# Search and Rescue in the Face of Uncertain Threats

## TL;DR

This paper models a search and rescue problem with uncertain risks using game theory, aiming to maximize the probability of rescuing all targets, and provides solutions for specific graph structures.

## Contribution

It introduces a game theoretic framework for search under uncertainty and extends it to graph-based scenarios, including solutions for trees with a single target.

## Key findings

- Optimal search strategies are derived for the game model.
- Solutions are provided for search on trees with one target.
- The model generalizes previous search game frameworks.

## Abstract

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.