Smith and Rawls share a room: stability and medians
We consider one-to-one, one-sided matching (roommate) problems in which agents can
either be matched as pairs or remain single. We introduce a so-called bi-choice graph for
each pair of stable matchings and characterize its structure. Exploiting this structure we
obtain as a corollary the “lone wolf” theorem and a decomposability result. The latter result
together with transitivity of blocking leads to an elementary proof of the so-called stable
median matching theorem, showing how the often incompatible concepts of stability …
either be matched as pairs or remain single. We introduce a so-called bi-choice graph for
each pair of stable matchings and characterize its structure. Exploiting this structure we
obtain as a corollary the “lone wolf” theorem and a decomposability result. The latter result
together with transitivity of blocking leads to an elementary proof of the so-called stable
median matching theorem, showing how the often incompatible concepts of stability …
[CITATION][C] Smith and Rawls share a room: stability and medians, Meteor RM/08-009
B KLAUS - http://edocs. ub. unimaas. nl/loader/file. asp? id= 1307, 2008 - cir.nii.ac.jp
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