Envy-freeness in 3D hedonic games
Michael McKay – Ágnes Cseh – David Manlove
Autonomous Agents and Multi-Agent Systems
Volume 38 – Published:
Abstract
We study the problem of fairly partitioning a set of agents into coalitions based on the agents’ additively separable preferences, which can also be viewed as a hedonic game. We study three successively weaker solution concepts, related to envy, weakly justified envy, and justified envy. In a model in which coalitions may have any size, trivial solutions exist for these concepts, which provides a strong motivation for placing restrictions on coalition size. In this paper, we require feasible coalitions to have size three. We study the existence of partitions that are envy-free, weakly justified envy-free, and justified envy-free, and the computational complexity of finding such partitions, if they exist. 
We impose various restrictions on the agents’ preferences and present a complete complexity classification in terms of these restrictions.
Keywords: Coalition formation · Hedonic games · Multidimensional roommates · Envy-freeness
