ABSTRACT
We study the evolution of cooperation in populations where individuals play prisoner's dilemma on a network. Every node of the network corresponds to an individual choosing whether to cooperate or defect in a repeated game. The players revise their actions by imitating those neighbors who have higher payoffs.
We show that when the interactions take place on graphs with large girth, cooperation is more likely to emerge. On the flip side, in graphs with many cycles of length 3 and 4, defection spreads more rapidly.
One of the key ideas of our analysis is that our dynamics can be seen as a perturbation of the voter model. We write the transition kernel of the corresponding Markov chain in terms of the pairwise correlations in the voter model. We analyze the pairwise correlation and show that in graphs with relatively large girth, cooperators cluster and help each other.
- D. Aldous and J. A. Fill. Reversible Markov Chains and Random Walks on Graphs. 1994.Google Scholar
- C. Alós-Ferrer and S. Weidenholzer. Contagion and efficiency. Journal of Economic Theory, 143(1):251--274, 2008.Google ScholarCross Ref
- P. Donnelly and D. Welsh. Finite particle systems and infection models. Mathematical Proceedings of the Cambridge Philosophical Society, 94:167--182, 1983.Google ScholarCross Ref
- G. Ellison. Cooperation in the prisoner's dilemma with anonymous random matching. The Review of Economic Studies, 61(3):567--588, 1994.Google ScholarCross Ref
- I. Eshel, L. Samuelson, and A. Shaked. Altruists, egoists, and hooligans in a local interaction model. The American Economic Review, 88(1):157--179, 1998.Google Scholar
- I. Eshel, E. Sansone, and A. Shaked. Evolutionary dynamics of populations with a local interaction structure, mimeo, 1996.Google Scholar
- D. Fudenberg, D. Levine, and E. Maskin. The folk theorem with imperfect public information. Econometrica, 62(5):997--1039, 1994.Google ScholarCross Ref
- D. Fundenberg and E. Maskin. Evolution and cooperation in noisy repeated games. The American Economic Review, 8(2):274--279, 1990.Google Scholar
- T. M. Liggett. Interacting Particle Systems. Springer, 2005.Google ScholarCross Ref
- M. A. Nowak. Five rules for the evolution of cooperation. Science 314, pages 1560--1563, 2006.Google Scholar
- M. A. Nowak, A. Sasaki, C. Taylor, and D. Fudenberg. Emergence of cooperation and evolutionary stability in finite populations. Nature 428, pages 646--650, 2004.Google Scholar
- H. Ohtsuki, C. Hauert, and E. Lieberman, and M. A. Nowak. A simple rule for the evolution of cooperation on graphs and social networks. Nature 441, pages 502--505, 2006.Google Scholar
- A. V. Outkin. Cooperation and local interactions in the prisoners' dilemma game. Journal of Economic Behavior Organization, 52(4):481--503, 2003.Google ScholarCross Ref
- J. Palacios and P. Tetali. A note on expected hitting times for birth and death chains. Statistics & Probability Letters, 30(2):119--125, 1996.Google ScholarCross Ref
- W. H. Sandholm. Population Games and Evolutionary Dynamics (Series on Economic Learning and Social Evolution). MIT Press, 2011.Google Scholar
- G. Szabó and G. Fáth. Evolutionary games on graphs. Physics Reports, 446:97--216, 2007.Google ScholarCross Ref
Index Terms
- Dynamics of prisoner's dilemma and the evolution of cooperation on networks
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