A search game with one object and two searchers

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Abstract
We consider a non-zero-sum game in which two searchers (player I and II) compete with each other for quicker detection of an object hidden in one of n boxes. Let p (q) be the prior location distribution of the object for player I (II). Exponential detection functions are assumed for both players. Each player wishes to maximize the probability that he detects the object before the opponent detects it. In the general case, a Nash equilibrium point is obtained in the form of a solution of simultaneous differential equations. In the case of p = q, we obtain an explicit solution showing the surprising result that both players have the same equilibrium strategy even though the detection rates are different.

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