Stability and values for games with coalition structures

Casajus (2008) established a link between coalition formation in hedonic games and players’ preferences over coalition structures. He showed that if a value concept for games with coalition structures (a CS-value) satisfies the splitting property and the aggregate component independence property, then the CS-value induces a hedonic game satisfying the common ranking property and yields a nonempty core. The following question was left open: What CS-values induce a hedonic game that does not satisfy the common ranking property but has a nonempty core? In this paper, we offer a set of properties that induces a hedonic game satisfying the top-coalition property, which is less demanding than the common ranking property but generates a nonempty core.