Nash-Implementation in Two-Sided Matching with Substitutable Contracts

I examine two types of mechanisms, demand revelation mechanisms and preference revelation mechanisms, in many-to-one matching problems. As in Hatfield and Milgrom (2005), I consider general matching problems with contracts. I show that the core correspondence is not Nash-implementable by any demand/preference revelation mechanism. A strong version of Maskin monotonicity plays a crucial role for this impossibility result. Second, I show that Nash equilibrium outcomes of the preference revelation game induced by any Pareto efficient matching procedure coincide with the set of individually rational allocations. This is a generalization of Alcalde (1996)’s result for one-to-one matching problems without contracts. In addition, I show that there exists a stable Nash equilibrium outcome with respect to the true preferences.