A SEQUENTIAL EVASION-SEARCH GAME WITH A GOAL

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Abstract
Infinite boxes 0, 1 , 2, ...... chooses at each period one of three decisions: to stay in the current box and to move to the nearest box either to the right or to the left. A searcher looks in any one box except box 0 which is a safe region (goal) for the evader because it is unsearchable. Two types of conditional detection probability are given, that is, one is used in the case that the evader stays and another is used in the case that he moves. It is assumed that the searcher is informed of' the evader's position at the end of each period. The evader maximizes the probability that he is not detected for given periods and the searcher minimizes it. This two-person zero-sum sequential game is solved recursively. The evader's optimal strategy indicates to run into the goal as soon as possible if his position is near the goal, to go ahead or stay if he is somewhat away from the goal, and to go back with a positive probability if he is far away from the goal.

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