Cores in Friend-Oriented Hedonic Games: Verification is Surprisingly Harder than Searching
share
We resolve an open question by Woeginger [Open Problem 13, SOFSEM '13] regarding the computational complexity of verifying whether a given coalition structure for friend-oriented preferences is stable. We show that this verification problem is coNP-complete. It remains so even when the directed friendship graph underlying the friend-oriented preferences is planar, has constant vertex-degree (i.e., each player has constant number of friends and is regarded as a friend by a constant number of other players), and the friendship preferences are symmetric. On the positive side, we observe that the verification problem becomes polynomial-time solvable if the friendship graph is acyclic or has maximum vertex-degree two.
READ FULL TEXT