Generalization of the social coalitional equilibrium structure

We generalize the notion of Ichiishi (Econometrica 49(2):369–377, 1981)’s social coalitional equilibrium to a multi-layered coalition structure with parameters, in which agents can incorporate simultaneously multiple coalition structures with multiple independent coalition-deviation opportunities. For each opportunity, agents play a social coalitional equilibrium (SCE) game, called a sub-parametric SCE game, constrained by external environment (parameters and joint decisions of all other sub-parametric SCE games). The generalized social coalitional equilibrium (GSCE) concept is, therefore, considered to be a synthesis of the Nash equilibrium concept and the cooperative solution concept. We provide the definition of GSCE and give the proof of existence theorem. Through some applications to general equilibrium models, the GSCE concept provides a conceptual framework for describing coexisting different industries having independent investment opportunities and their simultaneously determined industrial organizations.