Revisiting a Three-Player Pursuit-Evasion Game

We consider the game of a holonomic evader passing between two holonomic pursuers. The optimal trajectories of this game are known. We give a detailed explanation of the game of kind’s solution and present a computationally efficient way to obtain trajectories numerically by integrating the retrograde path equations. Additionally, we propose a method for calculating the partial derivatives of the Value function in the game of degree. This latter result applies to differential games with homogeneous Value.