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

Abstract

Tyt. z nagłówka.Bibliogr. s. 100.Based on the Bressan and Shen approach (Bressan and Shen, 2004; Shen, 2009), we present an extension of the class of non-zero sum differential 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.Dostępny również w formie drukowanej.KEYWORDS: duopoly models, semi-cooperative feedback strategies, Pareto optimality, hyperbolic partial differential equations