REPRESENTATION OF FINITE ACTION LARGE GAMES

A large game can be formalized as a probability distribution on the se t of players' characteristics or as a function from a measure space of players to the set of players' characteristics. Given a game as a pro bability distribution on the set of players' characteristics, a repres entation of that game is a function from a set of players to the set o f players' characteristics which induces the same distribution. It. is shown that if the playoffs are continuous and there are only finite n umber of actions, then the set of Nash equilibria of any representatio n of a game induces essentially all the Cournot-Nash equilibrium distr ibutions of the given game.