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Bankruptcy Games with Nontransferable Utility

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  • Dietzenbacher, Bas

    (Tilburg University, Center For Economic Research)

Abstract

This paper analyzes bankruptcy games with nontransferable utility as a generalization of bankruptcy games with monetary payoffs. Following the game theoretic approach to NTU-bankruptcy problems, we study some appropriate properties and the core of NTU-bankruptcy games. Generalizing the core cover and the reasonable set to the class of NTU-games, we show that NTU-bankruptcy games are compromise stable and reasonable stable. Moreover, we derive a necessary and sufficient condition for an NTU-bankruptcy rule to be game theoretic.

Suggested Citation

  • Dietzenbacher, Bas, 2017. "Bankruptcy Games with Nontransferable Utility," Discussion Paper 2017-005, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:1cc9f5ff-f889-43ec-93af-c8db469243d4
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    File URL: https://pure.uvt.nl/ws/portalfiles/portal/15071786/2017_005.pdf
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    References listed on IDEAS

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    1. Ruud Hendrickx & Judith Timmer & Peter Borm, 2002. "A note on NTU convexity," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 29-37.
    2. Borm, Peter & Keiding, H & McLean, R.P. & Oortwijn, S & Tijs, S, 1992. "The Compromise Value for NTU-Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(2), pages 175-189.
    3. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    4. 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.
    5. Marieke Quant & Peter Borm & Hans Reijnierse & Bas van Velzen, 2005. "The core cover in relation to the nucleolus and the Weber set," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 491-503, November.
    6. Bezalel Peleg & Stef Tijs & Peter Borm & Gert-Jan Otten, 1998. "The MC-value for monotonic NTU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 37-47.
    7. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    8. Orshan, Gooni & Zarzuelo, Jose M., 2000. "The Bilateral Consistent Prekernel for NTU Games," Games and Economic Behavior, Elsevier, vol. 32(1), pages 67-84, July.
    9. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
    10. Dietzenbacher, Bas & Estevez Fernandez, M.A. & Borm, Peter & Hendrickx, Ruud, 2016. "Proportionality, Equality, and Duality in Bankruptcy Problems with Nontransferable Utility," Discussion Paper 2016-026, Tilburg University, Center for Economic Research.
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    Cited by:

    1. Dietzenbacher, Bas & Borm, Peter & Estevez Fernandez, M.A., 2017. "NTU-Bankruptcy Problems : Consistency and the Relative Adjustment Principle," Discussion Paper 2017-044, Tilburg University, Center for Economic Research.
    2. Dietzenbacher, Bas & Borm, Peter & Hendrickx, Ruud, 2017. "Egalitarianism in Nontransferable Utility Games," Discussion Paper 2017-023, Tilburg University, Center for Economic Research.

    More about this item

    Keywords

    NTU-bankruptcy problem; NTU-bankruptcy game; compromise stability; reasonable stability; game theoretic bankruptcy rule;

    JEL classification:

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

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