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Learning in games with unstable equilibria

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Author Info
Benaïm, Michel
Hofbauer, Josef
Hopkins, Ed

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Abstract

We propose a new concept for the analysis of games, the TASP, which gives a precise prediction about non-equilibrium play in games whose Nash equilibria are mixed and are unstable under fictitious play-like learning. We show that, when players learn using weighted stochastic fictitious play and so place greater weight on recent experience, the time average of play often converges in these "unstable" games, even while mixed strategies and beliefs continue to cycle. This time average, the TASP, is related to the cycle identified by Shapley [L.S. Shapley, Some topics in two person games, in: M. Dresher, et al. (Eds.), Advances in Game Theory, Princeton University Press, Princeton, 1964]. The TASP can be close to or quite distinct from Nash equilibrium.

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Publisher Info
Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 4 (July)
Pages: 1694-1709
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Handle: RePEc:eee:jetheo:v:144:y:2009:i:4:p:1694-1709

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Web page: http://www.elsevier.com/locate/inca/622869

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Related research
Keywords: Games Learning Best response dynamics Stochastic fictitious play Mixed strategy equilibria TASP;

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References listed on IDEAS
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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. 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:
  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. 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!]
  4. Andriy Zapechelnyuk, 2009. "Limit Behavior of No-regret Dynamics," Discussion Papers 21, Kyiv School of Economics. [Downloadable!]
  5. 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!]
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