The Core of a coalitional exchange economy

In pure exchange economies, a poor attention has been given to how the individual consumption possibilities of the members of a coalition should be represented. It seems economically reasonable that our knowledge and our possibility to make decisions depend on the coalition we belong to. We define a coalitional exchange economy by considering a pure exchange economy in which the individual consumption sets of consumers within a coalition depend on the membership of the coalition. Our definition includes as a particular case the classical definition of pure exchange economy. We adapt the core concept to a coalitional exchange economy, and we show the non-emptiness of the core. Finally, we discuss more general setting where individual preferences are also depending on the coalitions.