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A Solution for General Exchange Markets with Indivisible Goods when Indifferences Are Allowed

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  • Subiza, Begoña

    (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica)

  • Peris, Josep

    (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica)

Abstract

It is well known that the core of an exchange market with indivisible goods is always non empty, although it may contain Pareto inecient allocations. The strict core solves this shortcoming when indiff erences are not allowed, but when agents' preferences are weak orders the strict core may be empty. On the other hand, when indifferences are allowed, the core or the strict core may fail to be stable sets, in the von Neumann and Morgenstern sense. We introduce a new solution concept that improves the behaviour of the strict core, in the sense that it solves the emptiness problem of the strict core when indifferences are allowed in the individuals' preferences and whenever the strict core is non-empty, our solution is included on it. We de fine our proposal, the MS-set, by using a stability property (m-stability ) that the strict core fulfills. Finally, we provide a min-max interpretation for this new solution.

Suggested Citation

  • Subiza, Begoña & Peris, Josep, 2013. "A Solution for General Exchange Markets with Indivisible Goods when Indifferences Are Allowed," QM&ET Working Papers 12-18, University of Alicante, D. Quantitative Methods and Economic Theory, revised 12 Feb 2014.
  • Handle: RePEc:ris:qmetal:2012_018
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    References listed on IDEAS

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    1. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    2. Thomas Quint & Jun Wako, 2004. "On Houseswapping, the Strict Core, Segmentation, and Linear Programming," Yale School of Management Working Papers ysm373, Yale School of Management.
    3. Peris, Josep E. & Subiza, Begona, 1994. "Maximal elements of not necessarily acyclic binary relations," Economics Letters, Elsevier, vol. 44(4), pages 385-388, April.
    4. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
    5. Peris, Josep E. & Subiza, Begoña, 2013. "A reformulation of von Neumann–Morgenstern stability: m-stability," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 51-55.
    6. Ma, Jinpeng, 1994. "Strategy-Proofness and the Strict Core in a Market with Indivisibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(1), pages 75-83.
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    Cited by:

    1. Han, Weibin & Van Deemen, Adrian, 2016. "On the solution of w-stable sets," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 87-92.

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    More about this item

    Keywords

    Indivisible goods; Exchange market; Strict core; Indifferences; MS-set; m-stability;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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