In accordance with determination, a mathematical game theory is the theory of mathematical models of acceptance of optimum decisions in the conditions of conflict (and also in the conditions of vagueness). Therefore questions, related to the optimum conduct of sides in conflicts, with the desirable ends of conflicts, are in it basic. Direct questions such three:

1) What principles of optimality it is necessary to follow at consideration of conflicts of one or another type? Otherwise speaking, what the decision of one or another conflict consists (optimum) of?

2) Will realize as it applies to this class of the principle of optimality chosen for him? Legalistically this question is taken to existence at conflicts from the class of those decisions which by the chosen principle of as optimum.

3) What application of the chosen principle of consists of to this conflict (or to this class of )? For this question, finding of decision of conflict must an answer serve in that sense of word, in what it is accepted to talk about finding of decision as it applies to any task.

Unfortunately, the concept of optimality made decision is considerably more difficult added formalization, what concepts of conflict and decision-making. This task and until now — one of the most important in a theory games.

Because a mathematical game theory is a theory of models of making decision, it is not engaged in these decisions as psychological or volitional acts; it does not get busy and by the questions of their actual realization.

Within the framework of game theory, made decision come forward as the simplified enough and idealized charts of the real phenomena. Thus, certainly, the degree of this simplification must not excel the known limits after which a model loses the substantial lines of the phenomenon already.

That a game theory is theory of mathematical models, and it is the section of mathematics, means that the models constructed in it are formal, sign (but not, say, by a model or analog) and their forming and facilities of analysis is also formal.

In particular, legalistically must be entered basic concepts.

It means practically, that these concepts must by the properties which sense of axioms is the same given. Further formation of concepts and establishment of properties can be conducted already without that, to come running to some «intuitional» considering. The said not at all contests practical expedience of the use of intuition, especially as a method of practical verification of the legalistically got results.

In accordance with said at the construction of theory from the beginning necessary those concepts which are included in its determination: 1) conflict, 2) decision-making and 3) optimality of decision.