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

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  • Cartwright, Edward

    (Department of Economics, EUREQua)

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/workingpapers/2008/twerp684.pdf
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Bibliographic Info

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

References

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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.
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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.
  4. Edward Cartwright, 2004. "Learning to Play Approximate Nash Equilibria in Games with Many Players," Working Papers 2004.85, Fondazione Eni Enrico Mattei.
  5. Allison, G. & Fudenberg, D., 1992. "Rules of Thumb for Social Learning," Working papers 92-12, Massachusetts Institute of Technology (MIT), Department of Economics.
  6. Reinhard Selten & Axel Ostmann, 2001. "Imitation Equilibrium," Homo Oeconomicus, Institute of SocioEconomics, vol. 18, pages 111-149.
  7. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  8. 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.
  9. 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.
  10. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February.
  11. A. Banerjee & Drew Fudenberg, 2010. "Word-of-Mouth Communication and Social Learning," Levine's Working Paper Archive 425, David K. Levine.
  12. Gale, D. & Rosental, R.W., 1996. "Experimentation, Imitation, and Stochastic Stability," Papers 65, Boston University - Industry Studies Programme.
  13. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
  14. Selten, Reinhard & Apesteguia, Jose, 2005. "Experimentally observed imitation and cooperation in price competition on the circle," Games and Economic Behavior, Elsevier, vol. 51(1), pages 171-192, April.
  15. Selten, Reinhard, . "Features of Experimentally Observed Bounded Rationality," Discussion Paper Serie B 421, University of Bonn, Germany, revised Nov 1997.
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  18. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-77, October.
  19. 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.
  20. Clark, Andrew E. & Oswald, Andrew J., 1996. "Satisfaction and comparison income," Journal of Public Economics, Elsevier, vol. 61(3), pages 359-381, September.
  21. Offerman, Theo & Potters, Jan & Sonnemans, Joep, 2002. "Imitation and Belief Learning in an Oligopoly Experiment," Review of Economic Studies, Wiley Blackwell, vol. 69(4), pages 973-97, October.
  22. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  23. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November.
  24. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  25. 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.
  26. 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.
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