The Usefulness of Cooperation in Two-Person Games with Quadratic Pay off Functions on the Rectangle

In 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 game, cooperation, usefulness, strategy, quadratic payoff functions