ИСТИНА

We study a dynamic model that describes the process of transition of a controlled object from the initial state to the terminal state. There is a group of m members of some economic project. The objectives and the interests of each of the participants are described by means of objective functions f_i(x_1), i=1,2,...,m, defined on a common set of resources X_1\subseteq \mathrm{R}^n. The problem facing the participants consists in the distribution of resources according to 3 factors: (i) each of the participants is interested in minimizing his contribution (resources) to the overall project; (ii) the project should be implemented with the least total cost; (iii) the situation should evolve in dynamics. Two-person game with the Nash equilibrium} is proposed as a model. Combining the linear dynamics with the boundary value problem, we have a dynamic model, which describes the transition process of the controlled object from the initial state x_0 to terminal state x(t_1)=x^{*}_1. Dual extraproximal method was used. The convergence of the method to solution was proved.