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Generalised weakened fictitious play (2004)
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@MISC{Leslie04generalisedweakened,
author = {David S. Leslie and E. J. Collins},
title = {Generalised weakened fictitious play},
year = {2004}
}
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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.
Keyphrases
fictitious play new actor critic process fictitious play property fictitious-play-like process adaptive process game theory rev nash equilibrium strategy two-person zero-sum game weakened form fictitious play van der genugten fictitious play process general model special case general class first step towards response differential inclusion
