Let (R1,...,Rk) be an arbitrary partition of the grand coalition in an atomless exchange economy with k "large enough." We prove that an optimal allocation x belongs to the core if and only if x cannot be improved upon by any coalition that includes at least one of the Ri's. K is "large enough" if k ≥ r + 1, where r is the linear dimension of the cone P of the efficiency price vectors for x. Recall that it is always true that r ≤ n, when n is the number of commodities in the market, and that under differentiability and interiority r = 1; thus k can be chosen to be 2 (i.e., for any coalition R, an allocation x belongs to the core of the market if and only if x is not blocked by any coalition that either contains R or contains its complement).
Bibliographical noteFunding Information:
work was initiated when the authors were fellows of the Institute The Hebrew University, Mount Scopus, Jerusalem. Israel. author gratefully acknowledges the support of the NSF under Grant SOC 79-08989. thank R. J. Aumann, J. Greenberg and D. Samet for valuable discussions.
ASJC Scopus subject areas
- Economics and Econometrics