  Pursuit-evasion scenarios appear widely in robotics, security domains, and
many other real-world situations. We focus on two-player pursuit-evasion games
with concurrent moves, infinite horizon, and discounted rewards. We assume that
the players have a partial observability, however, the evader is given an
advantage of knowing the current position of the units of the pursuer. This
setting is particularly interesting for security domains where a robust
strategy, designed to maximize the utility in the worst-case scenario, is often
desirable. We provide, to the best of our knowledge, the first algorithm that
provably converges to the value of a partially observable pursuit-evasion game
with infinite horizon. Our algorithm extends well-known value iteration
algorithm by exploiting that (1) the value functions of our game depend only on
position of the pursuer and the belief he has about the current position of the
evader, and (2) that these functions are piecewise linear and convex in the
belief space.
