Generalised weakened fictitious play

• 成果类型: Article
• 署名作者: Leslie, David S.; Collins, E. J.
• 署名单位: University of Bristol; University of Oxford
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2005.08.005
• 发表日期: 2006
• 页码: 285-298
• 关键词: Fictitious play; best response differential inclusion; stochastic approximation; actor-critic process

摘要

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. (c) 2005 Elsevier Inc. All rights reserved.