Choice correspondences that stay path-independent under every tie-breaking are rationalizable, produce generalized matroids, and allow a cycle-based characterization of constrained efficient stable matchings.
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Properties of Path-Independent Choice Correspondences and Their Applications to Efficient and Stable Matchings
Choice correspondences that stay path-independent under every tie-breaking are rationalizable, produce generalized matroids, and allow a cycle-based characterization of constrained efficient stable matchings.