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

29 Pages Posted: 26 May 2003

See all articles by Thomas Quint

Thomas Quint

University of Nevada-Reno, Department of Mathematics

Jun Wako

Gakushuin University - Department of Economics

Date Written: May 2003

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).

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

JEL Classification: C71, C78, C60

Suggested Citation

Quint, Thomas and Wako, Jun, On Houseswapping, the Strict Core, Segmentation, and Linear Programming (May 2003). Available at SSRN: https://ssrn.com/abstract=410807

Thomas Quint (Contact Author)

University of Nevada-Reno, Department of Mathematics ( email )

1664 North Virginia
Reno, NV 89557
United States
775-784-1366 (Phone)
775-784-6378 (Fax)

Jun Wako

Gakushuin University - Department of Economics ( email )

1-5-1 Mejiro
Toshima-ku Tokyo 171-8588
Japan
011-81-3-5992-4371 (Phone)
011-81-3-5992-1007 (Fax)

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
125
Abstract Views
1,928
rank
275,517
PlumX Metrics