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Two Competing Models of How People Learn in Games

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Author Info
Ed Hopkins () (University of Edinburgh)

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Abstract

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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Publisher Info
Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 70 (2002)
Issue (Month): 6 (November)
Pages: 2141-2166
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Handle: RePEc:ecm:emetrp:v:70:y:2002:i:6:p:2141-2166

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May. [Downloadable!] (restricted)
  2. Blume, A. & DeJong, D.V. & Neumann, G.R., 2000. "Learning and communication in sender-receiver games : an econometric investigation," Discussion Paper 9, Tilburg University, Center for Economic Research. [Downloadable!]
  3. 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. [Downloadable!] (restricted)
  4. George R. Neumann & Nathan E. Savin, 2000. "Learning and Communication in Sender-Receiver Games: An Econometric Investigation," Econometric Society World Congress 2000 Contributed Papers 1852, Econometric Society. [Downloadable!]
  5. Duffy, John & Hopkins, Ed, 2005. "Learning, information, and sorting in market entry games: theory and evidence," Games and Economic Behavior, Elsevier, vol. 51(1), pages 31-62, April. [Downloadable!] (restricted)
    Other versions:
  6. repec:att:wimass:199325 is not listed on IDEAS
  7. Binmore, Ken & Samuelson, Larry, 1999. "Evolutionary Drift and Equilibrium Selection," Review of Economic Studies, Blackwell Publishing, vol. 66(2), pages 363-93, April. [Downloadable!] (restricted)
  8. Erev, Ido & Roth, Alvin E, 1998. "Predicting How People Play Games: Reinforcement Learning in Experimental Games with Unique, Mixed Strategy Equilibria," American Economic Review, American Economic Association, vol. 88(4), pages 848-81, September. [Downloadable!] (restricted)
  9. Eddie Dekel & Drew Fudenberg & David K. Levine, 1999. "Payoff Information and Self-Confirming Equilibrium," Levine's Working Paper Archive 172, David K. Levine. [Downloadable!]
    Other versions:
  10. Jorgen W. Weibull, 1997. "Evolutionary Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262731215.
  11. Timothy C. Salmon, 2001. "An Evaluation of Econometric Models of Adaptive Learning," Econometrica, Econometric Society, vol. 69(6), pages 1597-1628, November. [Downloadable!] (restricted)
  12. Arthur, W Brian, 1993. "On Designing Economic Agents That Behave Like Human Agents," Journal of Evolutionary Economics, Springer, vol. 3(1), pages 1-22, February.
  13. Van Huyck, John B & Battalio, Raymond C & Rankin, Frederick W, 1997. "On the Origin of Convention: Evidence from Coordination Games," Economic Journal, Royal Economic Society, vol. 107(442), pages 576-96, May. [Downloadable!] (restricted)
  14. 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. [Downloadable!] (restricted)
  15. 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. [Downloadable!] (restricted)
    Other versions:
  16. 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. [Downloadable!] (restricted)
  17. Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207. [Downloadable!] (restricted)
  18. Hopkins, Ed, 1999. "Learning, Matching, and Aggregation," Games and Economic Behavior, Elsevier, vol. 26(1), pages 79-110, January. [Downloadable!] (restricted)
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  19. Cheung, Yin-Wong & Friedman, Daniel, 1997. "Individual Learning in Normal Form Games: Some Laboratory Results," Games and Economic Behavior, Elsevier, vol. 19(1), pages 46-76, April. [Downloadable!] (restricted)
  20. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July. [Downloadable!] (restricted)
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  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.
  22. Colin Camerer & Teck-Hua Ho, 1999. "Experience-weighted Attraction Learning in Normal Form Games," Econometrica, Econometric Society, vol. 67(4), pages 827-874, July.
  23. J.-F. Laslier & R. Topol & B. Walliser, 1999. "A behavioral learning process in games," THEMA Working Papers 99-03, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
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  24. Huck, Steffen & Normann, Hans-Theo & Oechssler, Jorg, 1999. "Learning in Cournot Oligopoly--An Experiment," Economic Journal, Royal Economic Society, vol. 109(454), pages C80-95, March. [Downloadable!] (restricted)
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  25. Josef Hofbauer & Ed Hopkins, 2004. "Learning in Perturbed Asymmetric Games," ESE Discussion Papers 53, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
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  26. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November. [Downloadable!] (restricted)
