Discrete and Continuous Models and Applied Computational ScienceDiscrete and Continuous Models and Applied Computational Science2658-46702658-7149Peoples' Friendship University of Russia named after Patrice Lumumba (RUDN University)8215Research ArticleThe Usefulness of Cooperation in Two-Person Games with Quadratic Pay off Functions on the RectangleAboubacarMDepartment of Mathematics and Computer Science Faculty of Sciences-Abdou Moumouni University1504201545908092016Copyright © 2015,2015In this paper we study an important question for the game theory of two players, about essentiality of such games. The investigation is carried out in a particular case, in the class of games with quadratic payoff functions on a rectangle. The essentiality in two players’ games means that by joining the two players in union, both players can get positive additions to guaranteed payoff. The essentiality of two players’ games has not always occurred. Thus, the joining of the two players in union, in general, may be useful and sometimes (in case of absence of essentiality) useless. In applications, for example in analysis of the economic activities of firms or countries, the question of usefulness of the union acquires a lot of interest. In the general game theory, the question of essentiality of games is given a little attention at the moment. Apparently, this is due to the difficulty of this problem in the general case. Note that the games with quadratic payoff functions are frequently used in game theory for modeling different kinds of processes being investigated, for example, in mathematical economics.two-person gamecooperationusefulnessstrategyquadratic payoff functionsигра двух игроковкооперацияполезностьстратегияквадратичные функции выигрыша[Воробьев Н.Н. Теория игр для экономистов-кибернетиков. М.: Наука, 1985.][Мулен Э. Теория игр с примерами из математической экономики. М.: Мир, 1985.][Петросян Л.А., Зенкевич Н.А., Семина Е.А. Теория игр. М.: Высшая школа, 1998.][Жуковский В.И. Кооперативные игры при неопределенности и их приложения. М.: Эдиториал УРСС, 1999.]