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Regular version of the site

Book chapter

Matchings with Simplest Semiorder Preference Relations

P. 119-121.

Matching problem with preferences being simplest semiorders is analysed. It is proved that a stable matching always exists. Furthermore, for any stable matching there exists a linear extension of preferences, which does not sontradict stability of a matching. In the college admission problem common goal is to find student-optimal stable matching. We provide a simple criteria (Stable Improvement Cycle existence), that allows to check, whether some particular stable matching is student-side Pareto optimal.

In book

St. Petersburg: Graduate School of Management, St. Petersburg University, 2011.