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Group Size and Cooperation Among Strangers

Author

Listed:
  • John Duffy
  • Huan Xie

Abstract

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 ≤ 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 → M.

Suggested Citation

  • John Duffy & Huan Xie, 2012. "Group Size and Cooperation Among Strangers," Working Paper 495, Department of Economics, University of Pittsburgh, revised Jan 2012.
    • Handle: RePEc:pit:wpaper:495
    as

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    References listed on IDEAS

    as
    1. 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.
    2. Glenn Ellison, 1994. "Cooperation in the Prisoner's Dilemma with Anonymous Random Matching," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(3), pages 567-588.
    3. Okada, Akira, 1993. "The Possibility of Cooperation in an n-Person Prisoners' Dilemma with Institutional Arrangements," Public Choice, Springer, vol. 77(3), pages 629-656, November.
    4. Isaac, R. Mark & Walker, James M. & Williams, Arlington W., 1994. "Group size and the voluntary provision of public goods : Experimental evidence utilizing large groups," Journal of Public Economics, Elsevier, vol. 54(1), pages 1-36, May.
    5. Xie, Huan & Lee, Yong-Ju, 2012. "Social norms and trust among strangers," Games and Economic Behavior, Elsevier, vol. 76(2), pages 548-555.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    N-player Prisoner's Dilemma; Repeated Games; Folk Theorem; Contagion;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • Z13 - Other Special Topics - - Cultural Economics - - - Economic Sociology; Economic Anthropology; Language; Social and Economic Stratification

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