@article{7d6a070e8dd44ac5ac808553d47388dc,
title = "Stability properties of the core in a generalized assignment problem",
abstract = "We show that the core of a generalized assignment problem satisfies two types of stability properties. First, the core is the unique stable set defined using the weak domination relation when outcomes are restricted to individually rational and pairwise feasible ones. Second, the core is the unique stable set with respect to a sequential domination relation that is defined by a sequence of weak domination relations that satisfy outsider independence. An equivalent way of stating this result is that the core satisfies the property commonly stated as the existence of a path to stability. These results add to the importance of the core in an assignment problem where agents' preferences may not be quasilinear.",
keywords = "Core, Generalized assignment problem, Path to stability, Stable set",
author = "Keisuke Bando and Ryo Kawasaki",
note = "Funding Information: The authors thank an advisory editor and two anonymous reviewers for their valuable comments that have greatly improved this paper. The authors also thank Toshiyuki Hirai, Manabu Toda, and the seminar participants at Shinshu University, Waseda University, and the Game Theory Workshop 2021 held online in Japan for valuable comments. The authors also thank Editage for English editing. This research is financially supported by JSPS KAKENHI Grant Numbers JP17K13696 (Kawasaki), JP20K01543 (Kawasaki), JP19K13647 (Bando), and JP16H03121 (both). Funding Information: The authors thank an advisory editor and two anonymous reviewers for their valuable comments that have greatly improved this paper. The authors also thank Toshiyuki Hirai, Manabu Toda, and the seminar participants at Shinshu University, Waseda University, and the Game Theory Workshop 2021 held online in Japan for valuable comments. The authors also thank Editage for English editing. This research is financially supported by JSPS KAKENHI Grant Numbers JP17K13696 (Kawasaki), JP20K01543 (Kawasaki), JP19K13647 (Bando), and JP16H03121 (both). Publisher Copyright: {\textcopyright} 2021 The Author(s)",
year = "2021",
month = nov,
doi = "10.1016/j.geb.2021.08.007",
language = "English",
volume = "130",
pages = "211--223",
journal = "Games and Economic Behavior",
issn = "0899-8256",
publisher = "Academic Press Inc.",
}