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Learning to play approximate Nash equilibria in games with many players

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  • Edward Cartwright

Abstract

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 David K. Levine in its series Levine's Working Paper Archive with number 506439000000000070.

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Date of creation: 20 Dec 2002
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Handle: RePEc:cla:levarc:506439000000000070

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  1. Fernando Vega-Redondo, 1997. "The Evolution of Walrasian Behavior," Econometrica, Econometric Society, vol. 65(2), pages 375-384, March.
  2. Allison, G. & Fudenberg, D., 1992. "Rules of Thumb for Social Learning," Working papers 92-12, Massachusetts Institute of Technology (MIT), Department of Economics.
  3. Reinhard Selten & Axel Ostmann, 2001. "Imitation Equilibrium," Homo Oeconomicus, Institute of SocioEconomics, vol. 18, pages 111-149.
  4. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, vol. 31(4), pages 493-522, May.
  5. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  6. 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.
  7. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, vol. 102(5), pages 841-77, October.
  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.
  9. David K Levine & Wolfgang Pesendorfer, 2000. "Evolution Through Imitation in a Single Population," Levine's Working Paper Archive 2122, David K. Levine.
  10. Gale, D. & Rosental, R.W., 1996. "Experimentation, Imitation, and Stochastic Stability," Papers 65, Boston University - Industry Studies Programme.
  11. Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers 925, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  12. Offerman, T.J.S. & Potters, J.J.M. & Sonnemans, J., 2002. "Imitation and belief learning in an oligopoly experiment," Open Access publications from Tilburg University urn:nbn:nl:ui:12-91663, Tilburg University.
  13. 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.
  14. Clark, Andrew E. & Oswald, Andrew J., 1994. "Satisfaction and comparison income," CEPREMAP Working Papers (Couverture Orange) 9408, CEPREMAP.
  15. Levine, David K. & Pesendorfer, Wolfgang, 2007. "The evolution of cooperation through imitation," Games and Economic Behavior, Elsevier, vol. 58(2), pages 293-315, February.
  16. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  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. 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.
  19. Lawrence Blume, 1993. "The Statistical Mechanics of Best-Response Strategy Revision," Game Theory and Information 9307001, EconWPA, revised 26 Jan 1994.
  20. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, vol. 108(1), pages 137-56, February.
  21. 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.
  22. Glen Ellison, 2010. "Learning, Local Interaction, and Coordination," Levine's Working Paper Archive 391, David K. Levine.
  23. Schlag, Karl H., 1994. "Why Imitate, and if so, How? Exploring a Model of Social Evolution," Discussion Paper Serie B 296, University of Bonn, Germany.
  24. 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).
  25. Selten, Reinhard, 1998. "Features of experimentally observed bounded rationality," European Economic Review, Elsevier, vol. 42(3-5), pages 413-436, May.
  26. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, vol. 68(5), pages 1181-1230, September.
  27. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, vol. 34(2), pages 331-341, February.
  28. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  29. 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.
  30. 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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Cited by:
  1. Edward Cartwright & Myrna Wooders, 2005. "Correlated Equilibrium and Behavioral Conformity," Vanderbilt University Department of Economics Working Papers 0526, Vanderbilt University Department of Economics.
  2. Myrna Wooders & Edward Cartwright & Reinhard Selten, 2003. "Social Conformity in Games with Many Players," Working Papers 2003.121, Fondazione Eni Enrico Mattei.
  3. Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2006. "Behavioral conformity in games with many players," Games and Economic Behavior, Elsevier, vol. 57(2), pages 347-360, November.
  4. Cartwright, Edward, 2003. "Imitation and the Emergence of Nash Equilibrium Play in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS) 684, University of Warwick, Department of Economics.
  5. Edward Cartwright, 2004. "Contagion and the Emergence of Convention in Small Worlds," Studies in Economics 0414, Department of Economics, University of Kent.

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