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

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Author Info
Cartwright, Edward (Department of Economics, EUREQua)

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Abstract

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/papers/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
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Handle: RePEc:wrk:warwec:684

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Keywords: imitation best reply convergence Nash equilibrium

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  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)
  2. 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. [Downloadable!]
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  3. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May. [Downloadable!] (restricted)
  4. 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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  5. 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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  6. 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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  7. Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2003. "Social Conformity in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS) 682, University of Warwick, Department of Economics. [Downloadable!]
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  8. 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. [Downloadable!] (restricted)
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  9. 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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  10. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
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  11. 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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  12. 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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  13. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November. [Downloadable!] (restricted)
  14. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February. [Downloadable!] (restricted)
  15. Reinhard Selten & Axel Ostmann, 2000. "Imitation Equilibrium," Bonn Econ Discussion Papers bgse16_2000, University of Bonn, Germany. [Downloadable!]
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  16. Edward Cartwright, 2002. "Learning to play approximate Nash equilibria in games with many players," Levine's Working Paper Archive 506439000000000070, UCLA Department of Economics. [Downloadable!]
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  17. Ellison, Glenn & Fudenberg, Drew, 1995. "Word-of-Mouth Communication and Social Learning," The Quarterly Journal of Economics, MIT Press, vol. 110(1), pages 93-125, February. [Downloadable!] (restricted)
  18. 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. [Downloadable!]
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  19. Douglas Gale & Robert W. Rosenthal, 1996. "Experimentation, Imitation, and Stochastic Stability," Papers 0065, Boston University - Industry Studies Programme.
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  20. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
  22. David K Levine & Wolfgang Pesendorfer, 2000. "Evolution Through Imitation in a Single Population," Levine's Working Paper Archive 2122, UCLA Department of Economics. [Downloadable!]
  23. 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. [Downloadable!] (restricted)
  24. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-77, October. [Downloadable!] (restricted)
  25. Selten, Reinhard, 1998. "Features of experimentally observed bounded rationality," European Economic Review, Elsevier, vol. 42(3-5), pages 413-436, May. [Downloadable!] (restricted)
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