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Two Competing Models of How People Learn in Games

  • Ed Hopkins

Reinforcement learning and stochastic fictitious play are apparent rivals as models of human learning. They embody quite different assumptions about the processing of information and optimization. This paper compares their properties and finds that they are far more similar than were thought. In particular, the expected motion of stochastic fictitious play and reinforcement learning with experimentation can both be written as a perturbed form of the evolutionary replicator dynamics. Therefore they will in many cases have the same asymptotic behavior. In particular, local stability of mixed equilibria under stochastic fictitious play implies local stability under perturbed reinforcement learning. The main identifiable difference between the two models is speed: stochastic fictitious play gives rise to faster learning. Copyright The Econometric Society 2002.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 625018000000000226.

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Date of creation: 21 Sep 2001
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Handle: RePEc:cla:levarc:625018000000000226
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  1. McKelvey Richard D. & Palfrey Thomas R., 1995. "Quantal Response Equilibria for Normal Form Games," Games and Economic Behavior, Elsevier, vol. 10(1), pages 6-38, July.
  2. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
  3. Nick Feltovich & John Duffy, 1999. "Does observation of others affect learning in strategic environments? An experimental study," International Journal of Game Theory, Springer, vol. 28(1), pages 131-152.
  4. Sarin, R. & Vahid, F., 1999. "Predicting how People Play Games: a Simple Dynamic Model of Choice," Monash Econometrics and Business Statistics Working Papers 12/99, Monash University, Department of Econometrics and Business Statistics.
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  8. Roth, Alvin E. & Erev, Ido, 1995. "Learning in extensive-form games: Experimental data and simple dynamic models in the intermediate term," Games and Economic Behavior, Elsevier, vol. 8(1), pages 164-212.
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  11. A. Gaunersdorfer & J. Hofbauer, 2010. "Fictitious Play, Shapley Polygons and the Replicator Equation," Levine's Working Paper Archive 438, David K. Levine.
  12. Binmore, Ken & Samuelson, Larry, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Wiley Blackwell, vol. 66(2), pages 363-93, April.
  13. David J. Cooper & Susan Garvin & John H. Kagel, 1997. "Signalling and Adaptive Learning in an Entry Limit Pricing Game," RAND Journal of Economics, The RAND Corporation, vol. 28(4), pages 662-683, Winter.
  14. Rustichini, Aldo, 1999. "Optimal Properties of Stimulus--Response Learning Models," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 244-273, October.
  15. Vriend, Nicolaas J., 1997. "Will reasoning improve learning?," Economics Letters, Elsevier, vol. 55(1), pages 9-18, August.
  16. Gale, John & Binmore, Kenneth G. & Samuelson, Larry, 1995. "Learning to be imperfect: The ultimatum game," Games and Economic Behavior, Elsevier, vol. 8(1), pages 56-90.
  17. John Duffy & Ed Hopkins, 2010. "Learning, Information and Sorting in Market Entry Games: Theory and Evidence," Levine's Working Paper Archive 506439000000000355, David K. Levine.
  18. Benaim, Michel & Hirsch, Morris W., 1999. "Mixed Equilibria and Dynamical Systems Arising from Fictitious Play in Perturbed Games," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 36-72, October.
  19. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  20. Andreas Blume & Douglas V. DeJong & George R. Neumann & N. E. Savin, 2002. "Learning and communication in sender-receiver games: an econometric investigation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(3), pages 225-247.
  21. Nick Feltovich, 2000. "Reinforcement-Based vs. Belief-Based Learning Models in Experimental Asymmetric-Information," Econometrica, Econometric Society, vol. 68(3), pages 605-642, May.
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