A preemptive detection game

The paper considers a zero-sum search game in which two players search for different stationary objects respectively and compete for the earlier detection than the opponent under the condition that the search effort allocated by one player diminishes the effect of the opponent’s search each other. A necessary condition for a strategy to be optimal and an important property are derived. Furthermore in one disturbance case we show that the optimal strategy for each player is the same as the optimal search policy for the detection search problem by only one player.