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Random Paths to Pairwise Stability in Many-to-Many Matching Problems: A Study on Market Equilibration

20 Pages Posted: 9 Mar 2006  

Fuhito Kojima

Harvard University - Department of Economics

M. Utku Ünver

Boston College - Department of Economics

Date Written: August 2006

Abstract

This paper considers a decentralized process in many-to-many matching problems. We show that if agents on one side of the market have substitutable preferences and those on the other side have responsive preferences, then, from an arbitrary matching, there exists a finite path of matchings such that each matching on the path is formed by satisfying a blocking individual or a blocking pair for the previous matching, and the final matching is pairwise-stable. This implies that an associated stochastic process converges to a pairwise-stable matching in finite time with probability one, if each blocking individual or pair is satisfied with a positive probability at each period along the process.

Keywords: Many-to-many matching, pairwise stability, stability, random paths

JEL Classification: C71, C78

Suggested Citation

Kojima, Fuhito and Ünver, M. Utku, Random Paths to Pairwise Stability in Many-to-Many Matching Problems: A Study on Market Equilibration (August 2006). Available at SSRN: https://ssrn.com/abstract=888640 or http://dx.doi.org/10.2139/ssrn.888640

Fuhito Kojima

Harvard University - Department of Economics ( email )

Littauer Center
Cambridge, MA 02138
United States

Utku Unver (Contact Author)

Boston College - Department of Economics ( email )

140 Commonwealth Ave.
Chestnut Hill, MA 02467
United States
+1 (617) 552 2217 (Phone)
+1 (617) 552 2318 (Fax)

HOME PAGE: http://www2.bc.edu/~unver

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