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Group Size and Cooperation among Strangers

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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 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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  • John Duffy & Huan Xie, 2012. "Group Size and Cooperation among Strangers," Working Papers 12010, Concordia University, Department of Economics.
    • Handle: RePEc:crd:wpaper:12010
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    Cited by:

    1. Shuguang Jiang & Marie Claire Villeval, 2024. "Dishonesty as a collective‐risk social dilemma," Economic Inquiry, Western Economic Association International, vol. 62(1), pages 223-241, January.
    2. March, Christoph, 2019. "The behavioral economics of artificial intelligence: Lessons from experiments with computer players," BERG Working Paper Series 154, Bamberg University, Bamberg Economic Research Group.
    3. Arianna Degan & Ming Li & Huan Xie, 2023. "An experimental investigation of persuasion through selective disclosure of evidence," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 56(4), pages 1490-1516, November.
    4. Helénsdotter, Ronja, 2019. "Experimental Evidence on Cooperation, Political Affiliation, and Group Size," Working Papers in Economics 765, University of Gothenburg, Department of Economics.
    5. Jens Gudmundsson & Jens Leth Hougaard, 2020. "Enabling reciprocity through blockchain design," IFRO Working Paper 2020/14, University of Copenhagen, Department of Food and Resource Economics, revised 09 Feb 2021.
    6. Iván Barreda-Tarrazona & Ainhoa Jaramillo-Gutiérrez & Marina Pavan & Gerardo Sabater-Grande, 2021. "The “Human Factor” in Prisoner’s Dilemma Cooperation," Working Papers 2021/10, Economics Department, Universitat Jaume I, Castellón (Spain).
    7. March, Christoph, 2021. "Strategic interactions between humans and artificial intelligence: Lessons from experiments with computer players," Journal of Economic Psychology, Elsevier, vol. 87(C).
    8. Jensen, Thomas & Markussen, Thomas, 2021. "Group size, signaling and the effect of democracy," Journal of Economic Behavior & Organization, Elsevier, vol. 187(C), pages 258-273.
    9. Ghidoni, Riccardo & Cleave, Blair L. & Suetens, Sigrid, 2019. "Perfect and imperfect strangers in social dilemmas," European Economic Review, Elsevier, vol. 116(C), pages 148-159.
    10. Normann, Hans-Theo & Sternberg, Martin, 2022. "Human-algorithm interaction: Algorithmic pricing in hybrid laboratory markets," DICE Discussion Papers 392, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    11. Serdarevic, Nina & Strømland, Eirik & Tjøtta, Sigve, 2018. "It Pays to be Nice: The Benefits of Cooperating in Markets," Working Papers in Economics 12/18, University of Bergen, Department of Economics.
    12. Caserta, Maurizio & Distefano, Rosaria & Ferrante, Livio & Reito, Francesco, 2023. "The Good of Rules: A pilot study on prosocial behavior," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 107(C).
    13. Camera, Gabriele & Gioffré, Alessandro, 2025. "Cooperation in temporary partnerships," Journal of Economic Dynamics and Control, Elsevier, vol. 172(C).
    14. Normann, Hans-Theo & Sternberg, Martin, 2023. "Human-algorithm interaction: Algorithmic pricing in hybrid laboratory markets," European Economic Review, Elsevier, vol. 152(C).

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    Keywords

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    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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