The investigation of Nash’s arbitrage scheme in a dynamic problem

A cooperative differential game of two persons is discussed in this paper. Nash’s arbitrage scheme is used as a principle of optimization – a method to choose one solution among optimal solutions according to Pareto. While considering dynamic or differential games the problem of dynamic stability occurs. In the paper analysis of dynamic stability of arbitrage scheme is carried out for the given problem, i.e. in differential games with two aim points.
The investigation has shown that, as it was obvious from general – theoretical points of view, the arbitrage scheme is dynamically non-stable, and the stability exists only for a special combination of parameters of the problem.