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Learning To Play Approximate Nash Equilibria In Games With Many Players

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  • Cartwright, Edward

    (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.

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Bibliographic Info

Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 671.

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Length: 47 pages
Date of creation: 2003
Date of revision:
Handle: RePEc:wrk:warwec:671

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Keywords: imitation ; best reply ; convergence ; Nash equilibrium;

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Citations

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Cited by:
  1. Edward Cartwright & Myrna Wooders, 2005. "Correlated Equilibrium and Behavioral Conformity," Vanderbilt University Department of Economics Working Papers 0526, Vanderbilt University Department of Economics.
  2. Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2003. "Social Conformity in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 682, University of Warwick, Department of Economics.
  3. Edward Cartwright, 2004. "Contagion and the Emergence of Convention in Small Worlds," Studies in Economics, Department of Economics, University of Kent 0414, Department of Economics, University of Kent.
  4. Cartwright, Edward, 2003. "Imitation and the Emergence of Nash Equilibrium Play in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 684, 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, Elsevier, vol. 57(2), pages 347-360, November.

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