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The Roommate Problem - Is More Stable Than You Think

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  • Pierre-André Chiappori
  • Alfred Galichon
  • Bernard Salanié

Abstract

Stable matchings may fail to exist in the roommate matching problem, both when utility is transferable and when it is not. We show that when utility is transferable, the existence of a stable matching is restored when there is an even number of individuals of indistinguishable characteristics and tastes (types). As a consequence, when the number of individuals of any given type is large enough there always exist “quasi-stable” matchings: a stable matching can be restored with minimal policy intervention. Our results build on an analogy with an associated bipartite problem; it follows that the tools crafted in empirical studies of the marriage problem can easily be adapted to the roommate problem.

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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 4676.

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Date of creation: 2014
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Handle: RePEc:ces:ceswps:_4676

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  1. Pierre-André Chiappori & Sonia Oreffice & Climent Quintana, 2009. "Fatter Attraction: Anthropometric and Socioeconomic Characteristics in the Marriage Market," Working Papers 2009-34, FEDEA.
  2. Klaus, Bettina & Klijn, Flip, 2008. "Smith and Rawls Share a Room: Stability and Medians," Research Memorandum, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR) 009, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  3. Abhijit Banerjee & Esther Duflo & Maitreesh Ghatak & Jeanne Lafortune, 2009. "Marry for What: Caste and Mate Selection in Modern India," NBER Working Papers 14958, National Bureau of Economic Research, Inc.
  4. Becker, Gary S, 1973. "A Theory of Marriage: Part I," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(4), pages 813-46, July-Aug..
  5. Bettina Klaus & Alexandru Nichifor, 2010. "Consistency in one-sided assignment problems," Social Choice and Welfare, Springer, Springer, vol. 35(3), pages 415-433, September.
  6. Eugene Choo & Aloysius Siow, 2006. "Who Marries Whom and Why," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 114(1), pages 175-201, February.
  7. Johan Karlander & Kimmo Eriksson, 2001. "Stable outcomes of the roommate game with transferable utility," International Journal of Game Theory, Springer, Springer, vol. 29(4), pages 555-569.
  8. Talman, A.J.J. & Yang, Z.F., 2008. "A Model of Partnership Formation," Discussion Paper, Tilburg University, Center for Economic Research 2008-103, Tilburg University, Center for Economic Research.
  9. Gunter J. Hitsch & Ali Horta�su & Dan Ariely, 2010. "Matching and Sorting in Online Dating," American Economic Review, American Economic Association, American Economic Association, vol. 100(1), pages 130-63, March.
  10. Weyl, E. Glen & White, Alexander & Azevedo, Eduardo M., 2013. "Walrasian equilibrium in large, quasi-linear markets," Theoretical Economics, Econometric Society, Econometric Society, vol. 8(2), May.
  11. Chung, Kim-Sau, 2000. "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, Elsevier, Elsevier, vol. 33(2), pages 206-230, November.
  12. Gretsky, Neil E. & Ostroy, Joseph M. & Zame, William R., 1999. "Perfect Competition in the Continuous Assignment Model," Journal of Economic Theory, Elsevier, Elsevier, vol. 88(1), pages 60-118, September.
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