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A Composite Run-to-the-Bank Rule for Multi-Issue Allocation Situations

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  • Gonzalez-Alcon, C.
  • Borm, P.E.M.

    (Tilburg University, Center For Economic Research)

  • Hendrickx, R.L.P.

    (Tilburg University, Center For Economic Research)

Abstract

In this paper, we propose a new extension of the run-to-the-bank rule for bankruptcy situations to the class of multi-issue allocation situations. We show that this rule always yields a core element and that it satisfies self-duality. We characterise our rule by means of a new consistency property, issue-consistency. Copyright Springer-Verlag 2007
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Suggested Citation

  • Gonzalez-Alcon, C. & Borm, P.E.M. & Hendrickx, R.L.P., 2003. "A Composite Run-to-the-Bank Rule for Multi-Issue Allocation Situations," Discussion Paper 2003-59, Tilburg University, Center for Economic Research.
    • Handle: RePEc:tiu:tiucen:285ef7fb-bff6-4451-ada7-ae5a33a76ff7
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    References listed on IDEAS

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    1. Peter Borm & Luisa Carpente & Balbina Casas-Méndez & Ruud Hendrickx, 2005. "The Constrained Equal Awards Rule for Bankruptcy Problems with a Priori Unions," Annals of Operations Research, Springer, vol. 137(1), pages 211-227, July.
    2. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
    3. 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.
    4. Casas-Mendez, B. & Borm, P.E.M. & Carpente, L. & Hendrickx, R.L.P., 2002. "The Constrained Equal Award Rule for Bankruptcy Problems with a Priori Unions," Discussion Paper 2002-83, Tilburg University, Center for Economic Research.
    5. Calleja, P. & Borm, P.E.M. & Hendrickx, R.L.P., 2001. "Multi-Issue Allocation Games," Other publications TiSEM db0ee5ec-5e97-4b1a-9e01-7, Tilburg University, School of Economics and Management.
    6. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
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    Cited by:

    1. Gong, Doudou & Dietzenbacher, Bas & Peters, Hans, 2022. "A random arrival rule for NTU-bankruptcy problems," Economics Letters, Elsevier, vol. 218(C).
    2. Silvia Lorenzo-Freire & Balbina Casas-Méndez & Ruud Hendrickx, 2010. "The two-stage constrained equal awards and losses rules for multi-issue allocation situations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 465-480, December.
    3. M. Hinojosa & A. Mármol & F. Sánchez, 2012. "A consistent talmudic rule for division problems with multiple references," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 661-678, October.
    4. Gustavo Bergantiños & Jose María Chamorro & Leticia Lorenzo & Silvia Lorenzo‐Freire, 2018. "Mixed rules in multi‐issue allocation situations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(1), pages 66-77, February.
    5. Ephraim Zehavi & Amir Leshem, 2018. "On the Allocation of Multiple Divisible Assets to Players with Different Utilities," Computational Economics, Springer;Society for Computational Economics, vol. 52(1), pages 253-274, June.
    6. Gustavo Bergantiños & Leticia Lorenzo & Silvia Lorenzo-Freire, 2011. "New characterizations of the constrained equal awards rule in multi-issue allocation situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 311-325, December.
    7. Algaba, E. & Márquez, G. & Martínez-Lozano, J. & Sánchez-Soriano, J., 2023. "A novel methodology for public management of annual greenhouse gas emissions in the European Union," Socio-Economic Planning Sciences, Elsevier, vol. 89(C).
    8. 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.
    9. Acosta-Vega, Rick K. & Algaba, Encarnación & Sánchez-Soriano, Joaquín, 2023. "Design of water quality policies based on proportionality in multi-issue problems with crossed claims," European Journal of Operational Research, Elsevier, vol. 311(2), pages 777-788.
    10. Qianqian Kong & Hans Peters, 2023. "Sequential claim games," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(3), pages 955-975, September.
    11. Rick K. Acosta-Vega & Encarnaci'on Algaba & Joaqu'in S'anchez-Soriano, 2022. "On priority in multi-issue bankruptcy problems with crossed claims," Papers 2205.00450, arXiv.org, revised Sep 2022.
    12. M. Hinojosa & A. Mármol & F. Sánchez, 2013. "Extended proportionality in division problems with multiple references," Annals of Operations Research, Springer, vol. 206(1), pages 183-195, July.
    13. Lorenzo-Freire, Silvia & Alonso-Meijide, Jose M. & Casas-Mendez, Balbina & Hendrickx, Ruud, 2007. "Balanced contributions for TU games with awards and applications," European Journal of Operational Research, Elsevier, vol. 182(2), pages 958-964, October.
    14. J. Sánchez-Pérez, 2023. "New results for multi-issue allocation problems and their solutions," Review of Economic Design, Springer;Society for Economic Design, vol. 27(2), pages 313-336, June.
    15. Miguel Hinojosa & Amparo Mármol, 2014. "Multi-commodity rationing problems with maxmin payoffs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 79(3), pages 353-370, June.

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