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Nontransferable Utility Bankruptcy Games

Author

Listed:
  • Arantza Estévez-Fernández

    (VU University Amsterdam)

  • Peter Borm

    (Tilburg University, the Netherlands)

  • M. Gloria Fiestras-Janeiro

    (Universidade de Vigo, Spain)

Abstract

In this paper, we analyze bankruptcy problems with nontransferable utility (NTU) from a game theoretical perspective by redefining corresponding NTU-bankruptcy games in a tailor-made way. It is shown that NTU-bankruptcy games are both coalitional merge convex and ordinal convex. Generalizing the notions of core cover and compromise stability for transferable utility (TU) games to NTU-games, we also show that each NTU-bankruptcy game is compromise stable. Thus, NTU-bankruptcy games are shown to retain the two characterizing properties of TU-bankruptcy games: convexity and compromise stability. As a first example of a game theoretical NTU-bankruptcy rule, we analyze the NTU-adjusted proportional rule and show that this rule corresponds to the compromise value of NTU-bankruptcy games.

Suggested Citation

  • Arantza Estévez-Fernández & Peter Borm & M. Gloria Fiestras-Janeiro, 2014. "Nontransferable Utility Bankruptcy Games," Tinbergen Institute Discussion Papers 14-030/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20140030
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    References listed on IDEAS

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    Cited by:

    1. Csóka, Péter & Illés, Ferenc & Solymosi, Tamás, 2022. "On the Shapley value of liability games," European Journal of Operational Research, Elsevier, vol. 300(1), pages 378-386.
    2. Dietzenbacher, Bas, 2018. "Bankruptcy games with nontransferable utility," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 16-21.
    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. 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.
    5. Bas Dietzenbacher & Hans Peters, 2022. "Characterizing NTU-bankruptcy rules using bargaining axioms," Annals of Operations Research, Springer, vol. 318(2), pages 871-888, November.

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    More about this item

    Keywords

    NTU-bankruptcy problem; NTU-bankruptcy game; Coalitional merge convexity; Ordinal convexity; Compromise stability; Core cover; Adjusted proportional rule;
    All these keywords.

    JEL classification:

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

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