Learning in games with unstable equilibria |
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Authors: | Michel Benaïm Josef Hofbauer Ed Hopkins |
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Institution: | a Institut de Mathématiques, Université de Neuchâtel, CH-2007 Neuchâtel, Switzerland b Department of Mathematics, University of Vienna, A-1090 Vienna, Austria c Department of Economics, University of Edinburgh, 31 Buccleuch Place, Edinburgh EH8 9JY, 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. 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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Keywords: | C72 C73 D83 |
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