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 .
JC was supported by the WWTF research project (VRG18-012). MS was supported by the Alexander von Humboldt Foundation.
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Chen, J., Chmurovic, A., Jogl, F., Sorge, M. (2021). On (Coalitional) Exchange-Stable Matching. In: Caragiannis, I., Hansen, K.A. (eds) Algorithmic Game Theory. SAGT 2021. Lecture Notes in Computer Science(), vol 12885. Springer, Cham. https://doi.org/10.1007/978-3-030-85947-3_14
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