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On Priority in Multi-Issue Bankruptcy Problems with Crossed Claims

Author

Listed:
  • Rick Acosta-Vega

    (Facultad de Ingeniería, Universidad del Magdalena, Santa Marta 470004, Colombia)

  • Encarnación Algaba

    (Department of Applied Mathematics II and IMUS, University of Seville, 41092 Seville, Spain)

  • Joaquín Sánchez-Soriano

    (Center of Operations Research (CIO), Miguel Hernández University of Elche, 03202 Elche, Spain)

Abstract

In this paper, we analyze the problem of how to adapt the concept of priority to situations where several perfectly divisible resources have to be allocated among a certain set of agents that have exactly one claim that is used for all resources. In particular, we introduce constrained sequential priority rules and two constrained random arrival rules which extend the classical sequential priority rules and the random arrival rule to these situations. We also provide an axiomatic analysis of these rules. Finally, we present a numerical example to compare the constrained random arrival rule to other solutions in this context.

Suggested Citation

  • Rick Acosta-Vega & Encarnación Algaba & Joaquín Sánchez-Soriano, 2025. "On Priority in Multi-Issue Bankruptcy Problems with Crossed Claims," Mathematics, MDPI, vol. 13(2), pages 1-18, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:246-:d:1566003
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    References listed on IDEAS

    as
    1. Juan D. Moreno-Ternero, 2009. "The proportional rule for multi-issue bankruptcy problems," Economics Bulletin, AccessEcon, vol. 29(1), pages 474-481.
    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. Yan-an Hwang & Tsung-fu Wang, 2009. "Population monotonicity, consistency and the random arrival rule," Economics Bulletin, AccessEcon, vol. 29(4), pages 2816-2821.
    4. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    5. 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.
    6. 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.
    7. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
    8. Sanchez-Soriano, Joaquin, 2021. "Families of sequential priority rules and random arrival rules with withdrawal limits," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 136-148.
    9. 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.
    10. Herrero, Carmen & Villar, Antonio, 2001. "The three musketeers: four classical solutions to bankruptcy problems," Mathematical Social Sciences, Elsevier, vol. 42(3), pages 307-328, November.
    11. 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.
    12. 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.
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