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New results for multi-issue allocation problems and their solutions

Author

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  • J. Sánchez-Pérez

    (UASLP
    Facultad de Economía, UASLP)

Abstract

In this paper we present a different perspective than the more traditional approaches to study solutions for multi-issue allocation problems. This perspective is based on a direct sum decomposition for the vector space of these problems by identifying those subspaces that are relevant to the study of linear symmetric solutions. We then use such decomposition to derive some basic applications involving characterizations of several classes of solutions. Finally, we present a brief set of results relating coalitional game theory and multi-issue allocation problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:reecde:v:27:y:2023:i:2:d:10.1007_s10058-022-00293-8
    DOI: 10.1007/s10058-022-00293-8
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    References listed on IDEAS

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    1. 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.
    2. Lars-Gunnar Svensson & Pär Torstensson, 2008. "Strategy-proof allocation of multiple public goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 181-196, February.
    3. Sánchez-Pérez, J. & Plata-Pérez, L. & Accinelli-Gamba, E., 2015. "Characterization of linear symmetric solutions for allocation problems," Economics Letters, Elsevier, vol. 130(C), pages 9-12.
    4. 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.
    5. 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.
    6. Herrero, Carmen & Maschler, Michael & Villar, Antonio, 1999. "Individual rights and collective responsibility: the rights-egalitarian solution," Mathematical Social Sciences, Elsevier, vol. 37(1), pages 59-77, January.
    7. 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.
    8. 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.
    9. 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.
    10. Kleinberg, Norman L. & Weiss, Jeffrey H., 1986. "Weak values, the core, and new axioms for the Shapley value," Mathematical Social Sciences, Elsevier, vol. 12(1), pages 21-30, August.
    11. Amparo Mármol & Clara Ponsatí, 2008. "Bargaining over multiple issues with maximin and leximin preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 30(2), pages 211-223, February.
    12. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
    13. 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.
    14. Gustavo Bergantiños & Luciano Méndez-Naya, 2001. "Additivity in bankruptcy problems and in allocation problems," Spanish Economic Review, Springer;Spanish Economic Association, vol. 3(3), pages 223-229.
    15. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, December.
    16. Norman L. Kleinberg & Jeffrey H. Weiss, 1985. "Equivalent N -Person Games and the Null Space of the Shapley Value," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 233-243, May.
    17. 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.
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    More about this item

    Keywords

    Multi-issue allocation problems; Axiomatic solutions; Linearity; Symmetry;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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