Nash equilibrium strategy of two-person bilinear-quadratic differential game: a recursive approach

This paper deals with the Nash equilibrium strategy problem of two-person bilinear–quadratic dynamic game. Using Adomian's decomposition method, we transform the bilinear system Nash equilibrium problem into a sequence of special linear system Nash equilibrium problem in a recursive manner. The series expansions of the Nash equilibrium strategy are derived, and the uniformly and absolutely convergence of algorithm are proved.