Rational expectations in games

A player i´s actions in a game are determined by her beliefs about other players; these depend on the game´s real-life context, not only its formal description. Define a game situation as a game together with such beliefs; call the beliefs—and i´s resulting expectation—rational if there is common knowledge of rationality and a common prior. In two-person zero-sum games, i´s only rational expectation is the game´s value. In an arbitrary game G, we characterize i´s rational expectations in terms of the correlated equilibria of the doubled game 2G in which each of i´s strategies in G appears twice.