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Lower bounds and recursive methods for the problem of adjudicating conflicting claims

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  • Diego Dominguez

Abstract

For the problem of adjudicating conflicting claims, we propose the following method to extend a lower bound rule: (i) for each problem, assign the amounts recommended by the lower bound rule and revise the problem accordingly; (ii) assign the amounts recommended by the lower bound rule to the revised problem. The “recursive-extension” of a lower bound rule is obtained by recursive application of this procedure. We show that if a lower bound rule satisfies positivity then it’s recursive extension singles out a unique awards rule.We then study the relation between desirable properties satisfied by a lower bound rule and properties satisfied by its recursive extension. Copyright Springer-Verlag 2013

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  • Diego Dominguez, 2013. "Lower bounds and recursive methods for the problem of adjudicating conflicting claims," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 663-678, March.
    • Handle: RePEc:spr:sochwe:v:40:y:2013:i:3:p:663-678
    DOI: 10.1007/s00355-011-0632-4
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    References listed on IDEAS

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    1. Thomson, William & Yeh, Chun-Hsien, 2008. "Operators for the adjudication of conflicting claims," Journal of Economic Theory, Elsevier, vol. 143(1), pages 177-198, November.
    2. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    3. 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.
    4. Diego Dominguez & William Thomson, 2006. "A new solution to the problem of adjudicating conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 283-307, June.
    5. Yeh, Chun-Hsien, 2008. "Secured lower bound, composition up, and minimal rights first for bankruptcy problems," Journal of Mathematical Economics, Elsevier, vol. 44(9-10), pages 925-932, September.
    6. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2002. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 1, number 1.
    7. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 327-386.
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    Cited by:

    1. José-manuel Giménez-gómez & Cori Vilella, 2017. "Recursive methods for discrete claims problems," Economics Bulletin, AccessEcon, vol. 37(3), pages 1653-1665.
    2. Giménez Gómez, José M. (José Manuel) & Peris, Josep E. & Solís Baltodano, María José, 2017. "Resource allocation with warranties in claims problems," Working Papers 2072/292437, Universitat Rovira i Virgili, Department of Economics.
    3. 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.
    4. María-José Solís-Baltodano & José-Manuel Giménez-Gómez & Josep E. Peris, 2022. "Distributing the European structural and investment funds from a conflicting claims approach [Verteilung der europäischen Struktur- und Investitionsfonds aus einem kollidierenden Forderung Ansatz]," Review of Regional Research: Jahrbuch für Regionalwissenschaft, Springer;Gesellschaft für Regionalforschung (GfR), vol. 42(1), pages 23-47, April.
    5. 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.
    6. 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.
    7. José-Manuel Giménez-Gómez & Josep Peris, 2014. "Mediation in claims problems," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 5(4), pages 357-375, November.
    8. José-Manuel Giménez-Gómez & Josep E. Peris & María-José Solís-Baltodano, 2023. "Resource allocations with guaranteed awards in claims problems," Review of Economic Design, Springer;Society for Economic Design, vol. 27(3), pages 581-602, September.

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