Non-revelation mechanisms for many-to-many matching: Equilibria versus stability

We study many-to-many matching markets in which agents from a set A are matched to agents from a disjoint set B through a two-stage non-revelation mechanism. In the first stage, A-agents, who are endowed with a quota that describes the maximal number of agents they can be matched to, simultaneously make proposals to the B-agents. In the second stage, B-agents sequentially, and respecting the quota, choose and match to available A-proposers. We study the subgame perfect Nash equilibria of the induced game. We prove that stable matchings are equilibrium outcomes if all A-agents' preferences are substitutable. We also show that the implementation of the set of stable matchings is closely related to the quotas of the A-agents. In particular, implementation holds when A-agents' preferences are substitutable and their quotas are non-binding.B. Klaus gratefully acknowledges financial support from the Swiss National Science Foundation (SNSF) for Project 100018_156201. F. Klijn gratefully acknowledges financial support from the Generalitat de Catalunya (2014-SGR-1064), the Spanish Ministry of Economy and Competitiveness through Plan Estatal de Investigación Científica y Técnica 2013–2016 (ECO2014-59302-P), and the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0563).Peer reviewe