On sufficient conditions for the existence of stable matchings with contracts

We introduce two new sufficient conditions for the existence of stable outcomes in many-to-one matching with contracts. The conditions subsume the observable substitutability of Hatfield et al. (2015) and the substitutable completability of Hatfield and Kominers (2016) as special cases. We also prove that unilaterally substitutability and irrelevance of rejected contracts imply substitutable completability

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 truncation-proof 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

一般化割当て問題における安定集合

研究種目：若手研究(B)研究期間：2016～2018課題番号：16K17079研究代表者：坂東　桂介研究者番号：50735412Other2016～2018年度科学研究費助成事業（若手研究(B)）研究成果報告書　課題番号：16K17079　研究代表者：坂東　桂介research repor

On sufficient conditions for the existence of stable matchings with contracts

We introduce two new sufficient conditions for the existence of stable outcomes in many-to-one matching with contracts. The conditions subsume the observable substitutability of Hatfield et al. (2015) and the substitutable completability of Hatfield and Kominers (2016) as special cases. We also prove that unilaterally substitutability and irrelevance of rejected contracts imply substitutable completability

Stability, Strategy-Proofness, and Cumulative Offer Mechanisms

We characterize when a stable and strategy-proof mechanism is guaranteed to exist in the setting of many-to-one matching with contracts. We introduce three novel conditions-observable substitutability, observable size monotonicity, and non-manipulability via contractual terms-and show that when these conditions are satisfied, the cumulative offer mechanism is the unique mechanism that is stable and strategy-proof (for workers). Moreover, we show that our three conditions are, in a sense, necessary: if the choice function of some firm fails any of our three conditions, we can construct unit-demand choice functions for the other firms such that no stable and strategy-proof mechanism exists. Thus, our results provide a rationale for the ubiquity of cumulative offer mechanisms in practice