Benaim, M.; Hofbauer, J.; Hopkins, E.; (2006) Learning in games with unstable equilibria. (ELSE Working Papers 213). ESRC Centre for Economic Learning and Social Evolution: London, UK.

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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 processes. We show that, when players learn using weighted stochastic fictitious play and so place greater weight on more 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 best response cycle first identified by Shapley (1964). Though conceptually distinct from Nash equilibrium, for many games the TASP is close enough to Nash 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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