Alpha cores of games with nonatomic asymmetric information

In this paper, we ask under what reasonable conditions a game with asymmetric information on a continuum of states admits a non-empty α-core. Players examine various private information-constrained contracts f (pure strategy profiles) for ex-ante efficiency by evaluating ex-ante expected payoffs and by forming ex-ante coalitions. Once the players agree on a contract, they implement it faithfully in the interim stage. Roughly speaking, our conclusion states that if players hold fine (non-atomic) and independent information, there exists an ex-ante efficient set of contracts (an ex-ante α-core pure strategy profile) that is implementable in the interim stage. To prove that α-cores are non-empty, we need a variant of Lyapunov's theorem for Young measures that preserves private information. We apply an iterated integral version of Lyapunov's theorem for Young measures to derive such a variant.