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Even Allocations For Generalised Rationing Problems

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  • Marco Mariotti

    (Royal Holloway)

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    Abstract

    We study an extension of the standard rationing problem, consisting of the allocation of utility losses. We assume neither linearly transferable utilities nor risk averse agents. As a consequence, the utility possibility sets need not be convex or smooth. This problem is referred to as the generalised rationing problem. We introduce the notion of even allocations as a solution concept that extends the random arrival rule to this general scenario. Moreover, we show that, when the feasible set is convex, this solution can be characterised by a suitable reformulation of the axioms that define the Nash bargaining solution.

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    File URL: http://www.ivie.es/downloads/docs/wpasad/wpasad-2003-10.pdf
    File Function: Fisrt version / Primera version, 2003
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    Bibliographic Info

    Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2003-10.

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    Length: 19 pages
    Date of creation: Mar 2003
    Date of revision:
    Publication status: Published by Ivie
    Handle: RePEc:ivi:wpasad:2003-10

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    Related research

    Keywords: Rationing Problems; Non-Transferable Utilities; Nash Bargaining Solution; Clarke Cones.;

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    1. 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.
    2. Moulin,Hervi, 1991. "Axioms of Cooperative Decision Making," Cambridge Books, Cambridge University Press, number 9780521424585, December.
    3. Vincenzo Denicolò & Marco Mariotti, 2000. "Nash Bargaining Theory, Nonconvex Problems and Social Welfare Orderings," Theory and Decision, Springer, vol. 48(4), pages 351-358, June.
    4. 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.
    5. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
    6. Carmen Herrero, 1997. "Endogenous reference points and the adjusted proportional solution for bargaining problems with claims," Social Choice and Welfare, Springer, vol. 15(1), pages 113-119.
    7. 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.
    8. 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.
    9. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    10. Volij, Oscar & Dagan, Nir, 1993. "The Bankruptcy Problem: A Cooperative Bargaining Approach," Staff General Research Papers 10571, Iowa State University, Department of Economics.
    11. Roth, Alvin E., 1977. "Independence of irrelevant alternatives, and solutions to Nash's bargaining problem," Journal of Economic Theory, Elsevier, vol. 16(2), pages 247-251, December.
    12. 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.
    13. Thomson, William, 1981. "A class of solutions to bargaining problems," Journal of Economic Theory, Elsevier, vol. 25(3), pages 431-441, December.
    14. Lin Zhou, 1997. "The Nash Bargaining Theory with Non-Convex Problems," Econometrica, Econometric Society, vol. 65(3), pages 681-686, May.
    15. Chun, Youngsub & Thomson, William, 1992. "Bargaining problems with claims," Mathematical Social Sciences, Elsevier, vol. 24(1), pages 19-33, August.
    16. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, January.
    17. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2001. "Strategy-proof Social Choice Correspondences," Journal of Economic Theory, Elsevier, vol. 101(2), pages 374-394, December.
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