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

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  • Subiza Begoña
  • Peris Josep E.

    (Universitat d'Alacant, Dep. de Mètodes Quantitatius i Teoria Econòmica, 03080 Alacant, Spain)

Abstract

It is well known that the core of an exchange market with indivisible goods is always non empty, although it may contain Pareto inefficient allocations. The strict core solves this shortcoming when indifferences 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.

Suggested Citation

  • Subiza Begoña & Peris Josep E., 2014. "A Solution for General Exchange Markets with Indivisible Goods when Indifferences are Allowed," Mathematical Economics Letters, De Gruyter, vol. 2(3-4), pages 1-5, November.
    • Handle: RePEc:bpj:maecol:v:2:y:2014:i:3-4:p:5:n:3
    DOI: 10.1515/mel-2014-0003
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    References listed on IDEAS

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    1. 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.
    2. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    3. 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.
    4. 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.
    5. Peris, Josep E. & Subiza, Begona, 1994. "Maximal elements of not necessarily acyclic binary relations," Economics Letters, Elsevier, vol. 44(4), pages 385-388, April.
    6. Thomas Quint & Jun Wako, 2004. "On Houseswapping, the Strict Core, Segmentation, and Linear Programming," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 861-877, November.
    7. 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.
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    Cited by:

    1. Han, Weibin & van Deemen, Adrian, 2021. "The solution of generalized stable sets and its refinement," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 60-67.
    2. 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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