Uncertain stochastic hybrid differential game system with V-n jumps: Saddle point equilibrium strategies and application to advertising duopoly game

Abstract

This paper focuses on the saddle point equilibrium strategies for uncertain stochastic hybrid differential game systems under chance theory. We consider systems with dynamics described by both an uncertain differential equation with V-n jumps (UDEV) and a stochastic differential equation (SDE), with linear and quadratic performance index functions. Based on chance theory and the equation of optimality of uncertain stochastic hybrid optimal control model, the saddle equilibrium equation for general uncertain stochastic hybrid differential game system is established. Furthermore, three classes of differential game models are discussed by using equilibrium equation. Finally, an advertising duopoly game problem as an application is provided, the corresponding optimal profit difference value and advertising strategies are analyzed.