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A Simple Test of Learning Theory?

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Author Info
Jim Engle-Warnick
Ed Hopkins ()

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Abstract

We report experiments designed to test the theoretical possibility, first discovered by Shapley (1964), that in some games learning fails to converge to any equilibrium, either in terms of marginal frequencies or of average play. Subjects played repeatedly in fixed pairings one of two 3 × 3 games, each having a unique Nash equilibrium in mixed strategies. The equilibrium of one game is predicted to be stable under learning, the other unstable, provided payoffs are sufficiently high. We ran each game in high and low payoff treatments. We find that, in all treatments, average play is close to equilibrium even though there are strong cycles present in the data.

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Publisher Info
Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 153.

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Length: 29
Date of creation: Dec 2006
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Handle: RePEc:edn:esedps:153

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Related research
Keywords: : Games; Learning; Experiments; Stochastic Fictitious Play; Mixed Strategy Equilibria.;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
C92 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Group Behavior
D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information

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References listed on IDEAS
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    Other versions:
  4. Simon P. Anderson & Jacob K. Goeree & Charles A. Holt, 2002. "The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies," Southern Economic Journal, Southern Economic Association, vol. 69(1), pages 21-47, July.
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  5. 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)
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  15. Cason, Timothy N. & Friedman, Daniel, 2003. "Buyer search and price dispersion: a laboratory study," Journal of Economic Theory, Elsevier, vol. 112(2), pages 232-260, October. [Downloadable!] (restricted)
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  16. 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)
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  21. Sergiu Hart & Andreu Mas-Colell, 2000. "A Simple Adaptive Procedure Leading to Correlated Equilibrium," Econometrica, Econometric Society, vol. 68(5), pages 1127-1150, September.
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  22. Hofbauer, Josef & Hopkins, Ed, 2005. "Learning in perturbed asymmetric games," Games and Economic Behavior, Elsevier, vol. 52(1), pages 133-152, July. [Downloadable!] (restricted)
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  23. Brown, James N & Rosenthal, Robert W, 1990. "Testing the Minimax Hypothesis: A Re-examination of O'Neill's Game Experiment," Econometrica, Econometric Society, vol. 58(5), pages 1065-81, September. [Downloadable!] (restricted)
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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. Michel Benaim & Josef Hofbauer & Ed Hopkins, 2005. "Learning in Games with Unstable Equilibria," Levine's Bibliography 784828000000000609, UCLA Department of Economics. [Downloadable!]
    Other versions:
  2. Jim Engle-Warnick, 2007. "Five Indefinitely Repeated Games in the Laboratory," CIRANO Working Papers 2007s-11, CIRANO. [Downloadable!]
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