Dynamic Programming for One-sided Partially Observable Pursuit-evasion Games

We study two player pursuit-evasion games with concurrent moves, infinite horizon, and discounted rewards. The players have partial observability, however, the evader is given an advantage of knowing the current position of the units of the pursuer. We show that (1) value functions of this game depend only on the position of the pursuing units and the belief the pursuer has about the position of the evader, and (2) that they are piecewise linear convex functions in the belief. Finally, we exploit this representation of value functions and design a value iteration algorithm that approximates the value of the game.