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Learning to Play Approximate Nash Equilibria in Games with Many Players

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  • Edward Cartwright

    (Department of Economics, University of Warwick)

Abstract

We illustrate one way in which a population of boundedly rational individuals can learn to play an approximate Nash equilibrium. Players are assumed to make strategy choices using a combination of imitation and innovation. We begin by looking at an imitation dynamic and provide conditions under which play evolves to an imitation equilibrium; convergence is conditional on the network of social interaction. We then illustrate, through example, how imitation and innovation can complement each other; in particular, we demonstrate how imitation can .help. a population to learn to play a Nash equilibrium where more rational methods do not. This leads to our main result in which we provide a general class of large game for which the imitation with innovation dynamic almost surely converges to an approximate Nash, imitation equilibrium.

Suggested Citation

  • Edward Cartwright, 2004. "Learning to Play Approximate Nash Equilibria in Games with Many Players," Working Papers 2004.85, Fondazione Eni Enrico Mattei.
    • Handle: RePEc:fem:femwpa:2004.85
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    References listed on IDEAS

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    Cited by:

    1. Edward Cartwright, 2004. "Contagion and the Emergence of Convention in Small Worlds," Studies in Economics 0414, School of Economics, University of Kent.
    2. Cartwright, Edward, 2003. "Imitation and the emergence of Nash equilibrium play in games with many players," Economic Research Papers 269568, University of Warwick - Department of Economics.
    3. Cartwright, Edward & Wooders, Myrna, 2004. "Correlated equilibrium and behavioral conformity," Economic Research Papers 269625, University of Warwick - Department of Economics.
    4. Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2003. "Social Conformity in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS) 682, University of Warwick, Department of Economics.
    5. Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2006. "Behavioral conformity in games with many players," Games and Economic Behavior, Elsevier, vol. 57(2), pages 347-360, November.

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    More about this item

    Keywords

    Imitation; Best replay; Convergence; Nash equilibrium;
    All these keywords.

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

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