Miranda Menéndez, PedroGrabisch, Michel2023-06-202023-06-2020100377-221710.1016/j.ejor.2008.12.020https://hdl.handle.net/20.500.14352/42370In this paper, we present a generalization of the concept of balanced game for finite games. Balanced games are those having a nonempty core, and this core is usually considered as the solution of the game. Based on the concept of k-additivity, we define the so-called k-balanced games and the corresponding generalization of core, the k-additive core, whose elements are not directly imputations but k-additive games. We show that any game is k-balanced for a suitable choice of k, so that the corresponding k-additive core is not empty. For the games in the k-additive core, we propose a sharing procedure to get an imputation and a representative value for the expectations of the players based on the pessimistic criterion. Moreover, we look for necessary and sufficient conditions for a game to be k-balanced. For the general case, it is shown that any game is either balanced or 2-balanced. Finally, we treat the special case of capacities.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S037722170801062Xhttp://www.sciencedirect.comrestricted access519.83Cooperative gamesk-AdditivityBalanced gamesCapacitiesCoreInvestigación operativa (Matemáticas)1207 Investigación Operativa