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  27. repec:att:wimass:199529 is not listed on IDEAS
  28. Vriend, Nicolaas J., 1997. "Will reasoning improve learning?," Economics Letters, Elsevier, vol. 55(1), pages 9-18, August. [Downloadable!] (restricted)
  29. Ellison, Glenn & Fudenberg, Drew, 2000. "Learning Purified Mixed Equilibria," Journal of Economic Theory, Elsevier, vol. 90(1), pages 84-115, January. [Downloadable!] (restricted)
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  30. Gaunersdorfer Andrea & Hofbauer Josef, 1995. "Fictitious Play, Shapley Polygons, and the Replicator Equation," Games and Economic Behavior, Elsevier, vol. 11(2), pages 279-303, November. [Downloadable!] (restricted)
  31. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October. [Downloadable!] (restricted)
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Dana Heller, 2000. "Parametric Adaptive Learning," Econometric Society World Congress 2000 Contributed Papers 1496, Econometric Society. [Downloadable!]
  2. Duncan Whitehead, 2008. "The El Farol Bar Problem Revisited: Reinforcement Learning in a Potential Game," ESE Discussion Papers 186, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
  3. Jim Engle-Warnick & Ed Hopkins, 2006. "A Simple Test of Learning Theory?," ESE Discussion Papers 153, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
    Other versions:
  4. Andriy Zapechelnyuk, 2009. "Limit Behavior of No-regret Dynamics," Discussion Papers 21, Kyiv School of Economics. [Downloadable!]
  5. Ed Hopkins & Josef Hofbauer & Michel Benaim, 2005. "Learning in Games with Unstable Equilibria," ESE Discussion Papers 135, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
    Other versions:
  6. Grimm, Veronika & Mengel, Friederike, 2009. "An Experiment on Learning in a Multiple Games Environment," Research Memoranda 007, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
  7. Friederike Mengel, 2007. "Learning Across Games," Working Papers. Serie AD 2007-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
  8. Wolf Ze'ev Ehrblatt & Kyle Hyndman & Erkut Y. ÄOzbay & Andrew Schotter, 2006. "Convergence: An Experimental Study," Levine's Working Paper Archive 122247000000001148, David K. Levine. [Downloadable!]
  9. Camerer, Colin F. & Ho, Teck H. & Chong, Juin-Kuan., 2000. "Sophisticated EWA Learning and Strategic Teaching in Repeated Games," Working Papers 1087, California Institute of Technology, Division of the Humanities and Social Sciences. [Downloadable!]
  10. Timothy N. Cason & Daniel Friedman & Ed Hopkins, 2009. "Testing the TASP: An Experimental Investigation of Learning in Games with Unstable Equilibria," ESE Discussion Papers 188, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
  11. Sudip Gupta, 2004. "Endogenous Asymmetry and Entry in Sequential Multi-Unit Auctions: Identification and Estimation," Econometric Society 2004 North American Summer Meetings 566, Econometric Society. [Downloadable!]
  12. Fabrizio Germano, 2007. "Stochastic Evolution of Rules for Playing Finite Normal Form Games," Theory and Decision, Springer, vol. 62(4), pages 311-333, May. [Downloadable!] (restricted)
  13. Theodore L. Turocy, 2002. "A Dynamic Homotopy Interpretation of Quantal Response Equilibrium Correspondences," Game Theory and Information 0212001, EconWPA, revised 16 Oct 2003. [Downloadable!]
  14. Josef Hofbauer & Ed Hopkins, 2004. "Learning in Perturbed Asymmetric Games," ESE Discussion Papers 53, Edinburgh School of Economics, University of Edinburgh. [Downloadable!]
    Other versions:
  15. Antonella Ianni, 2007. "Learning Strict Nash Equilibria through Reinforcement," Economics Working Papers ECO2007/21, European University Institute. [Downloadable!]
  16. Ed Hopkins, 2004. "Adaptative Learning Models of Consumer Behaviour (first version)," ESE Discussion Papers 80, Edinburgh School of Economics, University of Edinburgh.
  17. Kets, W. & Voorneveld, M., 2007. "Congestion, Equilibrium and Learning: The Minority Game," Discussion Paper 2007-61, Tilburg University, Center for Economic Research. [Downloadable!]
  18. Ed Hopkins, 2003. "Adaptive Learning Models of Consumer Behaviour," Levine's Bibliography 506439000000000346, UCLA Department of Economics. [Downloadable!]
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  19. Ed Hopkins & Martin Posch, 2003. "Attainability of Boundary Points under Reinforcement Learning," Levine's Bibliography 506439000000000350, UCLA Department of Economics. [Downloadable!]
    Other versions:
  20. repec:att:wimass:1919982 is not listed on IDEAS
  21. Reinoud Joosten & Berend Roorda, 2008. "Generalized projection dynamics in evolutionary game theory," Papers on Economics and Evolution 2008-11, Max Planck Institute of Economics, Evolutionary Economics Group. [Downloadable!]
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