Monotonicity and Nash Implementation in Matching Markets with Contracts

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hat eld and Milgrom (2005), and analyze (Maskin) mono- tonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable. Furthermore, any solution that is Pareto e cient, individually rational, and monotonic is a superso- lution of the stable correspondence. In other words, the stable correspondence is the minimal solution that is Pareto e cient, individually rational, and implementable.