中文摘要
在最近的一篇论文中，Lin 和 Palfrey (2024) 发展了序贯博弈中的认知层级（cognitive hierarchy, CH）理论，并观察到这一解概念不满足简化标准式不变性。本文对这一观察加以限定并作出解释。我证明 CH 模型满足标准式不变性，而将 CH 模型应用于简化标准式时所产生的差异仅取决于 level-0 类型的随机化如何建模。事实上，扩展式中的均匀行为策略在标准式中导出均匀混合策略，但后者并不对应于简化标准式中的均匀随机化，原因在于不同的简化策略可能对应于基数不同的等价策略集合。我还评述了：(i) CH 模型对序贯博弈某些变换的不变性，以及 (ii) 关于其他参与人层级类型的条件信念的独立性。
Abstract
In a recent paper, Lin & Palfrey (2024) developed a theory of cognitive hierarchies (CH) in sequential games and observed that this solution concept is not reduced-normal-form invariant. In this paper I qualify and explain this observation. I show that the CH model is normal-form invariant, and that the differences arising from the application of the CH model to the reduced normal form depend only on how randomization by level-0 types is modeled. Indeed, while the uniform behavior strategy in the extensive form yields the uniform mixed strategy in the normal form, the latter does not correspond to the uniform randomization in the reduced normal form, because different reduced strategies may correspond to sets of equivalent strategies with different cardinalities. I also comment on (i) the invariance of the CH model to some transformations of the sequential game, and (ii) the independence of conditional beliefs about co-players' level-types.