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Instability of defection in the prisoner's dilemma under best experienced payoff dynamics

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  • Arigapudi, Srinivas
  • Heller, Yuval
  • Milchtaich, Igal

Abstract

We study population dynamics under which each revising agent tests each action k times, with each trial being against a newly drawn opponent, and chooses the action whose mean payoff was highest during the testing phase. When k=1, defection is globally stable in the prisoner's dilemma. By contrast, when k>1 we show that, if the gains from defection are not too large, there exists a globally stable state in which agents cooperate with probability between 28% and 50%. Next, we characterize stability of strict equilibria in general games. Our results demonstrate that the empirically plausible case of k>1 can yield qualitatively different predictions than the case k=1 commonly studied in the literature.

Suggested Citation

  • Arigapudi, Srinivas & Heller, Yuval & Milchtaich, Igal, 2021. "Instability of defection in the prisoner's dilemma under best experienced payoff dynamics," Journal of Economic Theory, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:jetheo:v:197:y:2021:i:c:s0022053120301678
    DOI: 10.1016/j.jet.2020.105174
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    Cited by:

    1. Srinivas Arigapudi & Omer Edhan & Yuval Heller & Ziv Hellman, 2022. "Mentors and Recombinators: Multi-Dimensional Social Learning," Papers 2205.00278, arXiv.org, revised Nov 2023.
    2. Sawa, Ryoji & Wu, Jiabin, 2023. "Statistical inference in evolutionary dynamics," Games and Economic Behavior, Elsevier, vol. 137(C), pages 294-316.
    3. Aloysius Suratin & Suyud Warno Utomo & Dwi Nowo Martono & Kosuke Mizuno, 2023. "Indonesia’s Renewable Natural Resource Management in the Low-Carbon Transition: A Conundrum in Changing Trajectories," Sustainability, MDPI, vol. 15(14), pages 1-17, July.
    4. Izquierdo, Segismundo S. & Izquierdo, Luis R., 2023. "Strategy sets closed under payoff sampling," Games and Economic Behavior, Elsevier, vol. 138(C), pages 126-142.
    5. Ryoji Sawa, 2022. "Statistical Inference in Evolutionary Dynamics," Working Papers e170, Tokyo Center for Economic Research.
    6. Srinivas Arigapudi & Yuval Heller & Amnon Schreiber, 2021. "Sampling dynamics and stable mixing in hawk-dove games," Papers 2107.08423, arXiv.org, revised Jun 2022.
    7. Sethi, Rajiv, 2021. "Stable sampling in repeated games," Journal of Economic Theory, Elsevier, vol. 197(C).
    8. Izquierdo, Segismundo S. & Izquierdo, Luis R., 2022. "Stability of strict equilibria in best experienced payoff dynamics: Simple formulas and applications," Journal of Economic Theory, Elsevier, vol. 206(C).
    9. Arigapudi, Srinivas & Heller, Yuval & Schreiber, Amnon, 2021. "Sampling Dynamics and Stable Mixing in Hawk–Dove Games," MPRA Paper 108819, University Library of Munich, Germany.
    10. Srinivas Arigapudi & Yuval Heller & Amnon Schreiber, 2023. "Heterogeneous Noise and Stable Miscoordination," Papers 2305.10301, arXiv.org.

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    More about this item

    Keywords

    Learning; Cooperation; Best experienced payoff dynamics; Sampling equilibrium; Evolutionary stability;
    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

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