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On Houseswapping, the Strict Core, Segmentation, and Linear Programming

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  • Thomas Quint

    ()
    (University of Nevada, Reno)

  • Jun Wako

    ()
    (Gakushuin University)

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    Abstract

    We consider the n-player houseswapping game of Shapley-Scarf (1974), with indfferences in preferences allowed. It is well-known that the strict core of such a game may be empty, single-valued, or multi-valued. We define a condition on such games called "segmentability", which means that the set of players can be partitioned into a "top trading segmentation". It generalizes Gale's well-known idea of the partition of players into "top trading cycles" (which is used to find the unique strict core allocation in the model with no indifference). We prove that a game has a nonempty strict core if and only if it is segmentable. We then use this result to devise and O(n^3) algorithm which takes as input any houseswapping game, and returns either a strict core allocation or a report that the strict core is empty. Finally, we are also able to construct a linear inequality system whose feasible region's extreme points precisely correspond to the allocations of the strict core. This last result parallels the results of Vande Vate (1989) and Rothbum (1991) for the marriage game of Gale and Shapley (1962).

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    Bibliographic Info

    Paper provided by Yale School of Management in its series Yale School of Management Working Papers with number ysm373.

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    Date of creation: 28 Jul 2004
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    Handle: RePEc:ysm:somwrk:ysm373

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    Web page: http://icf.som.yale.edu/
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    Related research

    Keywords: Shapley-Scarf Economy; Strict Core; Linear Inequality System; Extreme Points;

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    Cited by:
    1. Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2005. "Efficient Kidney Exchange: Coincidence of Wants in a Structured Market," Boston College Working Papers in Economics 621, Boston College Department of Economics.
    2. Paula Jaramillo & Vikram Manjunath, 2011. "The Difference Indifference Makes in Strategy-Proof Allocation of Objects," DOCUMENTOS CEDE 008746, UNIVERSIDAD DE LOS ANDES-CEDE.
    3. Alcalde-Unzu, Jorge & Molis, Elena, 2011. "Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms," Games and Economic Behavior, Elsevier, vol. 73(1), pages 1-16, September.
    4. Subiza, Begoña & Peris, Josep, 2013. "A Solution for General Exchange Markets with Indivisible Goods when Indifferences Are Allowed," QM&ET Working Papers 12-18, Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica, revised 12 Feb 2014.

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