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Resource allocation with warranties in claims problems

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  • Giménez Gómez, José M. (José Manuel)
  • Peris, Josep E.
  • Solís Baltodano, María José

Abstract

The establishing of warranties in order to ensure some minimum awards to each agent involved in an allocation (claims) problem has been analyzed in the body of literature by introducing lower bounds. When focusing on claims problems, four main lower bounds on awards have been de ned: the minimal right (Curiel et al., 1987), the fair lower bound (Moulin, 2002), securement (Moreno-Ternero and Villar, 2004) and the min lower bound (Dominguez, 2013). The current approach analyzes the e ect of requiring the aforementioned lower bounds in an allocation mechanism. We compare the mechanisms thus obtained together with the use of some additional properties. By doing so, we show that there is a correspondence between lower bounds and claims rules, i.e., associated to each particular lower bound, we nd a particular claims rule. Consequently, we provide new characterizations for the constrained equal awards rule, as well as the Ibn Ezra proposal. Finally, a dual analysis, by using upper bounds in awards, provides characterizations of the dual rules of the previous ones: the constrained equal losses rule and the dual of the Ibn Ezra rule. Keywords: Claims problems, Warranties, Lower bounds, Claims rules JEL classifi cation: C71, D63, D71.

Suggested Citation

  • 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.
  • Handle: RePEc:urv:wpaper:2072/292437
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    References listed on IDEAS

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    1. José-Manuel Giménez-Gómez & Josep E. Peris, 2015. "Participation and Solidarity in Redistribution Mechanisms," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 9(1), pages 036-048, October.
    2. José Alcalde & María Marco & José Silva, 2005. "Bankruptcy games and the Ibn Ezra’s proposal," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 103-114, July.
    3. 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.
    4. 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.
    5. LUTTENS, Roland Iwan, 2010. "Minimal rights based solidarity," LIDAM Reprints CORE 2296, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Roland Luttens, 2010. "Minimal rights based solidarity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(1), pages 47-64, January.
    7. 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.
    8. Moreno-Ternero, Juan D. & Villar, Antonio, 2004. "The Talmud rule and the securement of agents' awards," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 245-257, March.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Economia; 33 - Economia;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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