Elsevier

Journal of Economic Theory

Volume 145, Issue 5, September 2010, Pages 1739-1756
Journal of Economic Theory

The roommates problem revisited

https://doi.org/10.1016/j.jet.2010.02.003Get rights and content

Abstract

One of the oldest matching problems is Gale and Shapley's (1962) [8] “roommates problem”: is there a stable way to assign 2N students into N roommate pairs? Unlike the classic marriage problem or college admissions problem, there need not exist a stable solution to the roommates problem. However, stability ignores the key physical constraint that roommates require a room and is therefore too restrictive. This motivates a new matching problem: matching agents subject to an initial assignment. A particularly important example is kidney exchange where after an assignment has been made, subsequent tests may determine that a patient and donor are incompatible. This paper introduces an efficient algorithm for finding a Pareto improvement starting from any status quo roommates assignment.

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This is the first chapter of my Ph.D. thesis at the University of Maryland-College Park. I am grateful to my adviser Lawrence Ausubel for his guidance and support throughout the project. I would also like to thank Peter Cramton, Melinda Morrill, Daniel Vincent, Daniel Aromi, Emel Filiz Ozbay, Jonah Gelbach, and Erkut Ozbay. Two anonymous referees provided a number of thoughtful comments that greatly benefited this paper.

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