Saddle-point equilibrium for Hurwicz model considering zero-sum differential game of uncertain dynamical systems with jump

As an effective vehicle, uncertainty theory is applicable for handling subjective indeterminacy. Based on uncertainty theory, the Hurwicz model of the zero-sum uncertain differential game with jump is formulated, in which the dynamic system is portrayed by an uncertain differential equation satisfying both the canonical Liu process and V-jump uncertain process. An equilibrium equation for solving the saddle-point of the above game is proposed. In addition, the game with a linear dynamic system and the quadratic objective function is further analysed. At last, a resource extraction problem using our theoretical results is described.

Automated summary

This article presents the Hurwicz model of the zero-sum uncertain differential game with jump based on uncertainty theory. It formulates a dynamic system using an uncertain differential equation that satisfies both the canonical Liu process and V-jump uncertain process. An equilibrium equation for solving the saddle-point of the game is proposed. Furthermore, the article analyzes the game with a linear dynamic system and quadratic objective function. Finally, it describes a resource extraction problem using the theoretical results.