An Equivalence Theorem for the Anonymous Core

The purpose of this paper is to establish the equivalence between the anonymous core and the set of the Walrasian equilibrium allocations in an atomless exchange economy. The anonymous (or, synonymously, incentive-compatible or envy-free) core is the set of those consumption allocations that are anonymous and cannot be blocked by any coalition via an allocation satisfying the following dual anonymity conditions. First, every member of the coalition prefers most the consumption bundle given to him among those arising in the blocking allocation. Second, any non-member (a consumer who does not belong to the coalition) does not prefer any consumption bundle arising in the blocking allocation to the bundle he receives at the blocked allocation. We also discuss implications of our equivalence theorem on the second-best insurance problem and the relationship with the literature on the incentive-compatible core with asymmetric information.