Characterizations of the cumulative offer process

Official URL: http://dx.doi.org/10.1007/s00355-016-0981-0

In the matching with contracts setting, we provide new axiomatic characterizations of the “cumulative offer process” ( COPCOP ) 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 COPCOP 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 COPCOP . Lastly, by extending Kojima and Manea’s (Econometrica 78:633–653, 2010) result, we show that the COPCOP is the unique stable and weakly Maskin monotonic mechanism. I am grateful to the associate editor and the anonymous referee for their through comments and suggestions. I thank Bertan Turhan for his comments. The author gratefully acknowledges the Marie Curie International Reintegration Grant (No: 618263) within the European Community Framework Programme and TÜBİTAK (The Scientific and Technological Research Council of Turkey) Grant (No: 113K763) within the National Career Development Program.