Stochastic games are discussed as a priva-te class of a general dynamic games. A certain class of lexicographic noncooperative games is studied - lexi-cographic stochastic matrix games . The problem of the existence of Nash equilibrium is studied with two analyses - standard and nonstandard way. Standard means using the same kind of mixed strategies in case of scalar games. In this case in lexi-cographic stochastic matrix game Nash equilibrium may not be existed. Its existence takes place in relevant stochastic affine matrix game to the existence of Nash equilibrium. In game a set of Nash equi-librium is given by means of relevant stochastic affine matrix game's set of equilibrium. The sufficient condi-tions of the existance such affine game is proved. In nonstandard way of analyses we use such mixed stra-tegies, they use components with lexicog-raphic probabilites. In this case the kinds of subsets of a set of equilibrium in game are described.

A system of interpersonal relationship and its modeling in the form of finite noncooperative game is studied in this article by means of payoff functions. In such games for the main principle of optimality Nash’s Equilibrium Situation is acknowledged. The stages of development of Game Theory are analyzed including the modern situation. Two groups – nonsolidary and solidary of different behaviors characterized for the relationship are defined. The strategies of nonsolidary behavior characterized for the strategic relationships of the players are described and the strategies of solidary behavior are connected with negotiations and agreements. Teaching organization is defined as a management of system comprising a teacher (professor) and collective of pupils (students). Each participant of system has its own interest and difference from each other. This situation gives us a ground to consider some aspects of Game Theory model for optimal management of

Neumann-Morgenstern’s solutions NM (v) as stable solution’s optimal principle is stated in a lexicographic v = (v1, v2 ,..., vm)T cooperative game. The conditions of NM (v) existence are proved for the cases, when: 1. v1 scalar cooperative game’s C-core C (v1) and NM (v1)solutions are equal; 2. Scalar cooperative v1 game’s C-core and NM (v1) solutions are different. In the first case the sufficient conditions are proved in order to say that a C-core C (v) of a lexicographic cooperative v game must not be empty and it should be coincided to NM (v) . In the second case the necessary condition of NM (v) existence is proved. In the case of the existence of NM (v) solutions their forms can be established. Some properties NM (v) of solutions are stated.