Rationalizability and mixed strategies in large games

We show that in large games with a finite set of actions in which the payoff of a player depends only on her own action and on an aggregate value that we call the (aggregate) state of the game, which is obtained from the complete action profile, it is possible to define and characterize the sets of (Point-)Rationalizable States in terms of pure and mixed strategies. We prove that the (Point-)Rationalizable States sets associated to pure strategies are equal to the sets of (Point-)Rationalizable States associated to mixed strategies. By example we show that, in general, the Point-Rationalizable States sets differ from the Rationalizable States sets.