近视均衡、生成性质和子博弈丛
Myopic equilibria, the spanning property, and subgame bundles
摘要：
对于流形的紧致子集$W$上的集值函数$F$，生成是一个拓扑性质，它意味着对于$W$的内点$x$，$F(x) \ne 0$。当每个行动都有一个其函数值在策略空间中不一定是仿射的回报时，近视均衡适用。我们表明，如果支付满足跨越性质，那么存在一个短视的均衡（虽然不一定是一个纳什均衡）。此外，给定一个参数化的博弈集合和该集合中收益结构的跨越性质，由此产生的近视均衡及其收益具有关于该参数化的跨越性质。这是Kohberg-Mertens结构定理的一个深远的扩展。至少有四个有用的应用，当收益是外生的有限博弈树（例如，一个无限重复的游戏，然后是一个无限重复的游戏），当一个人想要理解一个游戏的战略完全与行为策略，当一个人想要扩展子博弈的概念，以子集的博弈树是共同的，并为进化博弈论。证明涉及新的拓扑结果断言，跨度保持相关的操作集值函数。
英文摘要：
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.
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