2008): “Monotonicity and Nash Implementation in Matching Markets with Contracts.” Economic Theory

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hateld 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 (Theorems 1 and 3). Furthermore, any solution that is Pareto ecient, individually rational, and mono-tonic is a supersolution of the stable correspondence (Theorem 2). In other words, the stable correspondence is the minimal solution that is Pareto ecient, individually rational, and implementable. JEL classication: C62, C78, D78, J41