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In and out of equilibrium I: Evolution of strategies in repeated games with discounting

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  • García, Julián
  • van Veelen, Matthijs

Abstract

In the repeated prisoner's dilemma there is no strategy that is evolutionarily stable, and a profusion of neutrally stable ones. But how stable is neutrally stable? We show that in repeated games with large enough continuation probabilities, where the stage game is characterized by a conflict between individual and collective interests, there is always a neutral mutant that can drift into a population that is playing an equilibrium, and create a selective advantage for a second mutant. The existence of stepping stone paths out of any equilibrium determines the dynamics in finite populations playing the repeated prisoner's dilemma.

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  • García, Julián & van Veelen, Matthijs, 2016. "In and out of equilibrium I: Evolution of strategies in repeated games with discounting," Journal of Economic Theory, Elsevier, vol. 161(C), pages 161-189.
  • Handle: RePEc:eee:jetheo:v:161:y:2016:i:c:p:161-189
    DOI: 10.1016/j.jet.2015.11.007
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    Cited by:

    1. Matthijs van Veelen, 2020. "The evolution of morality," Tinbergen Institute Discussion Papers 20-063/I, Tinbergen Institute.
    2. Saral, Ali Seyhun, 2020. "Evolution of Conditional Cooperation in Prisoner's Dilemma," OSF Preprints wcpkz, Center for Open Science.
    3. Matthijs van Veelen & Benjamin Allen & Moshe Hoffman & Burton Simon & Carl Veller, 2016. "Inclusive Fitness," Tinbergen Institute Discussion Papers 16-055/I, Tinbergen Institute.
    4. Peter S. Park & Martin A. Nowak & Christian Hilbe, 2022. "Cooperation in alternating interactions with memory constraints," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    5. Heller, Yuval, 2015. "Three steps ahead," Theoretical Economics, Econometric Society, vol. 10(1), January.
    6. García, Julián & van Veelen, Matthijs, 2016. "In and out of equilibrium I: Evolution of strategies in repeated games with discounting," Journal of Economic Theory, Elsevier, vol. 161(C), pages 161-189.
    7. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Sandholm, William H., 2019. "An introduction to ABED: Agent-based simulation of evolutionary game dynamics," Games and Economic Behavior, Elsevier, vol. 118(C), pages 434-462.
    8. Benjamin M Zagorsky & Johannes G Reiter & Krishnendu Chatterjee & Martin A Nowak, 2013. "Forgiver Triumphs in Alternating Prisoner's Dilemma," PLOS ONE, Public Library of Science, vol. 8(12), pages 1-8, December.
    9. van Veelen, Matthijs & García, Julián, 2019. "In and out of equilibrium II: Evolution in repeated games with discounting and complexity costs," Games and Economic Behavior, Elsevier, vol. 115(C), pages 113-130.
    10. Shun Kurokawa & Joe Yuichiro Wakano & Yasuo Ihara, 2018. "Evolution of Groupwise Cooperation: Generosity, Paradoxical Behavior, and Non-Linear Payoff Functions," Games, MDPI, vol. 9(4), pages 1-24, December.
    11. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    12. Maria Kleshnina & Christian Hilbe & Štěpán Šimsa & Krishnendu Chatterjee & Martin A. Nowak, 2023. "The effect of environmental information on evolution of cooperation in stochastic games," Nature Communications, Nature, vol. 14(1), pages 1-11, December.

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    More about this item

    Keywords

    Repeated games; Evolutionary game theory;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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