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A Numerical Analysis of the Evolutionary Stability of Learning Rules

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  • Josephson, Jens

    (Dept. of Economics, Stockholm School of Economics)

Abstract

In this paper I define an evolutionary stability criterion for learning rules. Using Monte Carlo simulations, I then apply this criterion to a class of learning rules that can be represented by Camerer and Ho's (1999) model of learning. This class contains perturbed versions of reinforcement and belief learning as special cases. A large population of individuals with learning rules in this class are repeatedly rematched for a finite number of periods and play one out of four symmetric two-player games. Belief learning is the only learning rule which is evolutionarily stable in almost all cases, whereas reinforcement learning is unstable in almost all cases. I also find that in certain games, the stability of intermediate learning rules hinges critically on a parameter of the model and the relative payoffs.

Suggested Citation

  • Josephson, Jens, 2001. "A Numerical Analysis of the Evolutionary Stability of Learning Rules," SSE/EFI Working Paper Series in Economics and Finance 474, Stockholm School of Economics.
    • Handle: RePEc:hhs:hastef:0474
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
    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 1112, University of California, Davis, Department of Economics.
    8. Hanaki, Nobuyuki & Ishikawa, Ryuichiro & Akiyama, Eizo, 2009. "Learning games," Journal of Economic Dynamics and Control, Elsevier, vol. 33(10), pages 1739-1756, October.
    9. 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.
    10. 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.
    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. Jurjen Kamphorst & Gerard van der Laan, 2006. "Learning in a Local Interaction Hawk-Dove Game," Tinbergen Institute Discussion Papers 06-034/1, Tinbergen Institute.

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    Keywords

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    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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