Nash Stability in Hedonic Skill Games

Laurent Gourvès, Gianpiero Monaco

Abstract: This article deals with hedonic skill games, the strategic counterpart of coalitional skill games which model collaboration among entities through the abstract notions of tasks and the skills required to complete them. We show that deciding whether an instance of the game admits a Nash stable outcome is NP-complete in the weighted tasks setting. We then characterize the instances admitting a Nash stable outcome in the weighted tasks setting. This characterization relies on the fact that every agent holds (resp., every task requires) either a single skill or more than one skill. For these instances, the complexity of computing a Nash stable outcome is determined, together with the possibility that a natural dynamics converges to a Nash stable outcome from any initial configuration. Our study is completed with a thorough analysis of the price of anarchy of instances always admitting a Nash stable outcome.