On Cournot-Nash Equilibrium Distributions for Games with Differential Information and Discontinuous Payoffs.

Mas-Colell's model for equilibrium distributions in "large" anonymous games is extended by the introduction of an abstract, non-topological notion of players' characteristics. The generality of this model allows us to include as a component of a player's characteristic her/his degree of well-informedness (differential information). This makes it possible to address a generalization of a model recently formulated by Khan-Rustichini. We show that one can remove their rather unnatural compactness condition on the space of admissible decision rules, provided that one allows for decision rules which are randomized. Our utility functions need not be continuous; this particular technical aspect solves an open question of Khan concerning Mas-Colell's original model. Our method of proof is based on the novel observation that Cournot-Nash equilibrium distributions are precisely the solutions of a variational inequality for transition probabilities.