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Learning in Games with Unstable Equilibria

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Author Info
Ed Hopkins ()
Josef Hofbauer
Michel Benaim

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Abstract

We investigate games whose Nash equilibria are mixed and are unstable under fictitious play-like learning processes. We show that when players learn using weighted stochastic fictitious play and so place greater weight on more recent experience that the time average of play often converges in these “unstable” games, even while mixed strategies and beliefs continue to cycle. This time average is related to the best response cycle first identified by Shapley (1964). For many games, the time average is close enough to Nash equilibrium to create the appearance of convergence to equilibrium. We discuss how these theoretical results may help to explain data from recent experimental studies of price dispersion.

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Publisher Info
Paper provided by Edinburgh School of Economics, University of Edinburgh in its series ESE Discussion Papers with number 135.

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Length: 36
Date of creation: Jul 2005
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Handle: RePEc:edn:esedps:135

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Related research
Keywords: Games; Learning; Best Response Dynamics; Stochastic Fictitious Play; Mixed Strategy Equilibria; TASP.;

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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
D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations

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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.:
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  6. Glenn Ellison & Drew Fudenberg, 1998. "Learning Purified Mixed Equilibria," Harvard Institute of Economic Research Working Papers 1817, Harvard - Institute of Economic Research.
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  13. Cason, Timothy N. & Friedman, Daniel & Wagener, Florian, 2005. "The dynamics of price dispersion, or Edgeworth variations," Journal of Economic Dynamics and Control, Elsevier, vol. 29(4), pages 801-822, April. [Downloadable!] (restricted)
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  16. 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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  17. Varian, Hal R, 1980. "A Model of Sales," American Economic Review, American Economic Association, vol. 70(4), pages 651-59, September. [Downloadable!] (restricted)
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  19. 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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  24. Josef Hofbauer & William H. Sandholm, 2002. "On the Global Convergence of Stochastic Fictitious Play," Econometrica, Econometric Society, vol. 70(6), pages 2265-2294, November. [Downloadable!] (restricted)
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  31. 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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  32. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-67, May. [Downloadable!] (restricted)
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  34. 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. Aurora García-Gallego & Nikolaos Georgantzís & Pedro Pereira & José C. Pernías-Cerrillo, 2007. "Bias and Size Effects of Price-Comparison Search Engines: Theory and Experimental Evidence," Working Papers 20, Portuguese Competition Authority. [Downloadable!]
  2. Roger Waldeck & Eric Darmon, 2006. "Can boundedly rational sellers learn to play Nash?," Journal of Economic Interaction and Coordination, Springer, vol. 1(2), pages 147-169, November. [Downloadable!] (restricted)
  3. Jim Engle-Warnick & Ed Hopkins, 2006. "A Simple Test of Learning Theory," CIRANO Working Papers 2006s-30, CIRANO. [Downloadable!]
    Other versions:
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