Berge-Vaisman equilibrium for one linear-quadratic differential game

We obtained coefficient criteria for the existence of the Berge-Vaisman equilibrium in a non-cooperative positional linear-quadratic game of two persons with small parameter.

Keywords: non-cooperative positional linear-quadratic differential game, dynamic programming, Berge-Vaisman equilibrium, Nash equilibrium, continuous dependence and analyticity of the solution by parameter