On Sufficient Conditions for the Existence of Stable Matchings with Contracts

Abstract

We introduce two new sufficient conditions for the existence of stable outcomes in many-to-one matching with contracts. The conditions subsume the observable substitutability of Hatfield et al. (2015) and the substitutable completability of Hatfield and Kominers (2016) as special cases. We also prove that unilaterally substitutability and irrelevance of rejected contracts imply substitutable completability.