On a private information game without pure strategy equilibria

Abstract

We present an example of a two-person game of private information in which there is no equilibrium in pure strategies. Our example satisfies all the hypotheses of the existence theorems present in the literature on the subject of pure strategy equilibria, except for the fact that the action set of each player is given by the interval [-1,1]. As such, it illustrates the limitations that pertain to the purification of equilibria in a standard setting.