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Core and Walrasian equilibria when agents' characteristics are extremely dispersed

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  • Konrad Podczeck

Abstract

It is shown that core-Walras equivalence fails whenever the commodity space is a non-separable Banach space. The interpretation is that a large number of agents guarantees core-Walras equivalence only if there is actually a large number of agents relative to the size of the commodity space. Otherwise a large number of agents means that agents' characteristics may be extremely dispersed, so that the standard theory of perfect competition fails. Supplementing the core-Walras non-equivalence result, it is shown that in the framework of economies with weakly compact consumption sets – as developed by Khan and Yannelis (1991) – the core is always non-empty, even if consumption sets are non-separable. Copyright Springer-Verlag Berlin Heidelberg 2003

Suggested Citation

  • Konrad Podczeck, 2003. "Core and Walrasian equilibria when agents' characteristics are extremely dispersed," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 22(4), pages 699-725, November.
    • Handle: RePEc:spr:joecth:v:22:y:2003:i:4:p:699-725
    DOI: 10.1007/s00199-002-0354-z
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    Citations

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    Cited by:

    1. Jiuqiang Liu, 2022. "Equivalence of Competitive Equilibria, Fuzzy Cores, and Fuzzy Bargaining Sets in Finite Production Economies," Mathematics, MDPI, vol. 10(18), pages 1-16, September.
    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. Nicholas Yannelis, 2009. "Debreu’s social equilibrium theorem with asymmetric information and a continuum of agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 419-432, February.
    4. Anuj Bhowmik & Jiling Cao, 2013. "On the core and Walrasian expectations equilibrium in infinite dimensional commodity spaces," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 537-560, August.
    5. Bhowmik, Anuj & Cao, Jiling, 2013. "Robust efficiency in mixed economies with asymmetric information," Journal of Mathematical Economics, Elsevier, vol. 49(1), pages 49-57.
    6. Podczeck, K., 2005. "On core-Walras equivalence in Banach lattices," Journal of Mathematical Economics, Elsevier, vol. 41(6), pages 764-792, September.
    7. Achille Basile & Maria Gabriella Graziano & Ciro Tarantino, 2018. "Coalitional fairness with participation rates," Journal of Economics, Springer, vol. 123(2), pages 97-139, March.
    8. Podczeck, K., 2004. "On Core-Walras equivalence in Banach spaces when feasibility is defined by the Pettis integral," Journal of Mathematical Economics, Elsevier, vol. 40(3-4), pages 429-463, June.
    9. Evren, Özgür & Hüsseinov, Farhad, 2008. "Theorems on the core of an economy with infinitely many commodities and consumers," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1180-1196, December.
    10. Bhowmik, Anuj, 2013. "Edgeworth equilibria: separable and non-separable commodity spaces," MPRA Paper 46796, University Library of Munich, Germany.
    11. Niccolò Urbinati, 2023. "The Walrasian objection mechanism and Mas-Colell’s bargaining set in economies with many commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(1), pages 45-68, July.
    12. Michael Greinecker & Konrad Podczeck, 2016. "Edgeworth’s conjecture and the number of agents and commodities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 93-130, June.
    13. Suzuki, Takashi, 2013. "Core and competitive equilibria of a coalitional exchange economy with infinite time horizon," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 234-244.
    14. Greinecker, Michael & Podczeck, Konrad, 2017. "Core equivalence with differentiated commodities," Journal of Mathematical Economics, Elsevier, vol. 73(C), pages 54-67.

    More about this item

    Keywords

    Keywords and Phrases: Non-separable commodity space; Measure space of agents; Core; Walrasian equilibrium; Core-Walras equivalence.; JEL Classification Numbers: C62; C71; D41; D50.;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition

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