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The stable marriage problem with ties is a well-studied and interestingproblem in game theory. We are given a set of men and a set of women. Eachindividual has a preference ordering on the opposite group, which can possiblycontain ties. A stable marriage is given by a matching between men and womenfor which there is no blocking pair, i.e., a men and a women who strictlyprefer each other to their current partner in the matching.  In this paper, we study the diameter of the polytope given by the convex hullof characteristic vectors of stable marriages, in the setting with ties. Weprove an upper bound of $\lfloor \frac{n}{3}\rfloor$ on the diameter, where $n$is the total number of men and women, and give a family of instances for whichthe bound holds tight. Our result generalizes the bound on the diameter of thestandard stable marriage polytope (i.e., the well-known polytope that describesthe setting without ties), developed previously in the literature.

On the diameter of the polytope of the stable marriage with ties