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On the Non-emptiness of the Fuzzy Core

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Author Info
Nizar Allouch () (Queen Mary, University of London)
Arkadi Predtetchinski () (Maastricht University)

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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.

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Paper provided by Queen Mary, University of London, Department of Economics in its series Working Papers with number 531.

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Date of creation: May 2005
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Handle: RePEc:qmw:qmwecw:wp531

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Related research
Keywords: Fuzzy core; Payoff-dependent balancedness; Exchange economies;

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Find related papers by JEL classification:
D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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  1. Jean-Marc Bonnisseau & Vincent Iehle, 2004. "Payoffs-dependent Balancedness and Cores," Game Theory and Information 0403004, EconWPA. [Downloadable!]
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  2. Florenzano Monique, 1988. "Edgeworth equilibria, fuzzy core and equilibria of a production economy without ordered preferences," CEPREMAP Working Papers (Couverture Orange) 8822, CEPREMAP.
  3. Shapley, Lloyd & Vohra, Rajiv, 1991. "On Kakutani's Fixed Point Theorem, the K-K-M-S Theorem and the Core of a Balanced Game," Economic Theory, Springer, vol. 1(1), pages 108-16, January.
  4. Herves-Beloso, Carlos & Moreno-Garcia, Emma & Yannelis, Nicholas C., 2005. "An equivalence theorem for a differential information economy," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 844-856, November. [Downloadable!] (restricted)
  5. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May. [Downloadable!] (restricted)
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  6. Aliprantis, Charalambos D & Brown, Donald J & Burkinshaw, Owen, 1987. "Edgeworth Equilibria," Econometrica, Econometric Society, vol. 55(5), pages 1109-37, September. [Downloadable!] (restricted)
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