On the Non-emptiness of the Fuzzy Core

Nizar Allouch and Arkadi Predtetchinski

No 531, Working Papers from Queen Mary University of London, School of Economics and Finance

Abstract: The seminal contribution of Debreu-Scarf (1963) connects the two concepts of core and competitive equilibrium in exchange economies. In effect, their core-equilibrium equivalence result states that, when the set of economic agents is replicated, the set of core allocations of the replica economy shrinks to the set of competitive allocations. Florenzano (1989) defines the fuzzy core as the set of allocations which cannot be blocked by any coalition with an arbitrary rate of participation and then shows the asymptotic limit of cores of replica economics coincides with the fuzzy core. In this note, we provide an elementary proof of the non-emptiness of the fuzzy core for an exchange economy. Unlike the classical Debreu-Scarf limit theorem and its numerous extensions our result does not require any asymptotic intersection -or limit- of the set of core allocations of replica economies.

Keywords: Fuzzy core; Payoff-dependent balancedness; Exchange economies (search for similar items in EconPapers)
JEL-codes: C71 D51 (search for similar items in EconPapers)
Date: 2005-05-01
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Journal Article: On the non-emptiness of the fuzzy core (2008)
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