Pure strategies in games with private information
针对有限玩家且信息受限的博弈，在行动集可数无限时，基于对应分布的概念，扩展了Radner-Rosenthal纯化定理并证明了纯策略均衡的存在性。
Pure strategy equilibria of finite player games with informational constraints have been discussed under the assumptions of finite actions, and of independence and diffuseness of information. We present a mathematical framework, based on the notion of a distribution of a correspondence, that enables us to handle the case of countably infinite actions. In this context, we extend the Radner-Rosenthal theorems on the purification of a mixed-strategy equilibrium, and present a direct proof, as well as a generalized version of Schmeidler's large games theorem, on the existence of a pure strategy equilibrium. Our mathematical results pertain to the set of distributions induced by the measurable selections of a correspondence with a countable range, and rely on the Bollobás-Varopoulos extension of the marriage lemma.