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A Numerical Analysis of the Evolutionary Stability of Learning Rules

Author

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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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    References listed on IDEAS

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    15. Heller, Dana, 2004. "An evolutionary approach to learning in a changing environment," Journal of Economic Theory, Elsevier, vol. 114(1), pages 31-55, January.
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    17. Camerer, Colin F. & Ho, Teck-Hua & Chong, Juin-Kuan, 2002. "Sophisticated Experience-Weighted Attraction Learning and Strategic Teaching in Repeated Games," Journal of Economic Theory, Elsevier, vol. 104(1), pages 137-188, May.
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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. Hanaki, Nobuyuki & Ishikawa, Ryuichiro & Akiyama, Eizo, 2009. "Learning games," Journal of Economic Dynamics and Control, Elsevier, vol. 33(10), pages 1739-1756, October.
    4. 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.
    5. 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.
    6. 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.
    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. Dridi, Slimane & Lehmann, Laurent, 2014. "On learning dynamics underlying the evolution of learning rules," Theoretical Population Biology, Elsevier, vol. 91(C), pages 20-36.
    9. 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.
    10. Jurjen Kamphorst & Gerard van der Laan, 2006. "Learning in a Local Interaction Hawk-Dove Game," Tinbergen Institute Discussion Papers 06-034/1, Tinbergen Institute.
    11. Mohlin, Erik, 2012. "Evolution of theories of mind," Games and Economic Behavior, Elsevier, vol. 75(1), pages 299-318.
    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.

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    More about this item

    Keywords

    Bounded rationality; Evolutionary game theory; Evolutionary Stability; Learning in games; Belief learning; Reinforcement learning.;
    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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