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Instability of Defection in the Prisoner’s Dilemma: Best Experienced Payoff Dynamics Analysis

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

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

  • Arigapudi, Srinivas & Heller, Yuval & Milchtaich, Igal, 2020. "Instability of Defection in the Prisoner’s Dilemma: Best Experienced Payoff Dynamics Analysis," MPRA Paper 99594, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:99594
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    References listed on IDEAS

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    1. Sethi, Rajiv, 2000. "Stability of Equilibria in Games with Procedurally Rational Players," Games and Economic Behavior, Elsevier, vol. 32(1), pages 85-104, July.
    2. Kreindler, Gabriel E. & Young, H. Peyton, 2013. "Fast convergence in evolutionary equilibrium selection," Games and Economic Behavior, Elsevier, vol. 80(C), pages 39-67.
    3. Nax, Heinrich H. & Burton-Chellew, Maxwell N. & West, Stuart A. & Young, H. Peyton, 2016. "Learning in a black box," Journal of Economic Behavior & Organization, Elsevier, vol. 127(C), pages 1-15.
    4. Kosfeld, Michael & Droste, Edward & Voorneveld, Mark, 2002. "A myopic adjustment process leading to best-reply matching," Games and Economic Behavior, Elsevier, vol. 40(2), pages 270-298, August.
    5. Juan Camilo Cárdenas & César Mantilla & Rajiv Sethi, 2015. "Stable Sampling Equilibrium in Common Pool Resource Games," Games, MDPI, vol. 6(3), pages 1-19, August.
    6. William H. Sandholm, 2001. "Almost global convergence to p-dominant equilibrium," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 107-116.
    7. ,, 2006. "Competition over agents with boundedly rational expectations," Theoretical Economics, Econometric Society, vol. 1(2), pages 207-231, June.
    8. Sandholm, William H. & Izquierdo, Segismundo S. & Izquierdo, Luis R., 2020. "Stability for best experienced payoff dynamics," Journal of Economic Theory, Elsevier, vol. 185(C).
    9. , & , H. & ,, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    10. Friederike Mengel, 2018. "Risk and Temptation: A Meta‐study on Prisoner's Dilemma Games," Economic Journal, Royal Economic Society, vol. 128(616), pages 3182-3209, December.
    11. Thorsten Chmura & Werner Güth, 2011. "The Minority of Three-Game: An Experimental and Theoretical Analysis," Games, MDPI, vol. 2(3), pages 1-22, September.
    12. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-847, September.
    13. Heller, Yuval & Mohlin, Erik, 2018. "Social learning and the shadow of the past," Journal of Economic Theory, Elsevier, vol. 177(C), pages 426-460.
    14. César Mantilla & Rajiv Sethi & Juan Camilo Cárdenas, 2020. "Efficiency and stability of sampling equilibrium in public goods games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(2), pages 355-370, April.
    15. Robert Rowthorn & Rajiv Sethi, 2008. "Procedural Rationality and Equilibrium Trust," Economic Journal, Royal Economic Society, vol. 118(530), pages 889-905, July.
    16. Nax, Heinrich H. & Burton-Chellew, Maxwell N. & West, Stuart A. & Young, H. Peyton, 2016. "Learning in a black box," LSE Research Online Documents on Economics 68714, London School of Economics and Political Science, LSE Library.
    17. Jacek Miękisz & Michał Ramsza, 2013. "Sampling Dynamics of a Symmetric Ultimatum Game," Dynamic Games and Applications, Springer, vol. 3(3), pages 374-386, September.
    18. Michał Ramsza, 2005. "Stability of pure strategy sampling equilibria," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 515-521, November.
    19. Sandholm, William H. & Izquierdo, Segismundo S. & Izquierdo, Luis R., 2019. "Best experienced payoff dynamics and cooperation in the Centipede game," Theoretical Economics, Econometric Society, vol. 14(4), November.
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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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