This article shows that, for any transferable utility game in coalitional form with a nonempty coalition structure core, the number of steps required to switch from a payoff configuration out of the coalition structure core to a payoff configuration in the coalition structure core is less than or equal to , where is the cardinality of the player set. This number improves the upper bounds found so far. We also provide a sufficient condition for the stability of the coalition structure core, i.e. a condition which ensures the accessibility of the coalition structure core in one step. On the class of simple games, this sufficient condition is also necessary and has a meaningful interpretation.
