  Pursuit-Evasion Games (in discrete time) are stochastic games with
nonnegative daily payoffs, with the final payoff being the cumulative sum of
payoffs during the game. We show that such games admit a value even in the
presence of incomplete information and that this value is uniform, i.e. there
are epsilon-optimal strategies for both players that are epsilon-optimal in any
long enough prefix of the game. We give an example to demonstrate that
nonnegativity is essential and expand the results to leavable games.
