Characterizations of the cumulative offer process

In the matching with contracts setting, we provide new axiomatic characterizations of the "cumulative offer process" () in the domain of hospital choice functions that satisfy "unilateral substitutes" and "irrelevance of rejected contracts." We say that a mechanism is truncation-proof if no doctor can ever benefit from truncating his preferences. Our first result shows that the is the unique stable and truncation-proof mechanism. Next, we say that a mechanism is invariant to lower-tail preference change if no doctor's assignment changes after he changes his preferences over the contracts that are worse than his assignment. Our second result shows that a mechanism is stable and invariant to lower-tail preference change if and only if it is the . Lastly, by extending Kojima and Manea's (Econometrica 78:633-653, 2010) result, we show that the is the unique stable and weakly Maskin monotonic mechanism.