近视眼均衡、跨越性与子博弈束

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摘要翻译：
对于流形的紧致子集$W$上的集值函数$F$来说，跨越是一种拓扑性质，它意味着$F(x)\ne0$对于$W$的内点$x$。短视均衡适用于每个行动都有一个收益，其泛函值在策略空间中不一定是仿射的。我们证明了如果收益满足跨越性，那么存在一个短视均衡（尽管不一定是纳什均衡）。此外，给定一个参数化的博弈集合及其对该集合中收益结构的跨越性，所得的近视均衡及其收益对该参数化具有跨越性。这是Kohberg-Mertens结构定理的一个深远的推广。至少有四种有用的应用：当收益外生于有限博弈树（例如，有限重复博弈后接无限重复博弈）时，当人们希望完全用行为策略从策略上理解博弈时，当人们希望将子博弈概念扩展到共同已知的博弈树的子集时，以及对于进化博弈理论来说。这些证明涉及到新的拓扑结果，即通过对集值函数的相关运算来保持跨越性。
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英文标题：
《Myopic equilibria, the spanning property, and subgame bundles》
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作者：
Robert Simon, Stanislaw Spiez, Henryk Torunczyk
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最新提交年份：
2020
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分类信息：

一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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一级分类：Mathematics        数学
二级分类：Algebraic Topology        代数拓扑
分类描述：Homotopy theory, homological algebra, algebraic treatments of manifolds
同伦理论，同调代数，流形的代数处理
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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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PDF链接：
https://arxiv.org/pdf/2007.12876

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关键词：近视眼 子博弈 Evolutionary Contribution Applications game 策略 性质 函数 topological