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.