Discrete time stochastic multi-player competitive games with affine payoffs

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• 作者：Ivan Guo^a ; Marek Rutkowski^a ; ^b ; ^{marek.rutkowski@sydney.edu.au" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Multi-player game ; Redistribution game ; Affine game ; Dynkin stopping game ; Stochastic game ; Nash equilibrium ; Optimal equilibrium
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：126
• 期：1
• 页码：1-32
• 全文大小：352 K

文摘

A novel class of multi-player competitive stochastic games in discrete-time with an affine specification of the redistribution of payoffs at exercise is examined. The affine games cover as a very special case the classic two-person stochastic stopping games introduced by Dynkin (1969). We first extend to the case of a single-period deterministic affine game the results from Guo and Rutkowski (2012, 2014) where the so-called redistribution games were studied. We identify conditions under which optimal equilibria and value for a multi-player affine game exist. We also examine stochastic multi-period affine games and we show that, under mild assumptions, they can be solved by the method of backward induction.