Abstract
In this game of R. Isaacs, the players are a hider and a searcher. The payoff is the time until capture. The hider is assumed to be mobile within a bounded set $\mathcal{D}$. The searcher has an arbitrarily small detection radius. There is incomplete information in that neither player knows the present or past location of the other. For various sets $\mathcal{D}$, the value of the game is demonstrated by the presentation of $\varepsilon $-optimal strategies. Specifically, the game is solved in case $\mathcal{D}$ is convex or is the finite union of convex sets in $\mathbb{R}^n $ with $n \geqq 2$. Also the game is discussed in the case where $\mathcal{D}$ is a network. The results settle two conjectures of S. Gal.
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