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Generalised weakened fictitious play

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>1/08/2006
<mark>Journal</mark>Games and Economic Behavior
Issue number2
Volume56
Number of pages13
Pages (from-to)285-298
Publication StatusPublished
<mark>Original language</mark>English

Abstract

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.