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Learning To Play Approximate Nash Equilibria In Games With Many Players

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Author Info
Cartwright, Edward (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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File URL: http://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/publications/twerp671.pdf
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Publisher 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
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Handle: RePEc:wrk:warwec:671

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

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References listed on IDEAS
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. Levine, David K. & Pesendorfer, Wolfgang, 2007. "The evolution of cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 58(2), pages 293-315, February. [Downloadable!] (restricted)
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  3. Lawrence Blume, 1993. "The Statistical Mechanics of Best-Response Strategy Revision," Game Theory and Information 9307001, EconWPA, revised 26 Jan 1994. [Downloadable!]
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  4. Ellison, Glenn & Fudenberg, Drew, 1993. "Rules of Thumb for Social Learning," Journal of Political Economy, University of Chicago Press, vol. 101(4), pages 612-43, August. [Downloadable!] (restricted)
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  5. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September. [Downloadable!] (restricted)
  6. Alos-Ferrer, Carlos & Ania, Ana B. & Schenk-Hoppe, Klaus Reiner, 2000. "An Evolutionary Model of Bertrand Oligopoly," Games and Economic Behavior, Elsevier, vol. 33(1), pages 1-19, October. [Downloadable!] (restricted)
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  7. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February. [Downloadable!] (restricted)
  8. Reinhard Selten & Axel Ostmann, 2000. "Imitation Equilibrium," Bonn Econ Discussion Papers bgse16_2000, University of Bonn, Germany. [Downloadable!]
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  9. Kalai, Ehud & Lehrer, Ehud, 1991. "Rational Learning Leads to Nash Equilibrium," Working Papers 91-18, C.V. Starr Center for Applied Economics, New York University. [Downloadable!]
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  12. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February. [Downloadable!] (restricted)
  13. Robson, Arthur J. & Vega-Redondo, Fernando, 1996. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Journal of Economic Theory, Elsevier, vol. 70(1), pages 65-92, July. [Downloadable!] (restricted)
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  14. David K Levine & Wolfgang Pesendorfer, 2000. "Evolution Through Imitation in a Single Population," Levine's Working Paper Archive 2122, David K. Levine. [Downloadable!]
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  17. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May. [Downloadable!] (restricted)
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  19. Clark, Andrew E. & Oswald, Andrew J., 1996. "Satisfaction and comparison income," Journal of Public Economics, Elsevier, vol. 61(3), pages 359-381, September. [Downloadable!] (restricted)
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  20. Offerman, Theo & Potters, Jan & Sonnemans, Joep, 2002. "Imitation and Belief Learning in an Oligopoly Experiment," Review of Economic Studies, Blackwell Publishing, vol. 69(4), pages 973-97, October.
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  21. 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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  24. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  25. Karl H. Schlag, . "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers 028, ESRC Centre on Economics Learning and Social Evolution. [Downloadable!]
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  26. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July. [Downloadable!] (restricted)
  27. Douglas Gale & Robert W. Rosenthal, 1996. "Experimentation, Imitation, and Stochastic Stability," Papers 0065, Boston University - Industry Studies Programme.
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  28. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
  29. Rapoport, Amnon & Seale, Darryl A. & Winter, Eyal, 2002. "Coordination and Learning Behavior in Large Groups with Asymmetric Players," Games and Economic Behavior, Elsevier, vol. 39(1), pages 111-136, April. [Downloadable!] (restricted)
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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. Myrna Wooders & Edward Cartwright & Reinhard Selten, 2003. "Social Conformity in Games with Many Players," Working Papers 2003.121, Fondazione Eni Enrico Mattei. [Downloadable!]
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  3. 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!]
  4. Myrna Wooders & Edward Cartwright & Reinhard Selten, 2005. "Behavioral Conformity in Games with Many Players," Working Papers 0513, Department of Economics, Vanderbilt University. [Downloadable!]
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  5. Edward Cartwright & Myrna Wooders, 2005. "Correlated Equilibrium and Behavioral Conformity," Working Papers 0526, Department of Economics, Vanderbilt University. [Downloadable!]
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