Core allocations and the dimension of the cone of efficiency price vectors |
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Authors: | Hidesuke Okuda Benyamin Shitovitz |
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Affiliation: | College of Commerce, Nagasaki University, Katafuchi, Nagasaki, Japan;Department of Economics, University of Haifa, Israel |
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Abstract: | 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). |
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