AbstractThis paper proposes a new solution concept, based on the minimization, following the lexicographical order, of the complaint differences among coalitions in a cooperative n‐person game in characteristic function form. Such a solution minimizing the maximum complaint difference can be obtained as the pay‐off vector as the inequality constraints sequentially. A discussion is made on the pay‐off vector, which minimizes in the lexicographical order the complaint differences, taking the characteristics of the coalitions into consideration. Then as a method which can solve the formulated linear programming problem with less computational burden, an algorithm involving the relaxation method is proposed. A computer program was constructed and is applied to the cooperative water resource development pr