Characterizations of the cumulative offer process

In the matching with contracts setting, we provide new axiomatic characterizations of the “cumulative offer process” ( $${ COP}$$ C O P ) 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 $${ COP}$$ C O P 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 $${ COP}$$ C O P . Lastly, by extending Kojima and Manea’s (Econometrica 78:633–653, 2010) result, we show that the $${ COP}$$ C O P is the unique stable and weakly Maskin monotonic mechanism.