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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.

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Bibliographic Info

Paper provided by Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica in its series QM&ET Working Papers with number 12-18.

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Length: 11 pages
Date of creation: 23 Apr 2013
Date of revision: 12 Feb 2014
Handle: RePEc:ris:qmetal:2012_018

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Keywords: Indivisible goods; Exchange market; Strict core; Indifferences; MS-set; m-stability;

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  1. Peris, Josep E. & Subiza, Begona, 1994. "Maximal elements of not necessarily acyclic binary relations," Economics Letters, Elsevier, vol. 44(4), pages 385-388, April.
  2. 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.
  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. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
  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.
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