Fuzzy coalition structures and some particular cases: Stackelberg and Cournot structures

The paper provides a formalism for the notion of fuzzy coalition and coalition structures of firms as the general case of coalitions and coalition structures. We study the properties of fuzzy coalition structures and introduce operations on coalitions. We investigate an important particular case, the coalitions and coalition structures, for which two axiom systems are proposed, depending on the type of interaction between coalitions: Stackelberg system and Cournot system. We define the notion of stability for coalition structures, study the properties of the stable coalition structures and propose a criterion to determine them. We give a connection between Stackelberg and Cournot structures and their comparison.