Hyperadditive games and applications to networks or matching problems

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For the class of cooperative games with transferable utility, we introduce and study the notion of hyperadditivity, a new cohesiveness property weaker than convexity and stronger than superadditivity. It is first established that every hyperadditive game is balanced: we propose a formula allowing to compute some core allocations; and this leads to the definition of a single-valued solution that satisfies core selection for hyperadditive games. This new solution coincides with the Shapley value on the subclass of convex games. Furthermore, we prove that the bargaining set of a hyperadditive game is equal to its core. It is shown that many well-known economic applications satisfy hyperadditivity. Our work extends (and gives a unifying explanation for) various results found in the literature on network games, assignment games and convex games. In addition, some new results are derived for these respective families of games.