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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. Rapoport, Amnon & Seale, Darryl A. & Winter, Eyal, 2002. "Coordination and Learning Behavior in Large Groups with Asymmetric Players," Games and Economic Behavior, Elsevier, Elsevier, vol. 39(1), pages 111-136, April.
  2. Robson, Arthur J. & Vega-Redondo, Fernando, 1996. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Journal of Economic Theory, Elsevier, Elsevier, vol. 70(1), pages 65-92, July.
  3. Venkatesh Bala & Sanjeev Goyal, 2000. "A Noncooperative Model of Network Formation," Econometrica, Econometric Society, Econometric Society, vol. 68(5), pages 1181-1230, September.
  4. Selten, Reinhard, . "Features of Experimentally Observed Bounded Rationality," Discussion Paper Serie B, University of Bonn, Germany 421, University of Bonn, Germany, revised Nov 1997.
  5. Karl H. Schlag, . "Why Imitate, and if so, How? A Bounded Rational Approach to Multi- Armed Bandits," ELSE working papers, ESRC Centre on Economics Learning and Social Evolution 028, ESRC Centre on Economics Learning and Social Evolution.
  6. Kirman, Alan, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 108(1), pages 137-56, February.
  7. Ana B. Ania & Carlos Alós-Ferrer & Klaus R. Schenk-Hoppé, 1998. "- An Evolutionary Model Of Bertrand Oligopoly," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 1998-14, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  8. 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), University of Warwick, Department of Economics 636, University of Warwick, Department of Economics.
  9. Matthew O. Jackson & Asher Wolinsky, 1994. "A Strategic Model of Social and Economic Networks," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1098, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  10. Selten, Reinhard & Apesteguia, Jose, 2005. "Experimentally observed imitation and cooperation in price competition on the circle," Games and Economic Behavior, Elsevier, Elsevier, vol. 51(1), pages 171-192, April.
  11. Blume Lawrence E., 1995. "The Statistical Mechanics of Best-Response Strategy Revision," Games and Economic Behavior, Elsevier, Elsevier, vol. 11(2), pages 111-145, November.
  12. L. Blume, 2010. "The Statistical Mechanics of Strategic Interaction," Levine's Working Paper Archive 488, David K. Levine.
  13. Ehud Kalai & Ehud Lehrer, 1990. "Rational Learning Leads to Nash Equilibrium," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 895, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  14. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, Econometric Society, vol. 61(5), pages 1047-71, September.
  15. Fernando Vega Redondo, 1996. "The evolution of walrasian behavior," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 1996-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  16. Andrew E. Clark and Andrew J. Oswald, . "Satisfaction and Comparison Income," Economics Discussion Papers, University of Essex, Department of Economics 419, University of Essex, Department of Economics.
  17. Levine, David K. & Pesendorfer, Wolfgang, 2007. "The evolution of cooperation through imitation," Games and Economic Behavior, Elsevier, Elsevier, vol. 58(2), pages 293-315, February.
  18. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers, Princeton, Woodrow Wilson School - John M. Olin Program 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  19. Ellison, Glenn & Fudenberg, Drew, 1993. "Rules of Thumb for Social Learning," Scholarly Articles 3196332, Harvard University Department of Economics.
  20. Drew Fudenberg & David K. Levine, 1998. "Learning in Games," Levine's Working Paper Archive 2222, David K. Levine.
  21. Schlag, Karl H., 1999. "Which one should I imitate?," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 31(4), pages 493-522, May.
  22. Offerman, Theo & Potters, Jan & Sonnemans, Joep, 2002. "Imitation and Belief Learning in an Oligopoly Experiment," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 69(4), pages 973-97, October.
  23. Reinhard Selten & Axel Ostmann, 2000. "Imitation Equilibrium," Bonn Econ Discussion Papers, University of Bonn, Germany bgse16_2000, University of Bonn, Germany.
  24. Gale, D. & Rosental, R.W., 1996. "Experimentation, Imitation, and Stochastic Stability," Papers, Boston University - Industry Studies Programme 65, Boston University - Industry Studies Programme.
  25. Fudenberg, Drew & Ellison, Glenn, 1995. "Word-of-Mouth Communication and Social Learning," Scholarly Articles 3196300, Harvard University Department of Economics.
  26. David K Levine & Wolfgang Pesendorfer, 2000. "Evolution Through Imitation in a Single Population," Levine's Working Paper Archive 2122, David K. Levine.
  27. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, Econometric Society, vol. 61(1), pages 57-84, January.
  28. Watts, Alison, 2001. "A Dynamic Model of Network Formation," Games and Economic Behavior, Elsevier, Elsevier, vol. 34(2), pages 331-341, February.
  29. Bernheim, B Douglas, 1994. "A Theory of Conformity," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 102(5), pages 841-77, October.
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Citations

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Cited by:
  1. Cartwright, Edward & Wooders, Myrna, 2005. "Correlated equilibrium and behavioural conformity," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 732, University of Warwick, Department of Economics.
  2. Cartwright, Edward, 2003. "Imitation and the Emergence of Nash Equilibrium Play in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 684, University of Warwick, Department of Economics.
  3. Edward Cartwright, 2004. "Contagion and the Emergence of Convention in Small Worlds," Studies in Economics, Department of Economics, University of Kent 0414, Department of Economics, University of Kent.
  4. Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2003. "Social Conformity in Games with Many Players," The Warwick Economics Research Paper Series (TWERPS), University of Warwick, Department of Economics 682, University of Warwick, Department of Economics.
  5. Wooders, Myrna & Cartwright, Edward & Selten, Reinhard, 2006. "Behavioral conformity in games with many players," Games and Economic Behavior, Elsevier, Elsevier, vol. 57(2), pages 347-360, November.

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