Strongly balanced cooperative games

Kaneko/Wooders (1982) derived a list of necessary and sufficient conditions for a partitioning game to have a nonempty core regardless of the payoff functions of its effective coalitions. The main purpose of our paper is to provide a graph-theoretical characterization of this family of games whose associated hypergraphs we callstrongly balanced: we show that the strong balancedness condition is equivalent to thenormality of the hypergraph, which is a type ofcoloring property (Lovasz (1972)). We also study interesting economic examples ofcommunication andassignment games and provide direct proofs that their associated hypergraphs are strongly balanced.We wish to thank two anonymous referees of this journal for their useful comments and suggestions. The previous version of this paper was written while the authors were visiting Department of Economics, University of Bonn. The financial support of Sonderfor-schungsbereich 303 is gratefully acknowledged.