Continuous Search Games
Shmuel Gal · 2023
A searcher would like to detect a mobile hider as soon as possible. Such “hide and seek” games which people used to play in their childhood are formulated as mathematical problems. This chapter presents a survey that covers search games in graphs, in bounded regions, and in unbounded domains. A good way to introduce search games is to describe the princess and monster game presented by Rufus Isaacs in his book Differential Games . Each search problem is presented as a two-person zero-sum game. Searching in a graph is in general a very difficult problem. There exist closed solutions for some special families of graphs, but, in general, finding the optimal search strategy in a graph is an open problem for both a mobile and an immobile hider. In general, the search for an immobile hider in an uneven number of arcs is an open problem.