TY - GEN
T1 - On (Coalitional) Exchange-Stable Matching
AU - Chen, Jiehua
AU - Chmurovic, Adrian
AU - Jogl, Fabian
AU - Sorge, Manuel
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021/1/1
Y1 - 2021/1/1
N2 - We study, which Alcalde [Economic Design, 1995] introduced as an alternative solution concept for matching markets involving property rights, such as assigning persons to two-bed rooms. Here, a matching of a given Stable Marriage or Stable Roommates instance is called if it does not admit any, that is, a subset S of agents in which everyone prefers the partner of some other agent in S. The matching is if it does not admit any, that is, an exchange-blocking coalition of size two. We investigate the computational and parameterized complexity of the Coalitional Exchange-Stable Marriage (resp. Coalitional Exchange Roommates) problem, which is to decide whether a Stable Marriage (resp. Stable Roommates) instance admits a coalitional exchange-stable matching. Our findings resolve an open question and confirm the conjecture of Cechlárová and Manlove [Discrete Applied Mathematics, 2005] that Coalitional Exchange-Stable Marriage is NP-hard even for complete preferences without ties. We also study bounded-length preference lists and a local-search variant of deciding whether a given matching can reach an exchange-stable one after at most k, where a swap is defined as exchanging the partners of the two agents in an exchange-blocking pair.
AB - We study, which Alcalde [Economic Design, 1995] introduced as an alternative solution concept for matching markets involving property rights, such as assigning persons to two-bed rooms. Here, a matching of a given Stable Marriage or Stable Roommates instance is called if it does not admit any, that is, a subset S of agents in which everyone prefers the partner of some other agent in S. The matching is if it does not admit any, that is, an exchange-blocking coalition of size two. We investigate the computational and parameterized complexity of the Coalitional Exchange-Stable Marriage (resp. Coalitional Exchange Roommates) problem, which is to decide whether a Stable Marriage (resp. Stable Roommates) instance admits a coalitional exchange-stable matching. Our findings resolve an open question and confirm the conjecture of Cechlárová and Manlove [Discrete Applied Mathematics, 2005] that Coalitional Exchange-Stable Marriage is NP-hard even for complete preferences without ties. We also study bounded-length preference lists and a local-search variant of deciding whether a given matching can reach an exchange-stable one after at most k, where a swap is defined as exchanging the partners of the two agents in an exchange-blocking pair.
UR - https://www.scopus.com/pages/publications/85115883742
U2 - 10.1007/978-3-030-85947-3_14
DO - 10.1007/978-3-030-85947-3_14
M3 - Conference contribution
AN - SCOPUS:85115883742
SN - 9783030859466
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 205
EP - 220
BT - Algorithmic Game Theory - 14th International Symposium, SAGT 2021, Proceedings
A2 - Caragiannis, Ioannis
A2 - Hansen, Kristoffer Arnsfelt
PB - Springer Science and Business Media Deutschland GmbH
T2 - 14th International Symposium on Algorithmic Game Theory, SAGT 2021
Y2 - 21 September 2021 through 24 September 2021
ER -