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The Evolution of Algorithmic Learning Rules: A Global Stability Result

Author

Listed:
  • Luca Anderlini

    (St. John's College, Cambridge)

  • Hamid Sabourian

    (King's College, Cambridge)

Abstract

This paper consider the dynamic evolution of algorithmic (recursive) learning rules in a normal form game. It is shown that the system - the population frequencies - is globally stable for any arbitrary N-player normal form game, if the evolutionary process is algorithmic and the `birth process' guarantees that an appropriate set of `smart' rules is present in the population. The result is independent of the nature of the evolutionary process; in particular it does not require the dynamics of the system to be `monotonic in payoffs' - those rules which do better in terms of payoffs grow faster than those who do less well. The paper also demonstrates that any limit point of the distribution of actions in such an evolutionary process corresponds to a Nash equilibrium (pure or mixed) of the underlying game if the dynamics of the system are continuous and monotonic in payoffs.

Suggested Citation

  • Luca Anderlini & Hamid Sabourian, 1995. "The Evolution of Algorithmic Learning Rules: A Global Stability Result," Game Theory and Information 9510001, EconWPA.
  • Handle: RePEc:wpa:wuwpga:9510001
    Note: Type of Document - LaTex/PostScript; prepared on EmTex; to print on PostScript; pages: 53 ; figures: included
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    References listed on IDEAS

    as
    1. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
    2. Megiddo, Nimrod, 1989. "On computable beliefs of rational machines," Games and Economic Behavior, Elsevier, vol. 1(2), pages 144-169, June.
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    Cited by:

    1. 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.

    More about this item

    Keywords

    Evolution; Learning Rules; Computability; Monotonic Dynamics;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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