Matching Markets under (In)complete Information

Abstract

L. Ehlers acknowledges financial support from the SSHRC (Canada) and the FQRSC (Québec). Support for the research of J. Massó was received through the prize "ICREA Acadèmia" for excellence in research, funded by the Generalitat de Catalunya. He also acknowledges the support of MOVE (where he is an affiliated researcher) and the Government of Catalonia, through grants SGR 2009-419 and 2014-515. His work is also supported by the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centers of Excellence in R&D (SEV-2011-0075) and FEDER grant ECO2008-04756 (Grupo Consolidado C). Part of this research was done while J. Massó was visiting the Université de Montréal and while L. Ehlers was visiting the Universitat Autònoma de Barcelona; the visits were financed by CIREQ and CREA, respectively.

Altres ajuts: FEDER/ECO2008-04756

We introduce incomplete information to centralized many-to-one matching markets. This is important because in real life markets (i) any agent is uncertain about the other agents' true preferences and (ii) most entry-level matching is many-to-one (and not one-to-one). We show that given a common prior, a strategy profile is an ordinal Bayesian Nash equilibrium under incomplete information in a stable mechanism if and only if, for any true profile in the support of the common prior, the submitted profile is a Nash equilibrium under complete information in the direct preference revelation game induced by the stable mechanism.