Coalition structure values in differential information economies: Is unity a strength?

The coalition structure (CS) value, introduced by Owen [9] and Hart and Kurz [5], generalizes the Shapley value to social situations where coalitions form for the purpose of bargaining. This paper introduces the CS value to economies with differential information. We show that the private CS values exists and is Bayesian incentive compatible. Moreover, we construct examples that go against the intuitive viewpoint that “unity is strength.” In particular, we consider a three person economy in which two agents bargain as a unit against the third agent. We show that bargaining as a unit is advantageous if and only if information is complete. This result sheds new light on bargaining under differential information.