Issue: 2024/Vol.34/No.3, Pages 1-13
ON A MANY-SIDED MATCHING PROBLEM WITH MIXED PREFERENCES
Marcin Anholcer
, Maciej Bartkowiak
Cite as: M. Anholcer, M. Bartkowiak. On a many-sided matching problem with mixed preferences. Operations Research and Decisions 2024: 34(3), 1-13. DOI 10.37190/ord240301
Abstract
Motivated by recent results on lexicographic and cyclic preferences, we present new sufficient conditions for the existence of stable matching in many-sided matching problems. Here, our focus shifted towards integrating the two-sided matching problem, characterized by reciprocal preferences, with the many-sided matching problem, which involves cyclic preferences. In particular, we show that one of the configurations presented recently by Zhang and Zhong for three-sided matching problems can be generalized to more dimensions. In our setting, the preferences are cyclic and, in the case of all but two pairs of consecutive sets of agents, also reciprocal, which generalizes the three-set setting of Zhang and Zhong. Our approach can be also applied to generalize the problems with any system of cyclic preferences for which the existence of a stable matching is guaranteed.
Keywords: many-sided matching problem, stable matching, cyclic preferences, lexicographic preferences, mixed preferences, deferred acceptance algorithm
Received: 9 August 2023 Accepted: 14 July 2024
Published online: 17 October 2024