Construction of an n-person cooperative fuzzy game in international fuzzy decision environments is considered. The international decision environment for the game analysed is two-fold-internal and external for a coalition, with group decision situations explicitly accounted for. The fuzzy game is constructed upon the diversifield evaluations in group decision making for the assessment of the characteristic functions of the game. The diversification of evaluations is represented as possibility distribution in fuzzy set theoretic terms. The optimizing rule for fuzzy decisions is used in construction of the fuzzy game. The properties of its solutions are examined.