Hedonic Expertise Games

TL;DR

This paper models team formation with expertise considerations as hedonic games, demonstrating existence and computational properties of stable and optimal partitions, and extends results to a broader class of monotone submodular hedonic games.

Contribution

It introduces a novel hedonic game model for expertise-based team formation and proves existence, stability, and approximation results, extending to a larger class of monotone submodular hedonic games.

Findings

Existence of Nash stable, core stable, and Pareto optimal partitions.

Polynomial-time algorithms for certain stable partitions.

Approximation of core stability within a factor of 1 - 1/e.

Abstract

We consider a team formation setting where agents have varying levels of expertise in a global set of required skills, and teams are ranked with respect to how well the expertise of teammates complement each other. We model this setting as a hedonic game, and we show that this class of games possesses many desirable properties, some of which are as follows: A partition that is Nash stable, core stable and Pareto optimal is always guaranteed to exist. A contractually individually stable partition (and a Nash stable partition in a restricted setting) can be found in polynomial-time. A core stable partition can be approximated within a factor of $1 - \frac{1}{e}$, and this bound is tight unless $\sf P = NP$. We also introduce a larger and relatively general class of games, which we refer to as monotone submodular hedonic games with common ranking property. We show that the above multi-concept existence guarantee also holds for this larger class of games.