Randomized Pursuit-Evasion with Limited Visibility

We study the following pursuit-evasion game: One or more hunters are seeking to capture an evading rabbit on a graph. At each round, the rabbit tries to gather information about the location of the hunters but it can see them only if they are located on adjacent nodes. We show that two hunters suffice for catching rabbits with limited visibility with high probability. We distinguish between reactive rabbits who move only when the hunter is visible and general rabbits who can employ more sophisticated strategies. We present polynomial time algorithms that decide whether a graph G is hunter-win, that is, if a single hunter can capture a rabbit of either kind on G.