TL;DR
This paper introduces non-uniform stability as a generalization of super-stability and strong stability in stable matchings with ties, providing polynomial-time existence checks, a polyhedral characterization, and lattice structure analysis.
Contribution
It defines non-uniform stability, proves polynomial-time existence determination, offers a polyhedral characterization, and shows the set forms a distributive lattice.
Findings
Existence of non-uniformly stable matchings can be decided in polynomial time.
The set of non-uniformly stable matchings has a polyhedral structure.
Non-uniformly stable matchings form a distributive lattice.
Abstract
Super-stability and strong stability are properties of a matching in the stable matching problem with ties. In this paper, we introduce a common generalization of super-stability and strong stability, which we call non-uniform stability. First, we prove that we can determine the existence of a non-uniformly stable matching in polynomial time. Next, we give a polyhedral characterization of the set of non-uniformly stable matchings. Finally, we prove that the set of non-uniformly stable matchings forms a distributive lattice.
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Taxonomy
TopicsGame Theory and Voting Systems · Functional Equations Stability Results