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Nonemptiness of the f-Core Without Comprehensiveness

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Listed:
  • Hideo Konishi

    (Boston College)

  • Dimitar Simeonov

    (Bahçeşehir University)

Abstract

Kaneko and Wooders (1986) showed under general conditions that an atomless NTU game with finite types of players has a core allocation when coalitions have a finite number of players. In this paper, we provide a direct proof of the above result using Kakutani’s fixed point theorem when the sizes of coalitions are not only finite but also bounded above. This condition simplifies the presentation of the model and the existence proof. Most importantly, we can drop the comprehensiveness assumption, allowing for a much wider applicability of the result for matching problems, as well as for hedonic coalition formation problems. Additionally, without comprehensiveness, f-core allocations might not possess equal-treatment in payoffs for the same type. We also note that the nonemptiness of the core of NTU games by Scarf (1971) can be derived from our result as a corollary.

Suggested Citation

  • Hideo Konishi & Dimitar Simeonov, 2023. "Nonemptiness of the f-Core Without Comprehensiveness," Boston College Working Papers in Economics 1062, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:1062
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    References listed on IDEAS

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    1. Alchian, Armen A & Demsetz, Harold, 1972. "Production , Information Costs, and Economic Organization," American Economic Review, American Economic Association, vol. 62(5), pages 777-795, December.
    2. Wooders, Myrna, 2008. "Small group effectiveness, per capita boundedness and nonemptiness of approximate cores," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 888-906, July.
    3. Kaneko, Mamoru & Wooders, Myrna Holtz, 1996. "The Nonemptiness of the f-Core of a Game without Side Payments," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 245-258.
    4. Konishi, Hideo & Quint, Thomas & Wako, Jun, 2001. "On the Shapley-Scarf economy: the case of multiple types of indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 1-15, February.
    5. Bengt Holmstrom, 1982. "Moral Hazard in Teams," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 324-340, Autumn.
    6. Nizar Allouch & Myrna Wooders, 2017. "On the nonemptiness of approximate cores of large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 191-209, January.
    7. Kaneko, Mamoru & Wooders, Myrna Holtz, 1986. "The core of a game with a continuum of players and finite coalitions: The model and some results," Mathematical Social Sciences, Elsevier, vol. 12(2), pages 105-137, October.
    8. Dutta, Bhaskar & Masso, Jordi, 1997. "Stability of Matchings When Individuals Have Preferences over Colleagues," Journal of Economic Theory, Elsevier, vol. 75(2), pages 464-475, August.
    9. Legros, Patrick & Newman, Andrew F., 1996. "Wealth Effects, Distribution, and the Theory of Organization," Journal of Economic Theory, Elsevier, vol. 70(2), pages 312-341, August.
    10. Kaneko, Mamoru & Wooders, Myrna Holtz, 1989. "The core of a continuum economy with widespread externalities and finite coalitions: From finite to continuum economies," Journal of Economic Theory, Elsevier, vol. 49(1), pages 135-168, October.
    11. Konishi, Hideo, 2013. "Entrepreneurial land developers: Joint production, local externalities, and mixed housing developments," Journal of Urban Economics, Elsevier, vol. 75(C), pages 68-79.
    12. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    13. Hideo Konishi, 2011. "Entrepreneurial Land Developers: Joint Production, Local Externalities, and Mixed Housing," Boston College Working Papers in Economics 777, Boston College Department of Economics, revised 06 Apr 2013.
    14. Wooders, Myrna Holtz, 1983. "The epsilon core of a large replica game," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 277-300, July.
    15. Hammond, Peter J. & Kaneko, Mamoru & Wooders, Myrna Holtz, 1989. "Continuum economies with finite coalitions: Core, equilibria, and widespread externalities," Journal of Economic Theory, Elsevier, vol. 49(1), pages 113-134, October.
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    More about this item

    Keywords

    f-core; comprehensiveness; atomless players;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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