On the equivalence of pursuer strategies and the lack of nash equilibrium in a visibility pursuit-evasion game.

This work addresses a finite-time visibility-based target tracking problem. The aim of the pursuer is to keep the evader within its field of view, while the evader wants to escape the pursuer’s surveillance. Some main contributions of the work are the following: (1) It is proven that minimizing the travel time is equivalent to maximizing the definite integral of the angular speed of the border of the pursuer visibility region. (2) Using Euclidean geometry and set theory methods, the optimality of the player trajectories is demonstrated. (3) It is shown that the motion strategies provided in previous works are not always in Nash equilibrium.