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:我们考虑的是第一个作者最近推出的搜索和救援游戏。 一个非移动目标或目标(例如受伤徒徒步者)隐藏在图表上。 地形被假定为危险, 以便当图形的任何特定顶点被搜索时, 搜索有一定的可能性会结束, 否则, 补充的 {em 成功概率} 搜索可以继续下去 。 一个搜索者搜索图形, 目的是以最大的概率查找所有目标 。 这里, 我们集中关注在图形是一个循环的情况下的游戏 。 如果只有一个目标, 我们解决这个游戏, 以同样成功概率和不同成功概率的游戏。 对于多个目标和同等成功概率, 我们给出一个适应搜索者解决方案, 并在一个特殊案例中为非适应搜索者提供一个解决方案。 我们还考虑一个连续的模型版本, 给适应搜索者一个完整解决方案, 并在非适应案例中提供一个最优化的解决方案 。