More on the search for an infiltrator

We have asymptotically solved a discrete search game on an array of n ordered cells with two players: infiltrator (hider) and searcher, when the probability of survival approaches 1. The infiltrator wishes to reach the last cell in finite time, and the searcher has to defend that cell. When the players occupy the same cell, the searcher captures the infiltrator with probability 1 − z. The payoff to the hider is the probability that the hider reaches the last cell without getting captured.