  We consider a search problem in which one or more targets must be rescued by
a search party, or Searcher. The targets may be survivors of some natural
disaster, or prisoners held by an adversary. The targets are hidden among a
finite set of locations, but when a location is searched, there is a known
probability that the search will come to an end, perhaps because the Searcher
becomes trapped herself, or is captured by the adversary. If this happens
before all the targets have been recovered, then the rescue attempt is deemed a
failure. The objective is to find the search that maximizes the probability of
recovering all the targets. We present and solve a game theoretic model for
this problem, by placing it in a more general framework that encompasses
another game previously introduced by the author. We also consider an extension
to the game in which the targets are hidden on the vertices of a graph. In the
case that there is only one target, we give a solution of the game played on a
tree.
