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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.

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

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Citations

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Cited by:
  1. 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.
  2. Edward Cartwright & Myrna Wooders, 2005. "Correlated Equilibrium and Behavioral Conformity," Vanderbilt University Department of Economics Working Papers 0526, Vanderbilt University Department of Economics.
  3. Myrna Wooders & Edward Cartwright & Reinhard Selten, 2003. "Social Conformity in Games with Many Players," Working Papers, Fondazione Eni Enrico Mattei 2003.121, Fondazione Eni Enrico Mattei.
  4. Myrna Wooders & Edward Cartwright & Reinhard Selten, 2005. "Behavioral Conformity in Games with Many Players," Vanderbilt University Department of Economics Working Papers 0513, Vanderbilt University Department of Economics.
  5. 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.

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