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Equilibria in infinite-dimensional production economies with convexified coalitions

Author

Listed:
  • Maria Gabriella Graziano

    (Dipartimento di Organizzazione Aziendale ed Amministrazione Pubblica, Universit\' a degli Studi della Calabria, 87030 Arcavacata di Rende Cosenza, ITALY)

Abstract

This paper deals with a private ownership production economy assuming that the commodity space is infinite-dimensional. It is first showed that the fuzzy core allocations, a concept that goes back to J.-P. Aubin, are in a one-to-one correspondence with certain core allocations of a continuum economy suitably defined. This result is obtained under convexity of preferences and production sets and separability of the commodity space. In the case of nonconvex preferences and production sets, the set of fuzzy coalitions can be enlarged in order to obtain that every allocation of the core accordingly defined is supported by a non zero price. The proof of the equivalence result when the positive cone of the commodity space has the empty interior, is obtained under assumptions of properness for preferences relations and production sets.

Suggested Citation

  • Maria Gabriella Graziano, 2001. "Equilibria in infinite-dimensional production economies with convexified coalitions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 17(1), pages 121-139.
    • Handle: RePEc:spr:joecth:v:17:y:2001:i:1:p:121-139
    Note: Received: July 9, 1998; revised version: December 6, 1999
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    Citations

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    Cited by:

    1. Giovanna Bimonte & Maria Graziano, 2009. "The measure of blocking coalitions in differential information economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 331-350, February.
    2. Bhowmik, Anuj & Graziano, Maria Gabriella, 2015. "On Vind’s theorem for an economy with atoms and infinitely many commodities," Journal of Mathematical Economics, Elsevier, vol. 56(C), pages 26-36.
    3. Achille Basile & Maria Gabriella Graziano, 2012. "Core Equivalences for Equilibria Supported by Non-linear Prices," CSEF Working Papers 309, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    4. Achille Basile & Maria Gabriella Graziano & Ciro Tarantino, 2018. "Coalitional fairness with participation rates," Journal of Economics, Springer, vol. 123(2), pages 97-139, March.
    5. De Simone, Anna & Graziano, Maria Gabriella, 2003. "Cone conditions in oligopolistic market models," Mathematical Social Sciences, Elsevier, vol. 45(1), pages 53-73, February.

    More about this item

    Keywords

    Production economy; Infinite dimensional commodity space; Fuzzy core allocation; Walras allocation.;
    All these keywords.

    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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