Super altruistic hedonic games

Hedonic games are coalition formation games in which agents' utility depends only on their own coalition. The introduction of Altruistic Hedonic Games increased the expressive potential of Hedonic Games by considering the utility of each of the agent's friends within the coalition. We introduce Super Altruistic Hedonic Games (SAHGs), in which an agent's utility may depend on the utility of all other agents in the coalition, weighted according to their distance in the friendship graph. We establish the framework for this new model and investigate the complexity of multiple notions of stability. We show that SAHGs generalize Friend-oriented Hedonic Games, Enemy-oriented Hedonic Games, and selfish-first Altruistic Hedonic Games, inheriting the hardness results of these games as minimum upper complexity bounds. We also give SAHGs that have neither Nash stable nor strictly core stable partitions.