Equilibria of Large Games with Imperfect Observability

Abstract

In this paper we present two formulations of an equilibrium notion for large games in which each player cannot observe precisely the moves of the other players in the game. In the context of large anonymous games where the moves of the other players are summarized by a probability measure on the action space, imperfect observability is formulated as a map from the space of such measures to the space of probability measures on this space. In the context of large non-anonymous games where the moves of the other players are summarized by a measurable function from the space of players to the action space, imperfect observability is formulated as a conditional expectation of such a function with respect to a σ-subalgebra of the measure space of players. We report results both on the existence and upper hemicontinuity of equilibrium.