Matching with Contracts: Comment

The matching with contracts model (Hatfield and Milgrom 2005) is widely considered to be one of the most important advances of the last two decades in matching theory. One of their main messages is that the set of stable allocations is non-empty under a substitutes condition. We show that an additional irrelevance of rejected contracts (IRC) condition is implicitly assumed throughout their analysis, and in the absence of IRC several of their results, including the guaranteed existence of a stable allocation, fail to hold.