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The Bilateral Consistent Prekernel, the Core, and NTU Bankruptcy Problems

Author

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  • Guni Orshan

    (Dept. of Agriculture Economics and Management, The Hebrew University of Jerusalem, P.O. Box 12, Rehovot, 76100, Israel, and Dept. of Mathematics, The Open University of Israel, 16 Klaussner Street, P.O.B. 39382, Ramat Aviv, Tel Aviv, 61392, Israel)

  • Federico Valenciano

    (Dept. of Applied Economics IV, University of the Basque Country, Avda. Lehendakari Aguirre 83, E-48015 Bilbao, Spain)

  • José M. Zarzuelo

    (Dpto. de Economía Aplicada IV, Facultad de C. Económicas, University of the Basque Country, Avda. Lehendakari Aguirre 83, E-48015 Bilbao, Spain)

Abstract

It is shown that the bilateral consistent prekernel, an NTU solution concept that generalizes the Nash bargaining solution by means of a principle of bilateral consistency, is nonempty and intersects the core for a sufficiently rich class of NTU games: the class of boundary separating games, also introduced here. A second contribution of this paper is the NTU extension of the bankruptcy games introduced by Aumann and Maschler (1985). These games, which provide a new approach for dealing with bargaining problems with claims, are shown to be boundary separating, so that the results apply.

Suggested Citation

  • Guni Orshan & Federico Valenciano & José M. Zarzuelo, 2003. "The Bilateral Consistent Prekernel, the Core, and NTU Bankruptcy Problems," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 268-282, May.
  • Handle: RePEc:inm:ormoor:v:28:y:2003:i:2:p:268-282
    DOI: 10.1287/moor.28.2.268.14476
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    References listed on IDEAS

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    Cited by:

    1. Dietzenbacher, Bas, 2018. "Bankruptcy games with nontransferable utility," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 16-21.
    2. Arantza Estévez-Fernández & Peter Borm & M. Gloria Fiestras-Janeiro, 2020. "Nontransferable utility bankruptcy games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 154-177, April.
    3. Bas Dietzenbacher & Peter Borm & Arantza Estévez-Fernández, 2020. "NTU-bankruptcy problems: consistency and the relative adjustment principle," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 101-122, June.
    4. Dietzenbacher, Bas & Peters, Hans, 2018. "Characterizing NTU-bankruptcy rules using bargaining axioms," Research Memorandum 006, Maastricht University, Graduate School of Business and Economics (GSBE).
    5. Josune Albizuri, M. & Dietzenbacher, Bas & Zarzuelo, J., 2019. "Bargaining with Independence of Higher or Irrelevant Claims," Other publications TiSEM be1cb9ce-9018-46e7-96b6-2, Tilburg University, School of Economics and Management.
    6. B. Dietzenbacher & A. Estévez-Fernández & P. Borm & R. Hendrickx, 0. "Proportionality, equality, and duality in bankruptcy problems with nontransferable utility," Annals of Operations Research, Springer, vol. 0, pages 1-16.
    7. B. Dietzenbacher & A. Estévez-Fernández & P. Borm & R. Hendrickx, 2021. "Proportionality, equality, and duality in bankruptcy problems with nontransferable utility," Annals of Operations Research, Springer, vol. 301(1), pages 65-80, June.
    8. Albizuri, M.J. & Dietzenbacher, B.J. & Zarzuelo, J.M., 2020. "Bargaining with independence of higher or irrelevant claims," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 11-17.

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