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Learning to Play Approximate Nash Equilibria in Games with Many Players

  • Edward Cartwright

    (Department of Economics, University of Warwick)

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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  1. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  2. Reinhard Selten & Axel Ostmann, 2001. "Imitation Equilibrium," Homo Oeconomicus, Institute of SocioEconomics, vol. 18, pages 111-149.
  3. 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.
  4. Selten, Reinhard, 1998. "Features of experimentally observed bounded rationality," European Economic Review, Elsevier, vol. 42(3-5), pages 413-436, May.
  5. Douglas Gale & Robert W. Rosenthal, 1996. "Experimentation, Imitation, and Stochastic Stability," Papers 0065, Boston University - Industry Studies Programme.
  6. Schlag, Karl H., 1996. "Which one should I imitate?," Discussion Paper Serie B 365, University of Bonn, Germany.
  7. Ellison, Glenn & Fudenberg, Drew, 1993. "Rules of Thumb for Social Learning," Scholarly Articles 3196332, Harvard University Department of Economics.
  8. 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.
  9. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-77, October.
  10. Kalai, Ehud & Lehrer, Ehud, 1993. "Rational Learning Leads to Nash Equilibrium," Econometrica, Econometric Society, vol. 61(5), pages 1019-45, September.
  11. Levine, David K. & Pesendorfer, Wolfgang, 2007. "The evolution of cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 58(2), pages 293-315, February.
  12. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  13. David K Levine & Wolfgang Pesendorfer, 2000. "Evolution Through Imitation in a Single Population," Levine's Working Paper Archive 2122, David K. Levine.
  14. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
  15. 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.
  16. Offerman, T.J.S. & Potters, J.J.M. & Sonnemans, J., 2002. "Imitation and belief learning in an oligopoly experiment," Other publications TiSEM a6a771c5-31ba-4193-8f76-a, Tilburg University, School of Economics and Management.
  17. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  18. Clark, Andrew E. & Oswald, Andrew J., 1994. "Satisfaction and comparison income," CEPREMAP Working Papers (Couverture Orange) 9408, CEPREMAP.
  19. Reinhard Selten & Jose Apesteguia, 2002. "Experimentally Observed Imitation and Cooperation in Price Competition on the Circle," Bonn Econ Discussion Papers bgse19_2002, University of Bonn, Germany.
  20. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February.
  21. 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.
  22. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
  23. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  24. Lawrence Blume, 1993. "The Statistical Mechanics of Best-Response Strategy Revision," Game Theory and Information 9307001, EconWPA, revised 26 Jan 1994.
  25. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  26. 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.
  27. Fudenberg, Drew & Ellison, Glenn, 1995. "Word-of-Mouth Communication and Social Learning," Scholarly Articles 3196300, Harvard University Department of Economics.
  28. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
  29. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
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