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An Exchange Economy Can Have an Empty Alpha-Core

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  • Holly, Charles

Abstract

Yannelis has shown that under very mild conditions on preferences, a 2-agent exchange economy has a nonempty x-core. The purpose of the present paper is to demonstrate that an exchange economy with three or more agents can have an empty x-core. Hence, Yannelis' result would not extend to three or more agents. Examples are provided with and without free disposal, and all preferences are described by linear utility functions. These results are compared with those of Scarf, who proved the existence of an x-core solution for a large class of n-person games. The comparison is carried out on two levels. First, since Scarf and Yannelis use different definitions for the x-core of an exchange economy, we compare these definitions. Second, the present results show that a natural extension of Scarf's theorem for n-person games fails if certain feasibility constraints are incorporated.

Suggested Citation

  • Holly, Charles, 1994. "An Exchange Economy Can Have an Empty Alpha-Core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 453-461, May.
    • Handle: RePEc:spr:joecth:v:4:y:1994:i:3:p:453-61
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    Cited by:

    1. Christian Pietro & Maria Gabriella Graziano & Vincenzo Platino, 2022. "Social loss with respect to the core of an economy with externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 487-508, April.
    2. Martins-da-Rocha, Victor Filipe & Yannelis, Nicholas C., 2011. "Non-emptiness of the alpha-core," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 716, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    3. Yang, Zhe, 2020. "The weak α-core of exchange economies with a continuum of players and pseudo-utilities," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 43-50.
    4. Maria Gabriella Graziano & Claudia Meo & Nicholas C. Yannelis, 2023. "Core and stable sets of exchange economies with externalities," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 27-44, April.
    5. Graziano, Maria Gabriella & Meo, Claudia & Yannelis, Nicholas C., 2017. "Stable sets for exchange economies with interdependent preferences," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 267-286.
    6. Vincenzo Scalzo, 2022. "Existence of alpha-core allocations in economies with non-ordered and discontinuous preferences," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 1-12, May.
    7. Yang, Zhe & Song, Qingping, 2022. "A weak α-core existence theorem of generalized games with infinitely many players and pseudo-utilities," Mathematical Social Sciences, Elsevier, vol. 116(C), pages 40-46.
    8. Zhao, Jingang, 1996. "The hybrid equilibria and core selection in exchange economies with externalities," Journal of Mathematical Economics, Elsevier, vol. 26(4), pages 387-407.

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