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Learning in Games with Unstable Equilibria

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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.

Suggested Citation

  • Ed Hopkins & Josef Hofbauer & Michel Benaim, 2005. "Learning in Games with Unstable Equilibria," Edinburgh School of Economics Discussion Paper Series 135, Edinburgh School of Economics, University of Edinburgh.
    • Handle: RePEc:edn:esedps:135
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    More about this item

    Keywords

    games; learning; best response dynamics; stochastic fictitious play; mixed strategy equilibria; TASP;
    All these keywords.

    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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