Generalised weakened fictitious play

Leslie, David S. and Collins, E. J. (2006) Generalised weakened fictitious play. Games and Economic Behavior, 56 (2). pp. 285-298. ISSN 0899-8256

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A general class of adaptive processes in games is developed, which significantly generalises weakened fictitious play [Van der Genugten, B., 2000. A weakened form of fictitious play in two-person zero-sum games. Int. Game Theory Rev. 2, 307–328] and includes several interesting fictitious-play-like processes as special cases. The general model is rigorously analysed using the best response differential inclusion, and shown to converge in games with the fictitious play property. Furthermore, a new actor–critic process is introduced, in which the only information given to a player is the reward received as a result of selecting an action—a player need not even know they are playing a game. It is shown that this results in a generalised weakened fictitious play process, and can therefore be considered as a first step towards explaining how players might learn to play Nash equilibrium strategies without having any knowledge of the game, or even that they are playing a game.

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Journal Article
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Games and Economic Behavior
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12 Sep 2014 11:20
Last Modified:
22 Nov 2022 01:07