A Pursuit-Evasion Game with Incomplete Information

A pursuit-evasion game with partial information is studied. The evader observes the initial conditions only. The pursuer observes both the initial conditions and the relative evader-pursuer position in additive noise. The paper shows that the optimal strategies of a partial information game may differ qualitatively from its full information counterpart. In the particular case at hand the evader's strategy may be random, something that does not happen in the deterministic case.