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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. 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.
  2. Andrew E. Clark and Andrew J. Oswald, . "Satisfaction and Comparison Income," Economics Discussion Papers 419, University of Essex, Department of Economics.
  3. 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.
  4. 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.
  5. Ana B. Ania & Carlos Alós-Ferrer & Klaus R. Schenk-Hoppé, 1998. "- An Evolutionary Model Of Bertrand Oligopoly," Working Papers. Serie AD 1998-14, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  6. David K Levine & Wolfgang Pesendorfer, 2000. "Evolution Through Imitation in a Single Population," Levine's Working Paper Archive 2122, David K. Levine.
  7. 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.
  8. Selten, Reinhard, . "Features of Experimentally Observed Bounded Rationality," Discussion Paper Serie B 421, University of Bonn, Germany, revised Nov 1997.
  9. 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.
  10. Levine, David K. & Pesendorfer, Wolfgang, 2007. "The evolution of cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 58(2), pages 293-315, February.
  11. Gale, D. & Rosental, R.W., 1996. "Experimentation, Imitation, and Stochastic Stability," Papers 65, Boston University - Industry Studies Programme.
  12. Fernando Vega Redondo, 1996. "The evolution of walrasian behavior," Working Papers. Serie AD 1996-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  13. Lawrence Blume, 1993. "The Statistical Mechanics of Best-Response Strategy Revision," Game Theory and Information 9307001, EconWPA, revised 26 Jan 1994.
  14. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  15. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May.
  16. Reinhard Selten & Axel Ostmann, 2000. "Imitation Equilibrium," Bonn Econ Discussion Papers bgse16_2000, University of Bonn, Germany.
  17. Ritzberger, Klaus & Weibull, Jorgen W, 1995. "Evolutionary Selection in Normal-Form Games," Econometrica, Econometric Society, vol. 63(6), pages 1371-99, November.
  18. Ellison, Glenn & Fudenberg, Drew, 1992. "Rules of Thumb for Social Learning," IDEI Working Papers 17, Institut d'Économie Industrielle (IDEI), Toulouse.
  19. Cartwright, Edward, 2003. "Learning To Play Approximate Nash Equilibria In Games With Many Players," The Warwick Economics Research Paper Series (TWERPS) 671, University of Warwick, Department of Economics.
  20. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
  21. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-77, October.
  22. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February.
  23. 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.
  24. Myrna Wooders & Edward Cartwright & Reinhard Selten, 2003. "Social Conformity in Games with Many Players," Working Papers 2003.121, Fondazione Eni Enrico Mattei.
  25. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  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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