Aumann's Core Equivalence Theorem

General Equilibrium

Article

Robert J. Aumann's (1964) core equivalence theorem states that the set of core allocations in his atomless economy is identical to the set of Walrasian equilibrium allocations, i.e. C(E) = W(E). The method of proof we follow here is not identical to Aumann's original. In particular, we make use of some rather simplifying procedures -- notably, we use Aumann's (1965) definition of "integration of correspondences" and Lyapunov's theorem (introduced into economics by Karl Vind (1964)). However, the essence of the proof is basically the same.