Top coalitions, common rankings, and semistrict core stability

The top coalition property of Banerjee et al. (2001) and the common ranking property of Farrell and Scotchmer (1988) are sufficient conditions for core stability in hedonic games. We introduce the semistrict core as a stronger stability concept than the core, and show that the top coalition property guarantees the existence of semistrictly core stable coalition structures. Moreover, for each game satisfying the common ranking property, the core and the semistrict core coincide.