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

The Prisoner’s Dilemma

Networks

Evolving Networks Network Structure Network Dynamics

The Model 2, 20, 3 3, 01, 1 A strategy - probability of cooperating (0 - 1) Links to other agents (“neighbors”) Agents in a network play prisoners’ dilemma with all their “neighbors” Agent 1 Payoffs CD Agent 2 Payoffs D C Each agent has…

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

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

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

Why? Strategy Links

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

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) 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)

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) 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)

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 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

Sources Abramson, Guillermo, and Marcelo Kuperman. "Social games in a social network." Physical Review E 63.3 (2001). 10 Apr Calderon, Juan. "Games on Evolving Networks." Complex Systems Summer School at Santa Fe Institute. 18 Mar < vents%2Fworkshops%2Fimages%2F6%2F6e%2FSf_csss06_calderon_et_al.pdf&ei=nbwcSI2X EJf4eZXdsOgL&usg=AFQjCNHlQ5sdWKoe37oCPMEvjLY4_t1neQ&sig2=ZGkomgzCTy37x NR9nb52Ew>. Hanaki, Nobuyuki, Alexander Peterhansl, Peter Dodds, and Duncan Watts. "Cooperation in Evolving Social Networks." Management Science 53.7 (2007): Mar < uploads%2Fpapers%2Fhanaki_cooperation.pdf&ei=4JQaSLvBFJDqgwTQk6S4Dg&usg=AFQj CNF7aLFpLvwGQQdFQEtvy4BStmta4g&sig2=WSUWZyRpQRPt-9neDtyn-Q>. 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 Ostrom, Elinor. "Collective Action and the Evolution of Social Norms." The Journal of Economic Perspectives 14.3 (2000): Abramson, Guillermo, and Marcelo Kuperman. "Social games in a social network." Physical Review E 63.3 (2001). 10 Apr Calderon, Juan. "Games on Evolving Networks." Complex Systems Summer School at Santa Fe Institute. 18 Mar < vents%2Fworkshops%2Fimages%2F6%2F6e%2FSf_csss06_calderon_et_al.pdf&ei=nbwcSI2X EJf4eZXdsOgL&usg=AFQjCNHlQ5sdWKoe37oCPMEvjLY4_t1neQ&sig2=ZGkomgzCTy37x NR9nb52Ew>. Hanaki, Nobuyuki, Alexander Peterhansl, Peter Dodds, and Duncan Watts. "Cooperation in Evolving Social Networks." Management Science 53.7 (2007): Mar < uploads%2Fpapers%2Fhanaki_cooperation.pdf&ei=4JQaSLvBFJDqgwTQk6S4Dg&usg=AFQj CNF7aLFpLvwGQQdFQEtvy4BStmta4g&sig2=WSUWZyRpQRPt-9neDtyn-Q>. 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 Ostrom, Elinor. "Collective Action and the Evolution of Social Norms." The Journal of Economic Perspectives 14.3 (2000):