Core Equivalence for Hierarchic Equilibria

The standard equivalence result on core and Walras equilibrium allocations uses a non-satiation and an interiority assumption. Konovalov (1998) introduced the rejective core for exchange economies with possibly satiated preferences and proved that there, the fuzzy rejective core coincides with the set of dividend equilibria provided an interiority assumption holds. The hierarchic equilibrium exists without non-satiation and without an interiority condition. We show that without these assumptions the set of fuzzy rejective core allocations coincides with a set slightly larger than the set of hierarchic equilibrium allocations. In the case of an exchange economy this reduces to the equivalence between the hierarchic equilibrium allocations and the fuzzy rejective core allocations. Core equivalence for dividend equilibria and for Walras equilibria are deduced as a corollary.