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Existence of alpha-core allocations in economies with non-ordered and discontinuous preferences

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  • Vincenzo Scalzo

    (University of Napoli Federico II via Cinthia (Monte S. Angelo))

Abstract

We study exchange economies where the preference relation of each consumer depends also on the consumptions of the other consumers. In the setting of economies with a finite number $$n\ge 2$$ n ≥ 2 of consumers and non-ordered and discontinuous preferences, we give sufficient and necessary conditions for the existence of alpha-core allocations in the sense of Yannelis (Equilibrium theory in infinite dimensional spaces, 102–123, 1991). The result has been obtained by means of the Ky Fan minimax inequality.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:etbull:v:10:y:2022:i:1:d:10.1007_s40505-022-00223-5
    DOI: 10.1007/s40505-022-00223-5
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    References listed on IDEAS

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    1. Achille Basile & Vincenzo Scalzo, 2020. "Non-emptiness of the alpha-core: sufficient and necessary conditions," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 1143-1153, December.
    2. Efe A. Ok & Levent KoÚkesen, 2000. "Negatively interdependent preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(3), pages 533-558.
    3. Kockesen, Levent & Ok, Efe A. & Sethi, Rajiv, 2000. "The Strategic Advantage of Negatively Interdependent Preferences," Journal of Economic Theory, Elsevier, vol. 92(2), pages 274-299, June.
    4. Scalzo, Vincenzo, 2019. "Equilibrium existence in games: Slight single deviation property and Ky Fan minimax inequality," Journal of Mathematical Economics, Elsevier, vol. 82(C), pages 197-201.
    5. Scarf, Herbert E., 1971. "On the existence of a coopertive solution for a general class of N-person games," Journal of Economic Theory, Elsevier, vol. 3(2), pages 169-181, June.
    6. Philip J. Reny, 2020. "Nash Equilibrium in Discontinuous Games," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 439-470, August.
    7. Vincenzo Scalzo, 2013. "Essential equilibria of discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 27-44, September.
    8. Stanley Reiter, 2001. "Interdependent Preferences and Groups of Agents," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(1), pages 27-67, January.
    9. 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.
    10. Guoqiang Tian, 1993. "Necessary and Sufficient Conditions for Maximization of a Class of Preference Relations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 949-958.
    11. Rabia Nessah & Guoqiang Tian, 2016. "On the existence of Nash equilibrium in discontinuous games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(3), pages 515-540, March.
    12. Guoqiang Tian & Liyan Yang, 2009. "Theory of negative consumption externalities with applications to the economics of happiness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(3), pages 399-424, June.
    13. Drakopoulos, Stavros A., 2012. "The History Of Attitudes Towards Interdependent Preferences," Journal of the History of Economic Thought, Cambridge University Press, vol. 34(4), pages 541-557, December.
    14. Michael R. Baye & Guoqiang Tian & Jianxin Zhou, 1993. "Characterizations of the Existence of Equilibria in Games with Discontinuous and Non-quasiconcave Payoffs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(4), pages 935-948.
    15. Bill Dupor & Wen-Fang Liu, 2003. "Jealousy and Equilibrium Overconsumption," American Economic Review, American Economic Association, vol. 93(1), pages 423-428, March.
    16. Border, Kim C, 1984. "A Core Existence Theorem for Games without Ordered Preferences," Econometrica, Econometric Society, vol. 52(6), pages 1537-1542, November.
    17. 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.
    18. Borglin, Anders, 1973. "Price characterization of stable allocations in exchange economies with externalities," Journal of Economic Theory, Elsevier, vol. 6(5), pages 483-494, October.
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    Cited by:

    1. 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.
    2. Ken Urai & Hiromi Murakami & Weiye Chen, 2023. "Generalization of the social coalitional equilibrium structure," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(1), pages 1-25, April.

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