A Solution for General Exchange Markets with Indivisible Goods when Indifferences Are Allowed
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.
|Date of creation:||23 Apr 2013|
|Date of revision:||12 Feb 2014|
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- 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.
- 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.
- Josep Enric Peris Ferrando & Begoña Subiza Martínez, 1992.
"Maximal elements of non necessarily acyclic binary relations,"
Working Papers. Serie AD
1992-07, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Peris, Josep E. & Subiza, Begona, 1994. "Maximal elements of not necessarily acyclic binary relations," Economics Letters, Elsevier, vol. 44(4), pages 385-388, April.
- Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
- 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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