On sufficient conditions for the existence of stable matchings with contracts

- We propose two new sufficient conditions for stable outcomes to exist in many-to-one matching with contracts.
- The conditions subsume observable substitutability as a special case.
- The conditions also subsume substitutable completability as a special case.
- We also prove that unilateral substitutability and irrelevance of rejected contracts imply substitutable completability.

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.