论文标题
近视平衡，跨越物业和子游戏捆绑包
Myopic equilibria, the spanning property, and subgame bundles
论文作者
论文摘要
对于一个折射的紧凑型子集$ w $上的设置值函数$ f $，跨度是一种拓扑属性，意味着内部点$ f（x）\ ne 0 $ for Interios for Interios $ x $ of $ w $。近视平衡适用于每种动作的回报，其功能值不一定在策略空间中呈现。我们表明，如果收益满足生成属性，则存在近视平衡（尽管不一定是NASH平衡）。此外，给定对游戏的参数收集以及该集合中收益结构的跨性属性，由此产生的近视平衡及其收益具有与该参数化相对于该参数化的分散属性。这是Kohberg-Mertens结构定理的远距离扩展。当一个有限的游戏树外源时，至少有四个有用的应用程序（例如，有限重复的游戏，然后是无限重复的游戏），当一个人想通过行为策略从策略上完全理解游戏时，当一个人想将子游戏概念扩展到游戏树的子集中，并在共同的游戏中，以及进化游戏中的众所周知。证据涉及新的拓扑结果，断言跨性别的范围是通过针对设定值功能的相关操作保留的。
For a set-valued function $F$ on a compact subset $W$ of a manifold, spanning is a topological property that implies that $F(x) \ne 0$ for interior points $x$ of $W$. A myopic equilibrium applies when for each action there is a payoff whose functional value is not necessarily affine in the strategy space. We show that if the payoffs satisfy the spanning property, then there exist a myopic equilibrium (though not necessarily a Nash equilibrium). Furthermore, given a parametrized collection of games and the spanning property to the structure of payoffs in that collection, the resulting myopic equilibria and their payoffs have the spanning property with respect to that parametrization. This is a far reaching extension of the Kohberg-Mertens Structure Theorem. There are at least four useful applications, when payoffs are exogenous to a finite game tree (for example a finitely repeated game followed by an infinitely repeated game), when one wants to understand a game strategically entirely with behaviour strategies, when one wants to extends the subgame concept to subsets of a game tree that are known in common, and for evolutionary game theory. The proofs involve new topological results asserting that spanning is preserved by relevant operations on set-valued functions.
