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

Thomas Quint and Jun Wake
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Thomas Quint: University of Nevada, Reno
Jun Wake: Gakashuin University

No 1416, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: We consider the n-player houseswapping game of Shapley-Scarf (1974), with indifferences in preferences allowed. It is well-known that the strict core of such a game may be empty, single-valued, or multivalued. 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 GaleÌs 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 an O(n3) 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 regionÌs extreme points precisely correspond to the allocations of the strict core. This last result parallels the results of Vande Vate (1989) and Rothblum (1991) for the marriage game of Gale and Shapley (1962).

Keywords: Shapley-Scarf economy; Strict core; Linear inequality system; Extreme points (search for similar items in EconPapers)
JEL-codes: C60 C71 C78 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2003-05
New Economics Papers: this item is included in nep-gth
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