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Cooperation, imitation and partial rematching

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  • Rivas, Javier

Abstract

We study a setting in which imitative players are matched into pairs to play a Prisonerʼs Dilemma game. A well-known result in such setting is that under random matching cooperation vanishes for any interior initial condition. The novelty of this paper is that we consider partial rematching: players that belong to a pair in which both parties cooperate repeat partner next period, while all other players are randomly matched into pairs. Under certain conditions, this rematching mechanism makes cooperation the unique outcome in the long run. Furthermore, we show that if imitation happens infrequently enough then cooperative behavior is always present in the population.

Suggested Citation

  • Rivas, Javier, 2013. "Cooperation, imitation and partial rematching," Games and Economic Behavior, Elsevier, vol. 79(C), pages 148-162.
  • Handle: RePEc:eee:gamebe:v:79:y:2013:i:c:p:148-162
    DOI: 10.1016/j.geb.2013.01.011
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    1. Levine, David K. & Pesendorfer, Wolfgang, 2007. "The evolution of cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 58(2), pages 293-315, February.
    2. Bergstrom, Theodore C & Stark, Oded, 1993. "How Altruism Can Prevail in an Evolutionary Environment," American Economic Review, American Economic Association, vol. 83(2), pages 149-155, May.
    3. Tilman Börgers & Antonio J. Morales & Rajiv Sarin, 2004. "Expedient and Monotone Learning Rules," Econometrica, Econometric Society, vol. 72(2), pages 383-405, March.
    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. Rustichini, Aldo, 1999. "Optimal Properties of Stimulus--Response Learning Models," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 244-273, October.
    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. 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.
    9. Glenn Ellison & Drew Fudenberg, 1995. "Word-of-Mouth Communication and Social Learning," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(1), pages 93-125.
    10. Chun-Lei Yang & Ching-Syang Jack Yue & I-Tang Yu, 2007. "The rise of cooperation in correlated matching prisoners dilemma: An experiment," Experimental Economics, Springer;Economic Science Association, vol. 10(1), pages 3-20, March.
    11. Theodore C. Bergstrom, 2003. "The Algebra of Assortative Encounters and the Evolution of Cooperation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 211-228.
    12. Duffy, John & Ochs, Jack, 2009. "Cooperative behavior and the frequency of social interaction," Games and Economic Behavior, Elsevier, vol. 66(2), pages 785-812, July.
    13. Grimm, Veronika & Mengel, Friederike, 2009. "Cooperation in viscous populations--Experimental evidence," Games and Economic Behavior, Elsevier, vol. 66(1), pages 202-220, May.
    14. Abhijit V. Banerjee, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(3), pages 797-817.
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    Citations

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    Cited by:

    1. Ziwei Wang & Jiabin Wu, 2023. "Partner Choice and Morality: Preference Evolution under Stable Matching," Papers 2304.11504, arXiv.org, revised Oct 2023.
    2. Jiabin Wu, 2021. "Matching markets and cultural selection," Review of Economic Design, Springer;Society for Economic Design, vol. 25(4), pages 267-288, December.
    3. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Vega-Redondo, Fernando, 2014. "Leave and let leave: A sufficient condition to explain the evolutionary emergence of cooperation," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 91-113.
    4. Jiabin Wu, 2020. "Labelling, homophily and preference evolution," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 1-22, March.
    5. Martin Holubčík & Jakub Soviar & Viliam Lendel, 2022. "Through Synergy in Cooperation towards Sustainable Business Strategy Management," Sustainability, MDPI, vol. 15(1), pages 1-30, December.
    6. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    7. Simon D Angus & Jonathan Newton, 2020. "Collaboration leads to cooperation on sparse networks," PLOS Computational Biology, Public Library of Science, vol. 16(1), pages 1-11, January.
    8. Jiabin Wu, 2017. "Social Hierarchy and the Evolution of Behavior," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-16, December.
    9. Bilancini, Ennio & Boncinelli, Leonardo & Wu, Jiabin, 2018. "The interplay of cultural intolerance and action-assortativity for the emergence of cooperation and homophily," European Economic Review, Elsevier, vol. 102(C), pages 1-18.

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    More about this item

    Keywords

    Cooperation; Partial rematching; Imitation; Prisonerʼs Dilemma;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative 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

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