Infinite sequential games with real-valued payoffs

Stéphane Le Roux, A. Pauly
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引用次数: 26

Abstract

We investigate the existence of certain types of equilibria (Nash, ε-Nash, subgame perfect, ε-subgame perfect) in infinite sequential games with real-valued payoff functions depending on the class of payoff functions (continuous, upper semi-continuous, Borel) and whether the game is zero-sum. Our results hold for games with two or up to countably many players. Several of these results are corollaries of stronger results that we establish about equilibria in infinite sequential games with some weak conditions on the occurring preference relations. We also formulate an abstract equilibrium transfer result about games with compact strategy spaces and open preferences. Finally, we consider a dynamical improvement rule for infinite sequential games with continuous payoff functions.
具有实值收益的无穷连续博弈
研究了具有实值支付函数的无穷序列对策中某些类型的均衡(Nash, ε-Nash,子博弈完美,ε-子博弈完美)的存在性,这取决于支付函数的类别(连续,上半连续,Borel)和博弈是否是零和。我们的结果适用于两个或至多可数个玩家的游戏。这些结果中的一些是我们建立的关于无限序列博弈的均衡的较强结果的推论,这些结果具有发生偏好关系的一些弱条件。我们还给出了具有紧策略空间和开放偏好的博弈的抽象均衡转移结果。最后,我们考虑了具有连续支付函数的无限连续对策的动态改进规则。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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