Stability based on single-agent deviations in additively separable hedonic games

Coalition formation is a central concern in multiagent systems. A common desideratum for coalition structures is stability, defined by the absence of beneficial deviations of single agents. Such deviations require an agent to improve her utility by joining another coalition. On top of that, the feasibility of deviations may also be restricted by demanding consent of agents in the welcoming and/or the abandoned coalition. While most of the literature focuses on deviations constrained by unanimous consent, we also study consent decided by majority vote and introduce two new stability notions that can be seen as local variants of another solution concept called popularity. We investigate stability in additively separable hedonic games by pinpointing boundaries to computational complexity depending on the type of consent and friend-oriented utility restrictions. The latter restrictions shed new light on well-studied classes of games based on the appreciation of friends or the aversion to enemies. Many of our positive results follow from a new combinatorial observation that we call the Deviation Lemma and that we leverage to prove the convergence of simple and natural single-agent dynamics under fairly general conditions. Our negative results, in particular, resolve the complexity of contractual Nash stability in additively separable hedonic games.