A review of minimum cost box searching games

TL;DR

This paper reviews various solutions to zero-sum search games where a Hider hides targets in boxes with different search times and imperfect detection, focusing on minimizing or maximizing expected search time.

Contribution

It provides a comprehensive review of existing solutions for minimum cost box searching games with varying conditions and complexities.

Findings

Different cases of the game have known solutions.

Imperfect detection affects optimal search strategies.

Varying search times influence search order and tactics.

Abstract

We consider a class of zero-sum search games in which a Hider hides one or more target among a set of $n$ boxes. The boxes may require differing amount of time to search, and detection may be imperfect, so that there is a certain probability that a target may not be found when a box is searched, even when it is there. A Searcher must choose how to search the boxes sequentially, and wishes to minimize the expected time to find the target(s), whereas the Hider wishes to maximize this payoff. We review some known solutions to different cases of this game.