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Observations on Cooperation

Author

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  • Yuval Heller

    () (Bar-Ilan University)

  • Erik Mohlin

Abstract

We study environments in which agents are randomly matched to play a Prisoner’s Dilemma, and each player observes a few of the partner’s past actions against previous opponents. We depart from the existing related literature by allowing a small fraction of the population to be commitment types. The presence of committed agents destabilizes previously proposed mechanisms for sustaining cooperation. We present a novel intuitive combination of strategies that sustains cooperation in various environments. Moreover, we show that under an additional assumption of stationarity, this combination of strategies is essentially the unique mechanism to support full cooperation, and it is robust to various perturbations. Finally, we extend the results to a setup in which agents also observe actions played by past opponents against the current partner, and we characterize which observation structure is optimal for sustaining cooperation.

Suggested Citation

  • Yuval Heller & Erik Mohlin, 2017. "Observations on Cooperation," Working Papers 2017-12, Bar-Ilan University, Department of Economics.
  • Handle: RePEc:biu:wpaper:2017-12
    as

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    File URL: http://econ.biu.ac.il/files/economics/working-papers/2017-12.pdf
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    References listed on IDEAS

    as
    1. Robson, A.J., 1989. "Efficiency In Evolutionary Games: Darwin, Nash And Secret Handshake," Papers 89-22, Michigan - Center for Research on Economic & Social Theory.
    2. Takahashi, Satoru, 2010. "Community enforcement when players observe partners' past play," Journal of Economic Theory, Elsevier, vol. 145(1), pages 42-62, January.
    3. Takako Fujiwara-Greve & Masahiro Okuno-Fujiwara, 2009. "Voluntarily Separable Repeated Prisoner's Dilemma," Review of Economic Studies, Oxford University Press, vol. 76(3), pages 993-1021.
    4. József Sákovics & Jakub Steiner, 2012. "Who Matters in Coordination Problems?," American Economic Review, American Economic Association, vol. 102(7), pages 3439-3461, December.
    5. Heller, Yuval & Mohlin, Erik, 2019. "Coevolution of deception and preferences: Darwin and Nash meet Machiavelli," Games and Economic Behavior, Elsevier, vol. 113(C), pages 223-247.
    6. Parikshit Ghosh & Debraj Ray, 1996. "Cooperation in Community Interaction Without Information Flows," Review of Economic Studies, Oxford University Press, vol. 63(3), pages 491-519.
    7. Cripps, Martin W & Thomas, Jonathan P, 1995. "Reputation and Commitment in Two-Person Repeated Games without Discounting," Econometrica, Econometric Society, vol. 63(6), pages 1401-1419, November.
    8. Alp E. Atakan & Mehmet Ekmekci, 2012. "Reputation in Long-Run Relationships," Review of Economic Studies, Oxford University Press, vol. 79(2), pages 451-480.
    9. Hitoshi Matsushima & Tomomi Tanaka & Tomohisa Toyama, 2013. "Behavioral Approach to Repeated Games with Private Monitoring," CIRJE F-Series CIRJE-F-879, CIRJE, Faculty of Economics, University of Tokyo.
    10. Berger, Ulrich & Grüne, Ansgar, 2016. "On the stability of cooperation under indirect reciprocity with first-order information," Games and Economic Behavior, Elsevier, vol. 98(C), pages 19-33.
    11. 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.
    12. John Duffy & Jack Ochs, 2004. "Cooperative Behavior and the Frequency of Social Interaction," Levine's Bibliography 122247000000000108, UCLA Department of Economics.
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    Cited by:

    1. Gauer, Florian & Kuzmics, Christoph, 2016. "Cognitive empathy in conflict situations," Center for Mathematical Economics Working Papers 551, Center for Mathematical Economics, Bielefeld University.
    2. repec:eee:jetheo:v:177:y:2018:i:c:p:426-460 is not listed on IDEAS
    3. Heller, Yuval & Mohlin, Erik, 2019. "Coevolution of deception and preferences: Darwin and Nash meet Machiavelli," Games and Economic Behavior, Elsevier, vol. 113(C), pages 223-247.
    4. repec:the:publsh:2626 is not listed on IDEAS
    5. Gaudeul, Alexia & Keser, Claudia & Müller, Stephan, 2019. "The evolution of morals under indirect reciprocity," Center for European, Governance and Economic Development Research Discussion Papers 370, University of Goettingen, Department of Economics.

    More about this item

    Keywords

    Community enforcement; indirect reciprocity; random matching; Prisoner’s Dilemma; image scoring.;

    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
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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