Hyperbolicity of systems describing value functions in differential games which model duopoly problems

Abstract

Based on the Bressan and Shen approach ([2] or [7]), we present the extension of the class of non-zero sum dierential games for which value functions are described by a weakly hyperbolic Hamilton-Jacobi system. The considered value functions are determined by a Pareto optimality condition for instantaneous gain functions, for which we compare two methods of the unique choice Pareto optimal strategies. We present the procedure of applying this approach for duopoly.