@article{7473ec92fd464d4f8f5cc06b962ab990,
title = "Substitutes and stability for many-to-many matching with contracts",
abstract = "We examine the roles of (slightly weakened versions of) the observable substitutability condition and the observable substitutability across doctors condition of Hatfield et al. (2021) in many-to-many matching with contracts. We modify the standard cumulative offer algorithm to find stable outcomes and prove new results on the existence of stable outcomes. It is remarkable that size monotonicity at the offer-proposing side is essential for the existence result under observable substitutability across doctors.",
keywords = "Cumulative offer algorithm, Many-to-many matching, Observable substitutability, Size monotonicity, Stability",
author = "Keisuke Bando and Toshiyuki Hirai and Jun Zhang",
note = "Funding Information: This paper is the consolidation of the formerly circulated draft “Existence of a Stable Outcome Under Observable Substitutability Across Doctors in Many-to-Many Matching with Contracts” by Bando and Hirai and another draft “Observable Substitutability in Many-to-Many Matching with Contracts” by Zhang. We are grateful to an anonymous referee, an advisory editor, the participants of Microeconomics Workshop at Keio University, UECE Lisbon Meeting in Game Theory and Applications 2018, and 3rd East Asia Game Theory (EAGT) International Conference for their comments and suggestions. This research is supported by JSPS KAKENHI (Grant No. 19K13647 ). Jun Zhang is supported by National Natural Science Foundation of China (Grant No. 71903093 and 72033004 ). Funding Information: This paper is the consolidation of the formerly circulated draft ?Existence of a Stable Outcome Under Observable Substitutability Across Doctors in Many-to-Many Matching with Contracts? by Bando and Hirai and another draft ?Observable Substitutability in Many-to-Many Matching with Contracts? by Zhang. We are grateful to an anonymous referee, an advisory editor, the participants of Microeconomics Workshop at Keio University, UECE Lisbon Meeting in Game Theory and Applications 2018, and 3rd East Asia Game Theory (EAGT) International Conference for their comments and suggestions. This research is supported by JSPS KAKENHI (Grant No. 19K13647). Jun Zhang is supported by National Natural Science Foundation of China (Grant No. 71903093 and 72033004). Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",
year = "2021",
month = sep,
doi = "10.1016/j.geb.2021.07.002",
language = "English",
volume = "129",
pages = "503--512",
journal = "Games and Economic Behavior",
issn = "0899-8256",
publisher = "Academic Press Inc.",
}