A Note on the Core of 2-Matching Games

TL;DR

This paper studies the core of cooperative 2-matching games, providing a polynomial-time separation algorithm and establishing a compact extended formulation, thereby addressing previous gaps in understanding their structure.

Contribution

It introduces a polynomial-time separation procedure for the core of 2-matching games and proves the existence of a compact extended formulation, fixing prior inaccuracies.

Findings

Polynomial-time separation over the core of 2-matching games.

Existence of a compact extended formulation for the core.

Correction of a flaw in previous literature.

Abstract

Cooperative 2-matching games are a generalization of cooperative matching games, where the value function is given by maximum-weight b-matchings, for a vertex capacity vector $b \leq 2$. We show how to separate over the core of 2-matching games in polynomial time, fixing a small flaw in the literature, and prove the existence of a compact extended formulation for it.