# American Institute of Mathematical Sciences

March & April  2015, 2(3&4): 331-340. doi: 10.3934/jdg.2015009

## 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

 1 Department of Economics, Stanford University, Landau Economics Building, 579 Serra Mall, Room 344, Stanford University, Stanford, CA 94305-6072, United States

Received  April 2015 Revised  August 2015 Published  November 2015

Marilda Sotomayor is one of the pioneers of the theory of stable matching. She has published many important results, including some which are fundamental to subsequent developments. I will concentrate on one fundamental theorem, which today allows us to understand better why stable clearinghouses work so well. Demange, Gale and Sotomayor (1987)[16] proved a theorem which implies that when the set of stable matchings is small, participants in a stable clearinghouse will seldom be able to profit from strategically manipulating their preferences. More recent results show (empirically and theoretically) that the set of stable matchings can be expected to be small in typical applications. Therefore, reporting true preferences will be rewarded in clearinghouses that produce stable matchings in terms of stated preferences, and so there is a reason that such clearinghouses elicit sufficiently good preference data to produce matchings that are stable with respect to true preferences.
Citation: Alvin E. Roth. 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. Journal of Dynamics & Games, 2015, 2 (3&4) : 331-340. doi: 10.3934/jdg.2015009
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