论文标题
节点和选择大型游戏的类别
The Category of Node-and-Choice Extensive-Form Games
论文作者
论文摘要
本文开发了类别$ \ mathbf {ncg} $。它的对象是节点和选择游戏，其中包括所有广泛形式的游戏。它的形态允许对游戏节点，选择和玩家的任意转换，以及游戏玩家实用功能的单调转换。在形态中，包括子游戏夹。得出了同构的几种特征和许多特性。例如，表明同构保留了无毫无疑问，完美信息和（纯粹策略）nash-平衡的游戏理论概念。最后，为选择序列游戏和选择集游戏定义了完整的子类别，以及这两个子类别之间的关系和$ \ Mathbf {ncg} $本身是通过异构形式的包含和等价来表示和得出的。
This paper develops the category $\mathbf{NCG}$. Its objects are node-and-choice games, which include essentially all extensive-form games. Its morphisms allow arbitrary transformations of a game's nodes, choices, and players, as well as monotonic transformations of the utility functions of the game's players. Among the morphisms are subgame inclusions. Several characterizations and numerous properties of the isomorphisms are derived. For example, it is shown that isomorphisms preserve the game-theoretic concepts of no-absentmindedness, perfect-information, and (pure-strategy) Nash-equilibrium. Finally, full subcategories are defined for choice-sequence games and choice-set games, and relationships among these two subcategories and $\mathbf{NCG}$ itself are expressed and derived via isomorphic inclusions and equivalences.
