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Bankruptcy Games with Nontransferable Utility

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  • Dietzenbacher, Bas

    (Tilburg University, School of Economics and Management)

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 anNTU-bankruptcy rule to be game theoretic.
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Suggested Citation

  • Dietzenbacher, Bas, 2017. "Bankruptcy Games with Nontransferable Utility," Other publications TiSEM 1cc9f5ff-f889-43ec-93af-c, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:1cc9f5ff-f889-43ec-93af-c8db469243d4
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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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Dietzenbacher, Bas & Borm, Peter & Hendrickx, Ruud, 2017. "Egalitarianism in Nontransferable Utility Games," Other publications TiSEM b1bf227f-53df-4fad-93b8-8, Tilburg University, School of Economics and Management.
    8. 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.
    9. Dietzenbacher, Bas & Borm, Peter & Estevez Fernandez, M.A., 2017. "NTU-Bankruptcy Problems : Consistency and the Relative Adjustment Principle," Other publications TiSEM f023d53e-b84f-4520-aa5e-9, Tilburg University, School of Economics and Management.
    10. 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.
    11. William Thomson, 2013. "Game-Theoretic Analysis Of Bankruptcy And Taxation Problems: Recent Advances," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1-14.
    12. 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.
    13. 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.
    14. Tijs, S.H. & Lipperts, F.A.S., 1982. "The hypercube and the core cover of N-person cooperative games," Other publications TiSEM f86cf523-f36d-4652-b774-6, Tilburg University, School of Economics and Management.
    15. Dietzenbacher, Bas & Borm, Peter & Hendrickx, Ruud, 2017. "Egalitarianism in Nontransferable Utility Games," Other publications TiSEM b1bf227f-53df-4fad-93b8-8, Tilburg University, School of Economics and Management.
    16. 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.
    17. 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.
    18. 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.
    19. Luisa Carpente & Balbina Casas-Méndez & Javier Gozálvez & Natividad Llorca & Manuel Pulido & Joaquín Sánchez-Soriano, 2013. "How to divide a cake when people have different metabolism?," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(3), pages 361-371, December.
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    1. Dietzenbacher, Bas & Borm, Peter & Hendrickx, Ruud, 2017. "Egalitarianism in Nontransferable Utility Games," Other publications TiSEM b1bf227f-53df-4fad-93b8-8, Tilburg University, School of Economics and Management.
    2. Doudou Gong & Bas Dietzenbacher & Hans Peters, 2022. "Reduced two-bound core games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(3), pages 447-457, December.
    3. Miguel Ángel Mirás Calvo & Iago Núñez Lugilde & Carmen Quinteiro Sandomingo & Estela Sánchez-Rodríguez, 2024. "An algorithm to compute the average-of-awards rule for claims problems with an application to the allocation of CO $$_2$$ 2 emissions," Annals of Operations Research, Springer, vol. 336(3), pages 1435-1459, May.
    4. Dietzenbacher, Bas & Yanovskaya, Elena, 2023. "The equal split-off set for NTU-games," Mathematical Social Sciences, Elsevier, vol. 121(C), pages 61-67.
    5. Gong, Doudou & Dietzenbacher, Bas & Peters, Hans, 2022. "A random arrival rule for NTU-bankruptcy problems," Economics Letters, Elsevier, vol. 218(C).
    6. 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.
    7. Dietzenbacher, Bas & Borm, Peter & Estevez Fernandez, M.A., 2017. "NTU-Bankruptcy Problems : Consistency and the Relative Adjustment Principle," Other publications TiSEM f023d53e-b84f-4520-aa5e-9, Tilburg University, School of Economics and Management.
    8. Bas Dietzenbacher & Hans Peters, 2022. "Characterizing NTU-bankruptcy rules using bargaining axioms," Annals of Operations Research, Springer, vol. 318(2), pages 871-888, November.
    9. 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.
    10. Doudou Gong & Bas Dietzenbacher & Hans Peters, 2024. "Two-bound core games and the nucleolus," Annals of Operations Research, Springer, vol. 336(3), pages 1419-1433, May.
    11. 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.
    12. Dietzenbacher, Bas & Borm, Peter & Hendrickx, Ruud, 2017. "Egalitarianism in Nontransferable Utility Games," Other publications TiSEM b1bf227f-53df-4fad-93b8-8, Tilburg University, School of Economics and Management.

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