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.