An Exchange Economy Can Have an Empty Alpha-Core

Charles Holly

Economic Theory, 1994, vol. 4, issue 3, 453-61

Abstract: Yannelis has shown that under very mild conditions on preferences, a 2-agent exchange economy has a nonempty x-core. The purpose of the present paper is to demonstrate that an exchange economy with three or more agents can have an empty x-core. Hence, Yannelis' result would not extend to three or more agents. Examples are provided with and without free disposal, and all preferences are described by linear utility functions. These results are compared with those of Scarf, who proved the existence of an x-core solution for a large class of n-person games. The comparison is carried out on two levels. First, since Scarf and Yannelis use different definitions for the x-core of an exchange economy, we compare these definitions. Second, the present results show that a natural extension of Scarf's theorem for n-person games fails if certain feasibility constraints are incorporated.

Date: 1994
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