A Model of Decentralized Matching without Transfers

35 Pages Posted: 20 Dec 2016 Last revised: 26 Jun 2018

See all articles by Alfred Galichon

Alfred Galichon

NYU, Department of Economics and Courant Institute

Yu-Wei Hsieh

University of Southern California - Department of Economics; USC Dornsife Institute for New Economic Thinking

Multiple version iconThere are 2 versions of this paper

Date Written: June 20, 2018

Abstract

We propose a non-transferable utility (NTU) model of matching with unobserved heterogeneity in tastes that serves as a counterpart to Choo and Siow's celebrated model in the transferable utility (TU) case. Our model captures an exchange economy with indivisible goods, fixed prices and no centralized assignment mechanism. To study such decentralized matching markets, we suggest a solution concept called "equilibrium under rationing-by-waiting", which is new in a matching context, and in which a non-transferable numeraire (e.g., time) replaces a transferable numeraire (e.g., money) as the competitive market-clearing device. The matching function that we obtain is a Leontief function, whereas Choo and Siow obtained a Cobb-Douglas function. We then investigate the properties of equilibrium (existence, uniqueness, and welfare) and show that the equilibrium outcome can be obtained using a modified deferred-acceptance algorithm, with Gale-Shapley's proposal/disposal phases replaced by linear programming problems. Finally, we study the connection of equilibrium under rationing-by-waiting to the classical NTU matching theory based on pairwise stability and aggregate/large NTU matching.

Keywords: two-sided matching; non-transferable utility matching; rationing by waiting; non-price rationing; aggregate matching; matching function; disequilibrium; discrete choice; optimal transport

JEL Classification: C78, D58

Suggested Citation

Galichon, Alfred and Hsieh, Yu-Wei, A Model of Decentralized Matching without Transfers (June 20, 2018). Available at SSRN: https://ssrn.com/abstract=2887732 or http://dx.doi.org/10.2139/ssrn.2887732

Alfred Galichon (Contact Author)

NYU, Department of Economics and Courant Institute ( email )

269 Mercer Street, 7th Floor
New York, NY 10011
United States

Yu-Wei Hsieh

University of Southern California - Department of Economics ( email )

3620 South Vermont Ave. Kaprielian (KAP) Hall, 300
Los Angeles, CA 90089
United States

USC Dornsife Institute for New Economic Thinking ( email )

3620 S. Vermont Avenue, KAP 364F
Los Angeles, CA 90089-0253
United States

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