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The Constrained Equal Awards Rule for Bankruptcy Problems with a Priori Unions

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  • Peter Borm
  • Luisa Carpente
  • Balbina Casas-Méndez
  • Ruud Hendrickx

Abstract

In this paper, we provide two extensions of the constrained equal awards rule for bankruptcy situations to the class of bankruptcy situations with a priori unions. We present some characterisations and relations with corresponding games. The two new extensions are illustrated by a specific application. Copyright Springer Science + Business Media, Inc. 2005

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:137:y:2005:i:1:p:211-227:10.1007/s10479-005-2257-4
    DOI: 10.1007/s10479-005-2257-4
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    1. Hamiache, Gerard, 1999. "A new axiomatization of the Owen value for games with coalition structures," Mathematical Social Sciences, Elsevier, vol. 37(3), pages 281-305, May.
    2. Casas-Mendez, Balbina & Garcia-Jurado, Ignacio & van den Nouweland, Anne & Vazquez-Brage, Margarita, 2003. "An extension of the [tau]-value to games with coalition structures," European Journal of Operational Research, Elsevier, vol. 148(3), pages 494-513, August.
    3. Winter, Eyal, 1992. "The consistency and potential for values of games with coalition structure," Games and Economic Behavior, Elsevier, vol. 4(1), pages 132-144, January.
    4. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
    5. 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.
    6. Lorenzo-Freire, S. & Alonso-Meijide, J.M. & Casas-Mendez, B. & Hendrickx, R.L.P., 2005. "Balanced Contributions for Multi-Issue Allocation Situations," Discussion Paper 2005-93, Tilburg University, Center for Economic Research.
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    Cited by:

    1. Rick K. Acosta-Vega & Encarnaci'on Algaba & Joaqu'in S'anchez-Soriano, 2022. "On proportionality in multi-issue problems with crossed claims," Papers 2202.09877, arXiv.org.
    2. Carlos González-Alcón & Peter Borm & Ruud Hendrickx, 2007. "A composite run-to-the-bank rule for multi-issue allocation situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 339-352, April.
    3. Lorenzo-Freire, S. & Casas-Mendez, B. & Hendrickx, R.L.P., 2005. "The Two-stage Constrained Equal Awards and Losses Rules for Multi-Issue Allocation Situation," Other publications TiSEM a94f2306-7d29-4ad6-8e81-e, Tilburg University, School of Economics and Management.
    4. 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.
    5. 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.
    6. Josep Maria Izquierdo Aznar & Pere Timoner Lledó, 2016. "Decentralized rationing problems," UB School of Economics Working Papers 2016/345, University of Barcelona School of Economics.
    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. Rick K. Acosta & Encarnación Algaba & Joaquín Sánchez-Soriano, 2022. "Multi-issue bankruptcy problems with crossed claims," Annals of Operations Research, Springer, vol. 318(2), pages 749-772, November.
    9. 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).
    10. 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.
    11. 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.
    12. Saavedra-Nieves, Alejandro & Saavedra-Nieves, Paula, 2020. "On systems of quotas from bankruptcy perspective: the sampling estimation of the random arrival rule," European Journal of Operational Research, Elsevier, vol. 285(2), pages 655-669.
    13. A. Saavedra-Nieves, 2023. "On stratified sampling for estimating coalitional values," Annals of Operations Research, Springer, vol. 320(1), pages 325-353, January.
    14. Josep Maria Izquierdo Aznar & Pere Timoner Lledó, 2016. "Constrained multi-issue rationing problems," UB School of Economics Working Papers 2016/347, University of Barcelona School of Economics.

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