Linear–Quadratic Uncertain Differential Game With Application to Resource Extraction Problem

Uncertain differential game investigates interactive decision making of players over time, and the system dynamics is described by an uncertain differential equation. This paper goes further to study the two-player zero-sum uncertain differential game. In order to guarantee the saddle-point Nash equilibrium, a Max-Min theorem is provided. Furthermore, when the system dynamics is described by a linear uncertain differential equation and the performance index function is quadratic, the existence of saddle-point Nash equilibrium is obtained via the solvability of a corresponding Riccati equation. Finally, a resource extraction problem is analyzed by using the theory proposed in this paper.