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Learning to Play Approximate Nash Equilibria in Games with Many Players

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Author Info
Edward Cartwright (Department of Economics, University of Warwick)

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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.

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Paper provided by Fondazione Eni Enrico Mattei in its series Working Papers with number 2004.85.

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Date of creation: May 2004
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Handle: RePEc:fem:femwpa:2004.85

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Related research
Keywords: Imitation; Best replay; Convergence; Nash equilibrium;

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Find related papers by 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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References listed on IDEAS
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  10. Wooders, Myrna & Edward Cartwright & Selten, Reinhard, 2002. "Social Conformity And Equilibrium In Pure Strategies In Games With Many Players," The Warwick Economics Research Paper Series (TWERPS) 636, University of Warwick, Department of Economics. [Downloadable!]
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  17. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July. [Downloadable!] (restricted)
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  22. Douglas Gale & Robert W. Rosenthal, 1996. "Experimentation, Imitation, and Stochastic Stability," Papers 0065, Boston University - Industry Studies Programme.
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  30. Selten, Reinhard, 1998. "Features of experimentally observed bounded rationality," European Economic Review, Elsevier, vol. 42(3-5), pages 413-436, May. [Downloadable!] (restricted)
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Edward Cartwright, 2004. "Contagion and the Emergence of Convention in Small Worlds," Studies in Economics 0414, Department of Economics, University of Kent. [Downloadable!]
  2. Edward Cartwright & Myrna Wooders, 2005. "Correlated Equilibrium and Behavioral Conformity," Working Papers 0526, Department of Economics, Vanderbilt University. [Downloadable!]
    Other versions:
  3. Myrna Wooders & Edward Cartwright & Reinhard Selten, 2003. "Social Conformity in Games with Many Players," Working Papers 2003.121, Fondazione Eni Enrico Mattei. [Downloadable!]
    Other versions:
  4. Cartwright, Edward, 2003. "Imitation and the Emergence of Nash Equilibrium Play in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS) 684, University of Warwick, Department of Economics. [Downloadable!]
  5. Myrna Wooders & Edward Cartwright & Reinhard Selten, 2005. "Behavioral Conformity in Games with Many Players," Working Papers 0513, Department of Economics, Vanderbilt University. [Downloadable!]
    Other versions:
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