# American Institue of Mathematical Sciences

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Why do stable clearinghouses work so well? - Small sets of stable matchings in typical environments, and the limits-on-manipulation theorem of Demange, Gale and Sotomayor
2015, 2(3/4): 321-330. doi: 10.3934/jdg.2015008

## Finding all stable matchings with couples

 1 Department of Economics, Stanford University, 579 Serra Mall, Stanford, CA 94305, United States

Received  April 2015 Revised  May 2015 Published  November 2015

In two-sided matching markets in which some doctors form couples, a stable matching does not necessarily exist. We characterize the set of stable matchings as the fixed points of a function that is reminiscent of a tâtonnement process. Then we show that this function is monotone decreasing with respect to a certain partial order. Based on these results, we present an algorithm that finds all the stable matchings whenever one exists, and otherwise demonstrates that there is no stable matching.
Citation: Fuhito Kojima. Finding all stable matchings with couples. Journal of Dynamics & Games, 2015, 2 (3/4) : 321-330. doi: 10.3934/jdg.2015008
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