Bel coalitional games with application to market games

We define Bel coalitional games, that generalize classical coalitional games by introducing uncertainty in the framework. Unlike Bayesian coalitional games, 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 specifies how agents divide the values of the coalitions and we use the Choquet integral to model the agents' preferences between contracts. In a second step, we define 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 a singleton, i.e., when there is no uncertainty, we recover the classical definition of the core. We give some conditions for the nonemptiness of the ex-ante and the ex-t-interim core of Bel coalitional games, considering different types of agents' knowledge and different kind of games. Finally, we present Bel market games as an economical application.