Characterizations of the cumulative offer process

In the matching with contracts setting, we provide two new axiomatic characterizations of the “cumulative offer process” (COP ) in the domain of hospital choices satisfying “unilateral substitutes” and “irrelevance of rejected contracts.” We say that a mechanism is truncationproof if no doctor can ever benefit from truncating his preferences. Our first result shows that the COP is the unique stable and truncation-proof mechanism. Next, we say that a mechanism is invariant to lower tail preferences change if any doctor’s assignment does not depend on his preferences over worse contracts. Our second characterization shows that a mechanism is stable and invariant to lower tail preferences change if and only if it is the COP . JEL classification: C78, D44, D47.