Problem
Research questions and friction points this paper is trying to address.
Stable Matching
Complementary Preferences
Preference Misalignment
Many-to-One Matching
Computing Stable Matchings under Complementarities and Preference Misalignment
🤖 AI Summary
This study addresses the non-existence of many-to-one stable matchings arising from complementary preferences and preference misalignment by proposing the Combinatorial Deferred Acceptance (CDAR) algorithm. Methodologically, the existence of a stable matching is established through the identification of anchor workers and transitive alignment conditions. Furthermore, a re-proposal mechanism is designed, and an N-potential function analysis is introduced to guarantee finite-time convergence. Theoretically, the Pareto optimality of the output matching is formally proven. In terms of practical application, the effectiveness of the proposed approach is validated in scenarios such as traffic safety. Overall, this work systematically resolves the challenge of achieving many-to-one stable matchings under complex preference structures.
📝 Abstract
We study many-to-one, two-sided stable matching problems in which preferences are complementary and firms and workers may rank the same allocation differently. Here a coalition is a group of workers that can be jointly matched with a firm. With complementary preferences, a stable matching need not exist. We show that a stable matching exists for every instance when two conditions hold. The first requires each firm to have an anchor worker who is included in every feasible coalition that can be matched with that firm. The second is Transitive Alignment, which means there must be an overall ranking across different coalitions that is consistent with the workers'preferences. We propose CDAR (Combinatorial Deferred Acceptance with Reproposals), a Deferred Acceptance-style algorithm that permits reproposals, and prove its finite-time convergence and its output of a stable matching by constructing an $N$-digit potential function. Moreover, we show that, under strict preferences, the output of CDAR is Pareto optimal among stable matchings. The proposed framework naturally captures applications such as vehicle-route assignment for traffic safety and the misaligned interests of labor and management in wage negotiation.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Stable Matching
Complementary Preferences
Deferred Acceptance
Potential Function
Pareto Optimality
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