On the non-emptiness of the fuzzy core
The seminal contribution of Debreu-Scarf  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  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 economies 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.
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Volume (Year): 37 (2008)
Issue (Month): 2 (June)
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- Nizar Allouch & Arkadi Predtetchinski, 2008.
"On the non-emptiness of the fuzzy core,"
International Journal of Game Theory,
Springer, vol. 37(2), pages 203-210, June.
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