Rationalizability in games with a continuum of players

The concept of Rationalizability has been used in the last fifteen years to study stability of equilibria on models with continuum of players such as standard competitive markets, macroeconomic dynamics and currency attacks. However, Rationalizability has been formally defined in a general setting only for games with a finite number of players. We propose then a definition for Point-Rationalizable Strategies in the context of Games with a Continuum of Players. In a special class of this games where the payoff of a player depends only on his own strategy and an aggregate value that represents the state of the game, state that is obtained from the actions of all the players, we define the sets of Point-Rationalizable States and Rationalizable States. These sets are characterized and some of their properties are explored. We study as well standard Rationalizability in a subclass of these games.