Nonparametric probability bounds for Nash equilibrium actions in a simultaneous discrete game
同时离散博弈中纳什均衡行动的非参数概率界AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要研究同时离散行动博弈，以收益限制刻画均衡及其选择概率。
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同时离散博弈中纳什均衡行动的非参数概率界
- 研究问题
- 某行动组合少被观察到，是因为它很少属于纳什均衡，还是因为均衡选择机制很少选择允许该组合出现的均衡？
- 方法与思路
- 在观察到均衡行为的前提下，作者利用收益函数形状限制和已知战略互动方向，推导均衡存在及选择概率的界。
- 材料陈述的贡献
- 摘要称方法给出指定行动组合属于均衡的概率界，并导出条件均衡选择概率下界，以两家零售商的进入博弈示例说明。
- 阅读关注点
- 应核对收益形状限制、战略互动方向和均衡行为假设如何共同约束概率，以及行动组合与均衡选择事件的定义。
- 阅读边界
- 仅据所给 OpenAlex 版本摘要；界的具体表达与紧致性未说明，不能据此声称识别了唯一均衡或完整选择机制。
原文摘要
We study a simultaneous, complete-information game played by p = 1 P agents.Each p has an ordinal decision variable Y p ∈ A p = {0 1 M p }, where M p can be unbounded, A p is p's action space, and each element in A p is an action, that is, a potential value for Y p .The collective action space is the Cartesian product A = P p=1 A p .A profile of actions y ∈ A is a Nash equilibrium (NE) profile if y is played with positive probability in some existing NE.Assuming that we observe NE behavior in the data, we characterize bounds for the probability that a prespecified y in A is a NE profile.Comparing the resulting upper bound with Pr[Y = y] (where Y is the observed outcome of the game), we also obtain a lower bound for the probability that the underlying equilibrium selection mechanism M E chooses a NE where y is played given that such a NE exists.Our bounds are nonparametric, and they rely on shape restrictions on payoff functions and on the assumption that the researcher has ex ante knowledge about the direction of strategic interaction (e.g., that for q = p, higher values of Y q reduce p's payoffs).Our results allow us to investigate whether certain action profiles in A are scarcely observed as outcomes in the data because they are rarely NE profiles or because M E rarely selects such NE.Our empirical illustration is a multiple entry game played by Home Depot and Lowe's.