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A numerical analysis of the evolutionary stability of learning rules

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  • Josephson, Jens

Abstract

In this paper, we define an evolutionary stability criterion for learning rules. Using simulations, we then apply this criterion to three types of symmetric 2x2 games for a class of learning rules that can be represented by the parametric model of Camerer and Ho [1999. Experience-weighted attraction learning in normal form games. Econometrica 67, 827-874]. This class contains stochastic versions of reinforcement and fictitious play as extreme cases. We find that only learning rules with high or intermediate levels of hypothetical reinforcement are evolutionarily stable, but that the stable parameters depend on the game.

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  • Josephson, Jens, 2008. "A numerical analysis of the evolutionary stability of learning rules," Journal of Economic Dynamics and Control, Elsevier, vol. 32(5), pages 1569-1599, May.
    • Handle: RePEc:eee:dyncon:v:32:y:2008:i:5:p:1569-1599
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    Cited by:

    1. Jurjen Kamphorst & Gerard van der Laan, 2006. "Learning in a Local Interaction Hawk-Dove Game," Tinbergen Institute Discussion Papers 06-034/1, Tinbergen Institute.
    2. Wang, Xianjia & Lv, Shaojie, 2019. "The roles of particle swarm intelligence in the prisoner’s dilemma based on continuous and mixed strategy systems on scale-free networks," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 213-220.
    3. Ho, Teck H. & Camerer, Colin F. & Chong, Juin-Kuan, 2007. "Self-tuning experience weighted attraction learning in games," Journal of Economic Theory, Elsevier, vol. 133(1), pages 177-198, March.
    4. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
    5. Hanaki, Nobuyuki & Ishikawa, Ryuichiro & Akiyama, Eizo, 2009. "Learning games," Journal of Economic Dynamics and Control, Elsevier, vol. 33(10), pages 1739-1756, October.
    6. Josephson, Jens, 2009. "Stochastic adaptation in finite games played by heterogeneous populations," Journal of Economic Dynamics and Control, Elsevier, vol. 33(8), pages 1543-1554, August.
    7. Burkhard Schipper & Peter Duersch & Joerg Oechssler, 2011. "Once Beaten, Never Again: Imitation in Two-Player Potential Games," Working Papers 26, University of California, Davis, Department of Economics.
    8. Matros, Alexander, 2012. "Altruistic versus egoistic behavior in a Public Good game," Journal of Economic Dynamics and Control, Elsevier, vol. 36(4), pages 642-656.
    9. Jasmina Arifovic & John Ledyard, 2004. "Scaling Up Learning Models in Public Good Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 6(2), pages 203-238, May.
    10. Duersch, Peter & Oechssler, Jörg & Schipper, Burkhard C., 2012. "Once Beaten, Never Again: Imitation in Two-Player Potential Games," Working Papers 0529, University of Heidelberg, Department of Economics.
    11. Dridi, Slimane & Lehmann, Laurent, 2014. "On learning dynamics underlying the evolution of learning rules," Theoretical Population Biology, Elsevier, vol. 91(C), pages 20-36.
    12. Burkhard Schipper & Peter Duersch & Joerg Oechssler, 2011. "Once Beaten, Never Again: Imitation in Two-Player Potential Games," Working Papers 1112, University of California, Davis, Department of Economics.
    13. Teck H Ho & Colin Camerer & Juin-Kuan Chong, 2003. "Functional EWA: A one-parameter theory of learning in games," Levine's Working Paper Archive 506439000000000514, David K. Levine.

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    More about this item

    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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