Bayesian games with contracts

The set of all Bayesian-Nash equilibrium payoffs that the players can achieve by signing (conditional) commitments before playing a \nBayesian game coincides with the set of all feasible, incentive compatible and interim individually rational payoffs of the Bayesian game. \nFurthermore, the various equilibrium payoffs, which are achieved by means of different commitment devices, are also the equilibrium pay- \noffs of a universal, deterministic commitment game.