论文标题
库恩的等效定理以内在形式的游戏定理
Kuhn's Equivalence Theorem for Games in Intrinsic Form
论文作者
论文摘要
我们指出并证明了库恩的等效定理，用于新的游戏，即内在形式。首先，我们以固有形式介绍游戏，其中信息在产品集上以$σ$的代表。为此，我们适应了Witsenhausen在控制理论中介绍的游戏的内在表示。这些内在游戏不需要对游戏时间性的明确描述，而不是在树上广泛的表格游戏。其次，我们证明，对于这种新的，更一般的游戏代表，这种行为和混合策略在完美的召回下是等效的（Kuhn的定理）。当固有形式用产品结构代替树结构时，信息处理更加容易。这使得内在形成了使用信息分析游戏的新宝贵工具。
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 $σ$-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.
