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Instability of Defection in the Prisoner's Dilemma Under Best Experienced Payoff Dynamics

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  • Srinivas Arigapudi
  • Yuval Heller
  • Igal Milchtaich

Abstract

We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable in the prisoner`s dilemma. By contrast, when k > 1 we show that 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 of k = 1 that is commonly studied in the literature.

Suggested Citation

  • Srinivas Arigapudi & Yuval Heller & Igal Milchtaich, 2020. "Instability of Defection in the Prisoner's Dilemma Under Best Experienced Payoff Dynamics," Papers 2005.05779, arXiv.org, revised Jan 2021.
    • Handle: RePEc:arx:papers:2005.05779
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Srinivas Arigapudi & Yuval Heller & Amnon Schreiber, 2023. "Heterogeneous Noise and Stable Miscoordination," Papers 2305.10301, arXiv.org.
    2. Srinivas Arigapudi & Omer Edhan & Yuval Heller & Ziv Hellman, 2022. "Mentors and Recombinators: Multi-Dimensional Social Learning," Papers 2205.00278, arXiv.org, revised Nov 2023.
    3. Srinivas Arigapudi & Yuval Heller & Amnon Schreiber, 2021. "Sampling dynamics and stable mixing in hawk-dove games," Papers 2107.08423, arXiv.org, revised Jun 2022.
    4. Sawa, Ryoji & Wu, Jiabin, 2023. "Statistical inference in evolutionary dynamics," Games and Economic Behavior, Elsevier, vol. 137(C), pages 294-316.
    5. Sethi, Rajiv, 2021. "Stable sampling in repeated games," Journal of Economic Theory, Elsevier, vol. 197(C).
    6. Ryoji Sawa, 2022. "Statistical Inference in Evolutionary Dynamics," Working Papers e170, Tokyo Center for Economic Research.
    7. 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.
    8. Arigapudi, Srinivas, 2024. "Evolutionary dynamics in bilingual games," Journal of Economic Dynamics and Control, Elsevier, vol. 165(C).
    9. Arigapudi, Srinivas & Lahkar, Ratul, 2024. "Emergence of trust in the trust game under best experienced payoff dynamics," Economics Letters, Elsevier, vol. 236(C).
    10. Izquierdo, Segismundo S. & Izquierdo, Luis R., 2023. "Strategy sets closed under payoff sampling," Games and Economic Behavior, Elsevier, vol. 138(C), pages 126-142.
    11. 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).
    12. Berkemer, Rainer & Starke, Jens & Kawamoto, Atsushi, 2023. "Sampling dynamics applied to the traveler's dilemma reveals non-Nash behavior," Games and Economic Behavior, Elsevier, vol. 142(C), pages 339-356.
    13. Arigapudi, Srinivas & Heller, Yuval & Schreiber, Amnon, 2021. "Sampling Dynamics and Stable Mixing in Hawk–Dove Games," MPRA Paper 108819, University Library of Munich, Germany.

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