Abstract-The process of effective interrelation necessary for teaching the subject at higher school has been represented as a noncooperative game between the professor and the students. This process is the functioning of teaching of organizational S system which comprises P -pedagogue (professor) and K -collective of students.The preference is given to the democratic model of relation -to objective and optimal mutual responsibility of the pedagogue and a student to the rights-obligations imposed on them. Two classes of models of noncooperatve games corresponding to management of S system have been built -games with relations of preferences and the games with utility. The main principle of optimality is the Nash equilibrium, or it is such kind of situation, none of the player it is not profitable the unilateral deviation from it. According to the indicated principle of equilibrium the tasks originated in the process of S system functioning has been solved.According to the solving results students must study systamatically do their tasks and teachers must be responsible objective for their work

This article is about the full analysis of one concrete class of general non-cooperative lexicographic games and its computer programming. In such game, the payoffs of players are lexicographic vector payoffs — m scalar criteria vectors. At the same time, these criteria are strictly ranked on the set of the situations with lexicographic preference. In some such kind of game a Nash's equilibrium may not exist. In the given article the full analysis of one class of dyadic lexicographic games is worked out. Such kind of class is the non-cooperative lexicographic games, where each player has got two pure strategies and the payoff of each player solely depends on the strategies of two players in each situation. Therefore, the player's payoffs are given by 2 × 2 matrices, the elements of which are lexicographic utilities.

Abstract-A new concept of a mixed strategy is given for m -dimensional lexicographic noncooperative ) ,..., , (game when on a set of pure strategies m -dimensional probability distributions are given. In this case eachcriteria of  game corresponds to its probability distributions on sets of pure strategies. Besides, a lexicographic m -dimensional order relation is given on set of m -dimensional p robability distribution. The given construction is made by the methodology of nonstandard analysis Therefore, the given mixed strategy is called a nonstandard mixed strategy, and a lexicographic game in such strategies is called a nonstandard mixed extension. An equilibriu m situation in mixed strategies is defined in  game. A nonstandard mixed extension of lexicographic matrix games is studied thoroughly. In such games, necessary and sufficient conditions of the existence of a saddle point are proved. The analy zed examples show that if in a lexicographic matrix game doesn't exist a saddle point in standard mixed strategies then a saddle point maybe doesn't exist in nonstandard mixed strategies. If in a lexicographic matrix game doesn't exist a saddle point in standard mixed strategies then there can be existed a saddle point in nonstandard mixed strategies. Thus, lexicographic games' nonstandard mixed distribution is a generalization of a standard mixed extension.

Neumann-Morgenstern's solutions) (v NM as stable solution's optimal principle is stated in a lexicographic T m

Abstract-In the article m dimensional lexicographic noncooperative games