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Baseline Rationing

Author

Listed:
  • Jens L. Hougaard

    (University of Copenhagen)

  • Juan D. Moreno-Ternero

    (Department of Economic Theory, Universidad de Málaga)

  • Lars P. Østerdal

    (University of Copenhagen)

Abstract

We analyze a general model of rationing in which agents have baselines, in addition to claims against the (insufficient) endowment of the good to be allocated. Many real-life problems fit this extended model (e.g., bankruptcy with prioritized claims, resource allocation in the public health care sector, water distribution in drought periods). We introduce (and characterize) a natural class of allocation methods for such problems. Any method within the class is associated with a rule in the standard rationing model, and we show that if the latter obeys some properties reflecting principles of impartiality, priority and solidarity, the former obeys them too.

Suggested Citation

  • Jens L. Hougaard & Juan D. Moreno-Ternero & Lars P. Østerdal, 2011. "Baseline Rationing," Working Papers 2011-04, Universidad de Málaga, Department of Economic Theory, Málaga Economic Theory Research Center.
    • Handle: RePEc:mal:wpaper:2011-4
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    References listed on IDEAS

    as
    1. 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.
    2. Kaminski, Marek M., 2006. "Parametric rationing methods," Games and Economic Behavior, Elsevier, vol. 54(1), pages 115-133, January.
    3. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2012. "A unifying framework for the problem of adjudicating conflicting claims," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 107-114.
    4. Juan D. Moreno-Ternero, 2009. "The proportional rule for multi-issue bankruptcy problems," Economics Bulletin, AccessEcon, vol. 29(1), pages 474-481.
    5. 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.
    6. , & , E., 2011. "Judicial precedent as a dynamic rationale for axiomatic bargaining theory," Theoretical Economics, Econometric Society, vol. 6(2), May.
    7. Nir Dagan, 1996. "New characterizations of old bankruptcy rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 13(1), pages 51-59, January.
    8. Erik Ansink & Hans-Peter Weikard, 2012. "Sequential sharing rules for river sharing problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 187-210, February.
    9. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    10. Juan D Moreno-Ternero & John E Roemer, 2006. "Impartiality, Priority, and Solidarity in the Theory of Justice," Econometrica, Econometric Society, vol. 74(5), pages 1419-1427, September.
    11. 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.
    12. Hokari, Toru & Thomson, William, 2008. "On properties of division rules lifted by bilateral consistency," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1057-1071, December.
    13. Thomson, William, 1994. "Cooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 35, pages 1237-1284, Elsevier.
    14. 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.
    15. M. Pulido & P. Borm & R. Hendrickx & N. Llorca & J. Sánchez-Soriano, 2008. "Compromise solutions for bankruptcy situations with references," Annals of Operations Research, Springer, vol. 158(1), pages 133-141, February.
    16. Juan Moreno-Ternero & Antonio Villar, 2006. "The TAL-Family of Rules for Bankruptcy Problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 231-249, October.
    17. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
    18. Chalkley, Martin & Malcomson, James M., 2000. "Government purchasing of health services," Handbook of Health Economics, in: A. J. Culyer & J. P. Newhouse (ed.), Handbook of Health Economics, edition 1, volume 1, chapter 15, pages 847-890, Elsevier.
    19. 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.
    20. 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.
    21. Manuel Pulido & Joaquín Sánchez-Soriano & Natividad Llorca, 2002. "Game Theory Techniques for University Management: An Extended Bankruptcy Model," Annals of Operations Research, Springer, vol. 109(1), pages 129-142, January.
    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. Toru Hokari & William Thomson, 2003. "Claims problems and weighted generalizations of the Talmud rule," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 21(2), pages 241-261, March.
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    Cited by:

    1. Jens Hougaard & Juan Moreno-Ternero & Lars Østerdal, 2013. "Rationing with baselines: the composition extension operator," Annals of Operations Research, Springer, vol. 211(1), pages 179-191, December.
    2. Moreno-Ternero, Juan D. & Vidal-Puga, Juan, 2021. "Aggregator operators for dynamic rationing," European Journal of Operational Research, Elsevier, vol. 288(2), pages 682-691.
    3. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2012. "A unifying framework for the problem of adjudicating conflicting claims," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 107-114.

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    More about this item

    Keywords

    rationing; baselines; claims; priority; solidarity;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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