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Imitation and the Emergence of Nash Equilibrium Play in Games with Many Players

  • Cartwright, Edward

    (Department of Economics, EUREQua)

We model a learning dynamic in which players imitate and innovate. Of interest is to question whether Nash equilibrium play emerges, and if so, the role that imitation plays in this emergence. Our main result provides a general class of coordination games for which approximate Nash equilibrium play does emerge. Important conditions include that players imitate "similar" individuals. The role of imitation in learning is discussed in the context of two examples where it is shown that imitation can lead to pareto superio outcomes.

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File URL: http://www2.warwick.ac.uk/fac/soc/economics/research/workingpapers/2008/twerp684.pdf
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Paper provided by University of Warwick, Department of Economics in its series The Warwick Economics Research Paper Series (TWERPS) with number 684.

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Length: 29 pages
Date of creation: 2003
Date of revision:
Handle: RePEc:wrk:warwec:684
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Web page: http://www2.warwick.ac.uk/fac/soc/economics/
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  1. Gale, D. & Rosental, R.W., 1996. "Experimentation, Imitation, and Stochastic Stability," Papers 65, Boston University - Industry Studies Programme.
  2. Theo Offerman & Jan Potters & Joep Sonnemans, 2002. "Imitation and Belief Learning in an Oligopoly Experiment," Review of Economic Studies, Oxford University Press, vol. 69(4), pages 973-997.
  3. Lawrence Blume, 1993. "The Statistical Mechanics of Best-Response Strategy Revision," Game Theory and Information 9307001, EconWPA, revised 26 Jan 1994.
  4. Fudenberg, Drew & Ellison, Glenn, 1995. "Word-of-Mouth Communication and Social Learning," Scholarly Articles 3196300, Harvard University Department of Economics.
  5. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May.
  6. 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.
  7. K. Ritzberger & J. Weibull, 2010. "Evolutionary Selection in Normal-Form Games," Levine's Working Paper Archive 452, David K. Levine.
  8. Sergiu Hart & Andreu Mas-Colell, 2003. "Uncoupled Dynamics Do Not Lead to Nash Equilibrium," American Economic Review, American Economic Association, vol. 93(5), pages 1830-1836, December.
  9. Clark, Andrew E. & Oswald, Andrew J., 1996. "Satisfaction and comparison income," Journal of Public Economics, Elsevier, vol. 61(3), pages 359-381, September.
  10. Myrna Wooders & Edward Cartwright & Reinhard Selten, 2003. "Social Conformity in Games with Many Players," Working Papers 2003.121, Fondazione Eni Enrico Mattei.
  11. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-77, October.
  12. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February.
  13. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  14. Reinhard Selten & Axel Ostmann, 2001. "Imitation Equilibrium," Homo Oeconomicus, Institute of SocioEconomics, vol. 18, pages 111-149.
  15. 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.
  16. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
  17. 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.
  18. Karl H. Schlag, 1995. "Why Imitate, and if so, How? A Bounded Rational Approach to Multi-Armed Bandits," Discussion Paper Serie B 361, University of Bonn, Germany, revised Mar 1996.
  19. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  20. Selten, Reinhard, 1998. "Features of experimentally observed bounded rationality," European Economic Review, Elsevier, vol. 42(3-5), pages 413-436, May.
  21. Levine, David K. & Pesendorfer, Wolfgang, 2007. "The evolution of cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 58(2), pages 293-315, February.
  22. repec:ner:tilbur:urn:nbn:nl:ui:12-91663 is not listed on IDEAS
  23. Cartwright, Edward & Wooders, Myrna, 2003. "Conformity and Bounded Rationality in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS) 687, University of Warwick, Department of Economics.
  24. Edward Cartwright, 2002. "Learning to play approximate Nash equilibria in games with many players," Levine's Working Paper Archive 506439000000000070, David K. Levine.
  25. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  26. David K Levine & Wolfgang Pesendorfer, 2000. "Evolution Through Imitation in a Single Population," Levine's Working Paper Archive 2122, David K. Levine.
  27. 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.
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