Finding a minimum-regret many-to-many Stable Matching

Abstract

The many-to-many Stable Matching (MM) problem is defined on a set of workers and a set of firms and asks for an allocation of workers to firms that satisfies the firms' quotas and the preferences of workers for firms and vice-versa. This article proposes a time-optimal algorithm for solving the minimum-regret problem for the MM, i.e. the problem of finding the MM solution in which the agent that is least well off is matched with the best possible set of agents of the opposite set. The proposed algorithm utilizes the notion of rotations and extends an analogous result for the Stable Marriage problem.