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Group Size and Cooperation among Strangers

We study how group size affects cooperation in an infinitely repeated n-player Prisoner's Dilemma (PD) game. In each repetition of the game, groups of size n less than or equal to M are randomly and anonymously matched from a fixed population of size M to play the n-player PD stage game. We provide conditions for which the contagious strategy (Kandori, 1992) sustains a social norm of cooperation among all M players. Our main finding is that if agents are sufficiently patient, a social norm of society-wide cooperation becomes easier to sustain under the contagious strategy as n converges to M.

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Paper provided by Concordia University, Department of Economics in its series Working Papers with number 12010.

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Length: 16 pages
Date of creation: 12 Sep 2012
Date of revision:
Handle: RePEc:crd:wpaper:12010
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  1. Daniele Nosenzo & Simone Quercia & Martin Sefton, 2015. "Cooperation in small groups: the effect of group size," Experimental Economics, Springer, vol. 18(1), pages 4-14, March.
  2. R. M. Isaac & J. M. Walker, 2010. "Group size effects in public goods provision: The voluntary contribution mechanism," Levine's Working Paper Archive 310, David K. Levine.
  3. Pedro Bó, 2007. "Social norms, cooperation and inequality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 89-105, January.
  4. Drew Fudenberg & David G. Rand & Anna Dreber, 2012. "Slow to Anger and Fast to Forgive: Cooperation in an Uncertain World," American Economic Review, American Economic Association, vol. 102(2), pages 720-49, April.
  5. Pedro Dal Bó, 2005. "Cooperation under the Shadow of the Future: Experimental Evidence from Infinitely Repeated Games," American Economic Review, American Economic Association, vol. 95(5), pages 1591-1604, December.
  6. Glenn Ellison, 1994. "Cooperation in the Prisoner's Dilemma with Anonymous Random Matching," Review of Economic Studies, Oxford University Press, vol. 61(3), pages 567-588.
  7. Gabriele Camera & Marco Casari, 2009. "Cooperation among Strangers under the Shadow of the Future," American Economic Review, American Economic Association, vol. 99(3), pages 979-1005, June.
  8. Jim Engle-Warnick & Robert Slonim, 2006. "Inferring repeated-game strategies from actions: evidence from trust game experiments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 603-632, 08.
  9. John Duffy & Huan Xie & Yong-Ju Lee, 2008. "Social Norms, Information and Trust among Strangers: Theory and Evidence," Working Papers 08007, Concordia University, Department of Economics, revised Jul 2001.
  10. Huan Xie & Yong-Ju Lee, 2008. "Social Norms and Trust among Strangers," Working Papers 08006, Concordia University, Department of Economics, revised May 2011.
  11. Pedro Dal Bo & Guillaume R. Frechette, . "The Evolution of Cooperation in Infinitely Repeated Games: Experimental Evidence," Working Papers 2007-7, Brown University, Department of Economics.
  12. Okada, Akira, 1993. "The Possibility of Cooperation in an n-Person Prisoners' Dilemma with Institutional Arrangements," Public Choice, Springer, vol. 77(3), pages 629-56, November.
  13. Carpenter, Jeffrey P., 2004. "Punishing Free-Riders: How Group Size Affects Mutual Monitoring and the Provision of Public Goods," IZA Discussion Papers 1337, Institute for the Study of Labor (IZA).
  14. John Duffy & Jack Ochs, 2004. "Cooperative Behavior and the Frequency of Social Interaction," Levine's Bibliography 122247000000000108, UCLA Department of Economics.
  15. Michihiro Kandori, 1992. "Social Norms and Community Enforcement," Review of Economic Studies, Oxford University Press, vol. 59(1), pages 63-80.
  16. Bin Xu & C. Bram Cadsby & Liangcong Fan & Fei Song, 2013. "Group Size, Coordination, and the Effectiveness of Punishment in the Voluntary Contributions Mechanism: An Experimental Investigation," Games, MDPI, Open Access Journal, vol. 4(1), pages 89, February.
  17. Camera, Gabriele & Casari, Marco & Bigoni, Maria, 2012. "Cooperative strategies in anonymous economies: An experiment," Games and Economic Behavior, Elsevier, vol. 75(2), pages 570-586.
  18. Aoyagi, Masaki & Fréchette, Guillaume, 2009. "Collusion as public monitoring becomes noisy: Experimental evidence," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1135-1165, May.
  19. Camera, Gabriele & Gioffré, Alessandro, 2014. "A tractable analysis of contagious equilibria," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 290-300.
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