How Cooperation Arises in Evolving Social Networks An Agent-Based Model by Ariana Strandburg-Peshkin.
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How Cooperation Arises in Evolving Social Networks An Agent-Based Model by Ariana Strandburg-Peshkin The Prisoner’s Dilemma Networks Evolving Networks Network Structure Network Dynamics The Model Each agent has… A strategy - probability of cooperating (0 - 1) Links to other agents (“neighbors”) Agents in a network play prisoners’ dilemma with all their “neighbors” Agent 2 Payoffs QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. Agent 1 Payoffs C D C D 2,2 0,3 3,0 1,1 An Agent’s Universe Strategy Payoff Weight Strategy Payoff Strategy Weight Weight Payoff Strategy Payoff 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 Results QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. Break ties --> Cooperate No breaking ties --> Defect Links Why? QuickTime™ and QuickTime™ and aa QuickTime™ TIFF (Uncompressed) decompressor TIFF(Uncompressed) (Uncompressed) decompressor TIFF are are needed needed to to see see this this picture. picture. are Strategy Speed of Convergence QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. Parameters Explored: Probability of Breaking Ties Network Size (# agents) Network Density (# links) Time to Conv erge vs. Probability of Breaking Ties (25 Agents, 50 Links) 180000 Iterations until Average Strategy = .99 160000 140000 120000 100000 80000 60000 40000 20000 0 0 0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 Probabilit y of Breaking Ties 0 .7 0 .8 0 .9 1 Time to Conv erge vs. Probability of Breaking Ties Iterations until Average Strategy = .99 1000000 100000 10000 - y = 5 2 7 1 .2 x 0.7021 1000 0 .0 1 0 .1 Probabilit y of Breaking Ties 1 Time to Conv erge vs. Probability of Breaking Ties Time to Reach Average Strategy = .99 (Iterations) 100000 10000 1000 0 .0 1 0 .1 Probabilit y of Breaking Ties 1 Time to Conv erge vs. Network Size (Network Density = 2 Links / Iterations to Average Strategy = .99 100000 80000 60000 40000 20000 0 10 110 210 410 310 A gent s 510 610 710 Time to Conv erge vs. Number of Links Convergence Speed (Iterations to .99) 25000 20000 15000 10000 5000 0 0 20 40 60 80 100 Number of Links (A gents = 25) 120 140 160 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) 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) 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 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%2Fe 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): 1036-1050. 19 Mar. 2008 <http://www.google.com/url?sa=t&ct=res&cd=1&url=http%3A%2F%2Fcdg.columbia.edu%2F 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 RealWorld 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.