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Strong core and Pareto-optimality in the multiple partners matching problem under lexicographic preference domains

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  • Biró, Péter
  • Csáji, Gergely

Abstract

We study strong core and Pareto-optimal solutions for multiple partners matching problem under lexicographic preference domains from a computational point of view. The restriction to the two-sided case is called stable many-to-many matching problem and the general one-sided case is called stable fixtures problem. We provide an example to show that the strong core can be empty even for many-to-many problems, and that deciding the non-emptiness of the strong core is NP-hard. On the positive side, we give efficient algorithms for finding a near feasible strong core solution and for finding a fractional matching in the strong core of fractional matchings. In contrast with the NP-hardness result for the stable fixtures problem, we show that finding a maximum size matching that is Pareto-optimal can be done efficiently for many-to-many problems. Finally, we show that for reverse-lexicographic preferences the strong core is always non-empty in the many-to-many case.

Suggested Citation

  • Biró, Péter & Csáji, Gergely, 2024. "Strong core and Pareto-optimality in the multiple partners matching problem under lexicographic preference domains," Games and Economic Behavior, Elsevier, vol. 145(C), pages 217-238.
    • Handle: RePEc:eee:gamebe:v:145:y:2024:i:c:p:217-238
    DOI: 10.1016/j.geb.2024.03.010
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