We state and prove Kuhn's equivalence theorem for a new representation of games, the intrinsic form. First, we introduce games in intrinsic form where information is represented by $\sigma$-fields over a product set. For this purpose, we adapt to games the intrinsic representation that Witsenhausen introduced in control theory. Those intrinsic games do not require an explicit description of the play temporality, as opposed to extensive form games on trees. Second, we prove, for this new and more general representation of games, that behavioral and mixed strategies are equivalent under perfect recall (Kuhn's theorem). As the intrinsic form replaces the tree structure with a product structure, the handling of information is easier. This makes the intrinsic form a new valuable tool for the analysis of games with information.

中文翻译：

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内在形式博弈的库恩等价定理

我们陈述并证明了库恩的等价定理，用于博弈的新表示，即内在形式。首先，我们以内在形式介绍游戏，其中信息由产品集上的 $\sigma$-fields 表示。为此，我们将 Witsenhausen 在控制理论中引入的内在表征应用于博弈。与树上的广泛形式游戏相反，这些内在游戏不需要对游戏时间的明确描述。其次，我们证明，对于这种新的、更一般的游戏表示，行为策略和混合策略在完美回忆下是等价的（库恩定理）。由于内在形式用产品结构代替了树结构，因此信息的处理更加容易。这使得内在形式成为分析具有信息的游戏的新的有价值的工具。