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Cooperation in Large Societies, Second Version

Author

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  • Francesc Dilmé

    (Department of Economics, University of Bonn)

Abstract

This paper investigates how cooperation can be sustained in large societies even in the presence of agents who never cooperate. In order to do this, we consider a large but finite society where in each period agents are randomly matched in pairs. Nature decides, within each match, which agent needs help in order to avoid some loss, and which agent can help him incurring a cost smaller than the loss. Each agent observes only his own history, and we assume that agents do not recognize each other. We introduce and characterize a class of equilibria, named linear equilibria, in which cooperation takes place. Within this class, efficiency can be achieved with simple one-period strategies, which are close to a tit-for-tat strategy when the society is large, and which generate smooth dynamics of the expected average level of cooperation. Unlike previously suggested equilibria in similar environments, our equilibria are robust to the presence of behavioral agents and other perturbations of the base model. We also apply our model to bilateral trade with many traders, where we find that the mechanism of transmitting defections is transmissive and not contagious as in our base model.

Suggested Citation

  • Francesc Dilmé, 2012. "Cooperation in Large Societies, Second Version," PIER Working Paper Archive 14-021, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 01 Jun 2014.
    • Handle: RePEc:pen:papers:14-021
    as

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    File URL: https://economics.sas.upenn.edu/sites/default/files/filevault/14-021.pdf
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    References listed on IDEAS

    as
    1. Joyee Deb, 2008. "Cooperation and Community Responsibility: A Folk Theorem for Repeated Matching Games with Names," Working Papers 08-24, New York University, Leonard N. Stern School of Business, Department of Economics.
    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. Ely, Jeffrey C. & Valimaki, Juuso, 2002. "A Robust Folk Theorem for the Prisoner's Dilemma," Journal of Economic Theory, Elsevier, vol. 102(1), pages 84-105, January.
    4. Piccione, Michele, 2002. "The Repeated Prisoner's Dilemma with Imperfect Private Monitoring," Journal of Economic Theory, Elsevier, vol. 102(1), pages 70-83, January.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Cooperation; Many Agents; Repeated Games; Unilateral Help;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D64 - Microeconomics - - Welfare Economics - - - Altruism; Philanthropy; Intergenerational Transfers

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