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Observations on Cooperation

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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
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    Cited by:

    1. 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.
    2. Bester, Helmut & Sákovics, József, 2024. "Cooperation, competition, and welfare in a matching market," Games and Economic Behavior, Elsevier, vol. 143(C), pages 357-369.
    3. Block, Juan I. & Fudenberg, Drew & Levine, David K., 2019. "Learning dynamics with social comparisons and limited memory," Theoretical Economics, Econometric Society, vol. 14(1), January.
    4. Song, Zhao & Guo, Hao & Jia, Danyang & Perc, Matjaž & Li, Xuelong & Wang, Zhen, 2021. "Third party interventions mitigate conflicts on interdependent networks," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    5. Gaudeul, Alexia & Keser, Claudia & Müller, Stephan, 2021. "The evolution of morals under indirect reciprocity," Games and Economic Behavior, Elsevier, vol. 126(C), pages 251-277.
    6. Artyom Jelnov & Yair Tauman & Chang Zhao, 2021. "Stag Hunt with unknown outside options," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(1), pages 303-335, July.
    7. repec:grz:wpaper:2016-02 is not listed on IDEAS
    8. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    9. Heller, Yuval & Mohlin, Erik, 2018. "Social learning and the shadow of the past," Journal of Economic Theory, Elsevier, vol. 177(C), pages 426-460.
    10. 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.
    11. Tóbiás, Áron, 2023. "Rational Altruism," Journal of Economic Behavior & Organization, Elsevier, vol. 207(C), pages 50-80.
    12. Florian Gauer & Christoph Kuzmics, 2020. "Cognitive Empathy In Conflict Situations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 61(4), pages 1659-1678, November.
    13. Harry Pei, 2022. "Reputation Effects under Short Memories," Papers 2207.02744, arXiv.org, revised Jan 2023.
    14. Kamei, Kenju, 2020. "The Perverse Costly Signaling Effect on Cooperation under the Shadow of the Future," MPRA Paper 103678, University Library of Munich, Germany.

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    More about this item

    Keywords

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

    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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