Matching with contracts, substitutes and two-unit demand

- We consider the many-to-one matching with contracts model.
- We focus on choice functions that satisfy the IRC condition and two-unit demand.
- We show that weak and bilateral substitutability are equivalent.
- We obtain a new maximal domain for the existence of stable matchings with couples.

In the context of many-to-one matching with contracts, we show that for any choice function that satisfies the irrelevance of rejected contracts condition (Aygün and Sönmez, 2013) and selects at most two contracts from any given set of contracts (two-unit demand), bilateral substitutability and weak substitutability are equivalent. As a corollary, we obtain a new maximal domain for the existence of stable matchings in the unit-capacity couples model. Finally, we show with an example that the equivalence between bilateral and weak substitutability crucially depends on the two-unit demand condition.