Friend- and Enemy-oriented Hedonic Games With Strangers Full Version (2409.16579v1)

Abstract: We introduce friend- and enemy-oriented hedonic games with strangers (FOHGS and EOHGS respectively), two classes of hedonic games wherein agents are classified as friends, enemies, or strangers under the assumption that strangers will become either friends or enemies ex post facto. For several notions of stability in FOHGS and EOHGS, we characterize the hardness of verification for possible and necessary stability. We characterize the hardness of deciding whether possibly and necessarily X stable partitions exist for a given stability notion X. We prove that necessarily internally stable partitions always exist and provide sufficient conditions for necessary contractual individual stability.