PURE STRATEGIES IN GAMES WITH PRIVATE INFORMATION

Pure strategy equilibria of finite player games with informational con straints have been discussed under the assumptions of finite actions, and of independence and diffuseness of information. We present a mathe matical framework, based on the notion of a distribution of a correspo ndence, that enables us to handle the case of countably infinite actio ns. In this context, we extend the Radner-Rosenthal theorems on the pu rification 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 re sults pertain to the set of distributions induced by the measurable se lections of a correspondence with a countable range, and rely on the B ollobas-Varopoulos extension of the marriage lemma.