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Two Competing Models of How People Learn in Games

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  • Ed Hopkins

    (University of Edinburgh)

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.

Suggested Citation

  • Ed Hopkins, 2002. "Two Competing Models of How People Learn in Games," Econometrica, Econometric Society, vol. 70(6), pages 2141-2166, November.
    • Handle: RePEc:ecm:emetrp:v:70:y:2002:i:6:p:2141-2166
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    References listed on IDEAS

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    1. Fudenberg Drew & Kreps David M., 1993. "Learning Mixed Equilibria," Games and Economic Behavior, Elsevier, vol. 5(3), pages 320-367, July.
    2. Sarin, Rajiv & Vahid, Farshid, 2001. "Predicting How People Play Games: A Simple Dynamic Model of Choice," Games and Economic Behavior, Elsevier, vol. 34(1), pages 104-122, January.
    3. Dekel, Eddie & Fudenberg, Drew & Levine, David K., 1999. "Payoff Information and Self-Confirming Equilibrium," Journal of Economic Theory, Elsevier, vol. 89(2), pages 165-185, December.
    4. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    5. 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 848-881, September.
    6. 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.
    7. Hopkins, Ed, 1999. "Learning, Matching, and Aggregation," Games and Economic Behavior, Elsevier, vol. 26(1), pages 79-110, January.
    8. 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.
    9. 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.
    10. Martin Posch, 1997. "Cycling in a stochastic learning algorithm for normal form games," Journal of Evolutionary Economics, Springer, vol. 7(2), pages 193-207.
    11. 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.
    12. Huck, Steffen & Normann, Hans-Theo & Oechssler, Jorg, 1999. "Learning in Cournot Oligopoly--An Experiment," Economic Journal, Royal Economic Society, vol. 109(454), pages 80-95, March.
    13. 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.
    14. Borgers, Tilman & Sarin, Rajiv, 1997. "Learning Through Reinforcement and Replicator Dynamics," Journal of Economic Theory, Elsevier, vol. 77(1), pages 1-14, November.
    15. 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.
    16. Ken Binmore & Larry Samuelson, 1999. "Evolutionary Drift and Equilibrium Selection," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(2), pages 363-393.
    17. 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 576-596, May.
    18. 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.
    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. Ken Binmore & Larry Samuelson, "undated". "Evolutionary Drift And Equilibrium Selection," ELSE working papers 049, ESRC Centre on Economics Learning and Social Evolution.
    21. Vriend, Nicolaas J., 1997. "Will reasoning improve learning?," Economics Letters, Elsevier, vol. 55(1), pages 9-18, August.
    22. 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.
    23. Drew Fudenberg & David K. Levine, 1998. "The Theory of Learning in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061945, December.
    24. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July.
    25. Nick Feltovich & John Duffy, 1999. "Does observation of others affect learning in strategic environments? An experimental study," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(1), pages 131-152.
    26. Ken Binmore & Larry Samuelson, "undated". "Evolutionary Drift and Equilibrium Selection," ELSE working papers 011, ESRC Centre on Economics Learning and Social Evolution.
    27. Rustichini, Aldo, 1999. "Optimal Properties of Stimulus--Response Learning Models," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 244-273, October.
    28. Ellison, Glenn & Fudenberg, Drew, 2000. "Learning Purified Mixed Equilibria," Journal of Economic Theory, Elsevier, vol. 90(1), pages 84-115, January.
    29. 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.
    30. 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.
    31. Nick Feltovich, 2000. "Reinforcement-Based vs. Belief-Based Learning Models in Experimental Asymmetric-Information," Econometrica, Econometric Society, vol. 68(3), pages 605-642, May.
    32. 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.
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    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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