Lattice structure of the random stable set in many-to-many matching market

TL;DR

This paper investigates the lattice structure of random stable matchings in many-to-many markets, defining operations that reveal the dual lattice properties of these matchings.

Contribution

It introduces a partial order and binary operations that demonstrate the dual lattice structure of random stable matchings in many-to-many markets.

Findings

The set of random stable matchings forms two dual lattices.

Binary operations for least upper bound and greatest lower bound are defined.

The lattice structure provides new insights into the organization of matchings.

Abstract

For a many-to-many matching market, we study the lattice structure of the set of random stable matchings. We define a partial order on the random stable set and present two intuitive binary operations to compute the least upper bound and the greatest lower bound for each side of the matching market. Then, we prove that with these binary operations the set of random stable matchings forms two dual lattices.