We consider a search and rescue game introduced recently by the first author. An immobile target or targets (for example, injured hikers) are hidden on a graph. The terrain is assumed to dangerous, so that when any given vertex of the graph is searched, there is a certain probability that the search will come to an end, otherwise with the complementary {\em success probability} the search can continue. A Searcher searches the graph with the aim of finding all the targets with maximum probability. Here, we focus on the game in the case that the graph is a cycle. In the case that there is only one target, we solve the game for equal success probabilities, and for a class of games with unequal success probabilities. For multiple targets and equal success probabilities, we give a solution for an adaptive Searcher and a solution in a special case for a non-adaptive Searcher. We also consider a continuous version of the model, giving a full solution for an adaptive Searcher and approximately optimal solutions in the non-adaptive case.

翻译：本文研究了由第一作者近期引入的一种搜救博弈问题。不可移动的目标（例如受伤的徒步者）被隐藏在图结构上。地形被假设为危险环境，因此当搜索图中任意顶点时，存在一定概率搜索会终止，否则以互补的“成功概率”搜索可以继续进行。搜索者以最大化找到所有目标的概率为目标在图中进行搜索。本文重点研究图结构为循环图的博弈情形。当仅存在单一目标时，我们求解了等成功概率情形下的博弈，并针对一类非等成功概率的博弈给出了解。针对多目标且等成功概率的情形，我们给出了自适应搜索者的解，以及非自适应搜索者在特殊情况下的解。此外，我们还考虑了该模型的连续版本，给出了自适应搜索者的完整解以及非自适应情形下的近似最优解。