Relaxing the substitutes condition in matching markets with contracts

- New necessary condition for existence of a stable allocation (matching with contracts).
- New sufficient conditions for existence of a stable allocation.
- Conditioning on feasible worker preferences allows for new firm preferences.

In the many-to-one matching model with contracts, I provide new necessary and new sufficient conditions for the existence of a stable allocation. These new conditions exploit the fact that one side of the market has strict preferences over individual contracts.