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| Author: | Zhou, L. |
| Title: | A theorem on open coverings of a simplex and Scarf's core existence theorem through Brouwer's fixed point theorem |
| Journal: | Economic Theory
1994 : VOL. 4:3, p. 473-477 |
| Index terms: | ECONOMIC THEORY ECONOMICS MATHEMATICS |
| Language: | eng |
| Abstract: | This paper provides simple proofs of a theorem on open coverings of a simplex and Scarf's core existence theorem through Brouwer's fixed point theorem. In two seminal papers, Scarf used an ingenious algorithm to prove a theorem on closed coverings of a simplex (Scarf, 1967a) and applied it to establish one of the fundamental theorems in cooperative game theory that the core of any balanced game is nonempty (Scarf, 1976b). Since then these results have been proved by many others. |
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