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Matching markets consist of two disjoint sets of agents, where each agent has a preference list over agents on the other side. The primary objective is to find a stable matching between the agents such that no unmatched pair of agents prefer each other to their matched partners. The incompatibility between stability and strategy-proofness in this domain gives rise to a variety of strategic behavior of agents, which in turn may influence the resulting matching. In this paper, we discuss fundamental properties of stable matchings, review essential structural observations, survey key results in manipulation algorithms and their game-theoretical aspects, and more importantly, highlight a series of open research questions.
Hosseini et al. (Fri,) studied this question.