We introduce Bel coalitional games, that generalize classical coalitional games, where uncertainty is modelled through the Dempster-Shafer theory and every agent can have different knowledge. We propose the notion of contract in our framework, that specify how agents divide the values of the coalitions and we use the Choquet integral to model the agents’ preferences between contracts. Next, we study the core under two different moments of the game by defining the ex-ante core and the ex-t-interim core, where, in the latter, we need the Dempster conditional rule to update the mass functions of agents. In particular, in the last step of the ex-t-interim case and when the set of states reduces to singleton, i.e. when there is no uncertainty, we recover the classical definition of the core. Finally, we show some results about the ex-ante and the ex-t-interim core of Bel coalitional games, following the well-known results about classical coalitional games.