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On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices

Author

Listed:
  • Teresa Estañ

    (Centro de Investigación Operativa (CIO), Universidad Miguel Hernández de Elche)

  • Natividad Llorca

    (Centro de Investigación Operativa (CIO), Universidad Miguel Hernández de Elche)

  • Ricardo Martínez

    (Universidad de Granada)

  • Joaquín Sánchez-Soriano

    (Centro de Investigación Operativa (CIO), Universidad Miguel Hernández de Elche)

Abstract

In this paper we study the class of claims problems where the amount to be divided is perfectly divisible and claims are made on indivisible units of several items. Each item has a price, and the available amount falls short to be able to cover all the claims at the given prices. We propose several properties that may be of interest in this particular framework. These properties represent the common principles of fairness, efficiency, and non-manipulability by merging or splitting. Efficiency is our focal principle, which is formalized by means of two axioms: non-wastefulness and Pareto efficiency. We show that some combinations of the properties we consider are compatible, others are not.

Suggested Citation

  • Teresa Estañ & Natividad Llorca & Ricardo Martínez & Joaquín Sánchez-Soriano, 2021. "On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices," Group Decision and Negotiation, Springer, vol. 30(5), pages 1133-1159, October.
    • Handle: RePEc:spr:grdene:v:30:y:2021:i:5:d:10.1007_s10726-021-09750-1
    DOI: 10.1007/s10726-021-09750-1
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    1. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1157-1160, December.
    2. Vito Fragnelli & Stefano Gagliardo & Fabio Gastaldi, 2014. "Integer solutions to bankruptcy problems with non-integer claims," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 892-933, October.
    3. Carmen Herrero & Ricardo Martínez, 2011. "Allocation problems with indivisibilities when preferences are single-peaked," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 2(4), pages 453-467, December.
    4. Juan D. Moreno-Ternero, 2009. "The proportional rule for multi-issue bankruptcy problems," Economics Bulletin, AccessEcon, vol. 29(1), pages 474-481.
    5. Andreas Darmann & Christian Klamler, 2014. "Knapsack cost sharing," Review of Economic Design, Springer;Society for Economic Design, vol. 18(3), pages 219-241, September.
    6. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
    7. ,, 2001. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 17(5), pages 1025-1031, October.
    8. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
    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. Carmen Herrero & Antonio Villar, 2002. "Sustainability in bankruptcy problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 261-273, December.
    11. José-Manuel Giménez-Gómez & M. Marco-Gil, 2014. "A new approach for bounding awards in bankruptcy problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 447-469, August.
    12. M. Angeles de Frutos, 1999. "Coalitional manipulations in a bankruptcy problem," Review of Economic Design, Springer;Society for Economic Design, vol. 4(3), pages 255-272.
    13. George B. Dantzig, 1957. "Discrete-Variable Extremum Problems," Operations Research, INFORMS, vol. 5(2), pages 266-288, April.
    14. 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.
    15. R. Pablo Arribillaga & G. Bergantiños, 2022. "Cooperative and axiomatic approaches to the knapsack allocation problem," Annals of Operations Research, Springer, vol. 318(2), pages 805-830, November.
    16. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    17. 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.
    18. Joaquín Sánchez-Soriano & Natividad Llorca & Encarnación Algaba, 2016. "Valuing managerial flexibility: An application of real-option theory to steel industry investments," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 26(2), pages 127-145.
    19. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    20. Siwei Chen, 2015. "Systematic favorability in claims problems with indivisibilities," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 283-300, February.
    21. 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.
    22. 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.
    23. Martin Feuerman & Harvey Weiss, 1973. "A Mathematical Programming Model for Test Construction and Scoring," Management Science, INFORMS, vol. 19(8), pages 961-966, April.
    24. 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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