Learning in Games with Unstable Equilibria

Ed Hopkins, Josef Hofbauer, Michel Benaim

Research output: Working paperDiscussion paper


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 â??unstableâ?� 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.
Original languageEnglish
PublisherEdinburgh School of Economics Discussion Paper Series
Number of pages35
Publication statusPublished - Jul 2005

Publication series

NameESE Discussion Papers


  • games
  • learning
  • best response dynamics
  • stochastic fictitious play
  • mixed strategy equilibria
  • TASP
  • C72
  • C73
  • D83


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