5 problems

Assume there are $n$ representatives of each of three genders, with complete cyclic preference lists: representatives of the first gender rank representatives of the second, repres…

Circular-rule existence conjecture. Under the circular rule, every 3G matching market has a stable matching.

Strongest-link multiplicity conjecture. Under the strongest link rule, every 3G matching market has at least two stable matchings.

Circular matching existence conjecture. A stable outcome always exists for any circular 3D matching market.

Let $d\geq 2$, and let $X$ denote the distance from a typical point in one of two independent Poisson processes to its matched point under the two-color stable matching. Write…