Repeated Large Games with Incomplete Information

We examine repeated games with incomplete information where the type spaces of the players may be large. It is shown that if the belief of each player, regarding future play of the game, accommodates the true play then a Nash equilibrium of the incomplete information game will evolve, with time, into an equilibrium of the complete information game, i.e., the realized game where the types of all players are common knowledge. We introduce the notion of accommodating beliefs which involves two requirements. The first is that the belief assigns positive probability to neighborhoods of the true distribution and the second is that what lies outside of a neighborhood is separated from the true distribution by sufficient incoming observations this is the separation property defined in the paper