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Non-Revelation Mechanisms for Many-to-Many Matching: Equilibria versus Stability

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Working paper
Author/s: 
Non-Revelation Mechanisms for Many-to-Many Matching: Equilibria versus Stability
Issue number: 
894
Series: 
Barcelona GSE Working Paper
Publisher: 
Barcelona Graduate School of Economics
Year: 
2016
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.
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