Accessibility and stability of the coalition structure core (original) (raw)

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 (n 2 + 4n)/4, where n 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. We would like to thank two anonymous referees for very valuable suggestions which have led to an improvement of the article. We have also benefited from comments of participants at the SING VII conference in Paris where an earlier draft of the article circulated under the title "On the number of blocks required to access the coalition structure core". Financial support the National Agency for Research (ANR)-research programs "Models of Influence and Network Theory" ANR.09.BLANC-0321.03 and "Mathématiques de la décision pour l'ingénierie physique et sociale" (MODMAD)-is gratefully acknowledged.