Core Stability in Altruistic Coalition Formation Games

Matthias Hoffjan, Anna Maria Kerkmann, Jörg Rothe

Abstract: Coalition formation games model settings where sets of agents have to partition into groups. We study the notion of core stability in the context of altruistic coalition formation games (ACFGs). While in most commonly studied classes of coalition formation games agents seek to maximize their individual valuations, agents are not completely selfish in ACFGs. Given some underlying network of friendship, the agents also take into account their friends’ valuations when comparing different coalitions or coalition structures. The notion of the core has been extensively studied for several classes of (hedonic) coalition formation games. Kerkmann and Rothe [7] initiated the study of core stability in ACFGs. They showed that verifying core stability is \(\textrm{coNP}\)-complete for selfish-first ACFGs—their least altruistic case of ACFGs. The complexity of the other two (more altruistic) degrees of altruism, however, remained an open problem. We show that the core stability verification problem is \(\textrm{coNP}\)-complete for all cases of ACFGs, i.e., for all three degrees of altruism and for both sum-based and minimum-based aggregation of the friends’ preferences.