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Imitating cooperation and the formation of long-term relationships

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  • Schumacher, Heiner

Abstract

We study the infinitely repeated prisonerʼs dilemma with the option to maintain or to quit relationships. We show that if agents imitate successful strategies infrequently, defection is not dynamically stable and cooperation emerges regardless of the initial distribution of strategies.

Suggested Citation

  • Schumacher, Heiner, 2013. "Imitating cooperation and the formation of long-term relationships," Journal of Economic Theory, Elsevier, vol. 148(1), pages 409-417.
    • Handle: RePEc:eee:jetheo:v:148:y:2013:i:1:p:409-417
    DOI: 10.1016/j.jet.2012.12.008
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    References listed on IDEAS

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    1. Apesteguia, Jose & Huck, Steffen & Oechssler, Jorg, 2007. "Imitation--theory and experimental evidence," Journal of Economic Theory, Elsevier, vol. 136(1), pages 217-235, September.
    2. repec:ebl:ecbull:v:3:y:2008:i:12:p:1-8 is not listed on IDEAS
    3. Matthew Jackson & Alison Watts, 2008. "Equilibrium Existence in Bipartite Social Games: A Generalization of Stable Matchings," Economics Bulletin, AccessEcon, vol. 3(12), pages 1-8.
    4. Ilan Eshel & Larry Samuelson & Avner Shaked, "undated". "Altruists Egoists and Hooligans in a Local Interaction Model," ELSE working papers 005, ESRC Centre on Economics Learning and Social Evolution.
    5. Eshel, Ilan & Samuelson, Larry & Shaked, Avner, 1998. "Altruists, Egoists, and Hooligans in a Local Interaction Model," American Economic Review, American Economic Association, vol. 88(1), pages 157-179, March.
    6. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    7. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    8. Parikshit Ghosh & Debraj Ray, 1996. "Cooperation in Community Interaction Without Information Flows," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(3), pages 491-519.
    9. Binmore, Kenneth G. & Samuelson, Larry, 1992. "Evolutionary stability in repeated games played by finite automata," Journal of Economic Theory, Elsevier, vol. 57(2), pages 278-305, August.
    10. Takako Fujiwara-Greve & Masahiro Okuno-Fujiwara, 2009. "Voluntarily Separable Repeated Prisoner's Dilemma," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 993-1021.
    11. Edward Cartwright, 2007. "Imitation, coordination and the emergence of Nash equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 119-135, September.
    12. Kranton, Rachel E, 1996. "The Formation of Cooperative Relationships," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 12(1), pages 214-233, April.
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    Citations

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    Cited by:

    1. García-Martínez, José A. & Vega-Redondo, Fernando, 2015. "Social cohesion and the evolution of altruism," Games and Economic Behavior, Elsevier, vol. 92(C), pages 74-105.
    2. Nosenzo, Daniele & Tufano, Fabio, 2017. "The effect of voluntary participation on cooperation," Journal of Economic Behavior & Organization, Elsevier, vol. 142(C), pages 307-319.
    3. Daniele Nosenzo & Fabio Tufano, 2015. "Entry or Exit? The Effect of Voluntary Participation on Cooperation," Discussion Papers 2015-20, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    4. Takako Fujiwara-Greve & Masahiro Okuno-Fujiwara, 2013. "Diverse Behavior Patterns in a Symmetric Society with Voluntary Partnerships," Working Papers e062, Tokyo Center for Economic Research.
    5. Tom Potoms & Tom Truyts, 2020. "Unhappy is the land without symbols - Group symbols in infinitely repeated public good games," Working Paper Series 1720, Department of Economics, University of Sussex Business School.

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    More about this item

    Keywords

    Prisonerʼs dilemma; Imitation; Random matching; Relationships;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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