Stable families of coalitions and normal hypergraphs

Abstract The core of a game is defined as the set of outcomes acceptable for all coalitions. This is probably the simplest and most natural concept of cooperative game theory. However, the core can be empty because there are too many coalitions. Yet, some players may not like or know each other, so they cannot form a coalition. The following generalization seems natural. Let K be a fixed family of coalitions. The K -core is defined as the set of outcomes acceptable for all the coalitions from K . Let us call a family K g-stable if the K -core is not empty for any finite normal form game, and similarly, let K be called V-stable if the K -core is not empty for any compact superadditive NTU-game. We prove that both V- and g-stability of a family K are equivalent with the normality of K . Normal hypergraphs can be characterized by several equivalent properties, e.g. they are dual to clique hypergraphs of perfect graphs.

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