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 rst established that every hyperadditive game is balanced: we propose a formula allowing to compute some core allocations; and this leads to the denition of a single-valued solution (for hyperadditive games) satisfying the axioms of symmetry, dummy and core selection. This solution coincides with the Shapley value on the subclass of convex games. Furthermore, we prove that the bargaining set of a hyperadditive game always coincides with 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. Some new results are also derived for these classes of games.