无限对策下库恩定理的推广

Masayuki Takahashi
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引用次数: 1

摘要

广泛的^人博弈通常用定向平面上的有限树来描述。博弈的结构涉及到每个参与者的混合策略和行为策略与一些特定的信息集密切相关。在假设每一步棋至少有两种选择的前提下,H.W. Kuhn[1]证明了博弈具有完全回忆的定理,当且仅当给定任意混合策略μu β2、•••、βn时,可能存在与它们相关的行为策略βu /32、•••、/?»,每个/?,仅依赖于相应的混合策略/*,-,因此它们产生等式,
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A generalization of Kuhn's theorem for an infinite game
An extensive ^-person game is usually described in terms of a finite tree in an oriented plane. The game involves in its structure the mixed and behavior strategies of each player closely related to some specified information sets. Under the assumption that each move possesses at least two alternatives, H.W. Kuhn [1] proved the theorem that the game has perfect recall if and only if, given any mixed strategies μu β2, •••, βn, there may be associated with them behavior strategies βu /32, •••, /?», each /?,depending only on the corresponding mixed strategy /*,-, so that they give rise to the equalities,
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