Existence of equilibrium in Bayesian games with infinitely many players

We prove the existence of a Bayesian Nash equilibrium for a Bayesian game with infinitely many players. We make three main advances to the existing literature. In particular: 1. We provide existence theorems where the set of agents can be an infinite set (countable or uncountable) as well as a measure space. 2. We use the information partition approach to model the differential information rather than the type set approach and therefore, our equilibrium is in behavioral strategies rather than in distributional strategies. This enables us to dispense with the independent type assumption used by the others in the literature. 3. Our modeling allows the individual's action set to depend on the states of nature and to be an arbitrary subset of an infinite dimensional space. In order to incorporate all the above generalizations. we offer a new proof of a novel type. (C) 1997 Academic Press.