strategies and payoffs • No complex strategies (e.g. Tit-For-Tat)

  13. Other Cool Things To Look At • Different Payoff Schemes • More complex strategies • Network Structure • How is it affected by the game played? • Cost of keeping so many ties? Cost of making and breaking ties? • Robustness

  14. Sources • Abramson, Guillermo, and Marcelo Kuperman. "Social games in a social network." Physical Review E 63.3 (2001). 10 Apr. 2008 <http://arxiv.org/abs/nlin.AO/0010015>. • Calderon, Juan. "Games on Evolving Networks." Complex Systems Summer School at Santa Fe Institute. 18 Mar. 2008 <http://www.google.com/url?sa=t&ct=res&cd=1&url=http%3A%2F%2Fwww.santafe.edu%2Fevents%2Fworkshops%2Fimages%2F6%2F6e%2FSf_csss06_calderon_et_al.pdf&ei=nbwcSI2XEJf4eZXdsOgL&usg=AFQjCNHlQ5sdWKoe37oCPMEvjLY4_t1neQ&sig2=ZGkomgzCTy37xNR9nb52Ew&gt;. • Hanaki, Nobuyuki, Alexander Peterhansl, Peter Dodds, and Duncan Watts. "Cooperation in Evolving Social Networks." Management Science 53.7 (2007): 1036-1050. 19 Mar. 2008 <http://www.google.com/url?sa=t&ct=res&cd=1&url=http%3A%2F%2Fcdg.columbia.edu%2Fuploads%2Fpapers%2Fhanaki_cooperation.pdf&ei=4JQaSLvBFJDqgwTQk6S4Dg&usg=AFQjCNF7aLFpLvwGQQdFQEtvy4BStmta4g&sig2=WSUWZyRpQRPt-9neDtyn-Q&gt;. • Holme, Peter, Ala Trusina, Beon Jun Kim, and Petter Minnhagen. "Prisoners' Dilemma in Real-World Acquaintance Networks: Spikes and Quasiequilibria Induced by the Interplay Between Structure and Dynamics." Physical Review E 68 (2003). 10 Apr. 2008 <http://arxiv.org/abs/cond-mat?papernum=0308392>. • Ostrom, Elinor. "Collective Action and the Evolution of Social Norms." The Journal of Economic Perspectives 14.3 (2000): 137-158.

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