Computing Optimal Strategies for a Search Game in Discrete Locations

Abstract

Consider a two-person zero-sum search game between a hider and a searcher. The hider hides among n discrete locations, and the searcher successively visits individual locations until finding the hider. Known to both players, a search at location i takes ti time units and detects the hider—if hidden there—independently with probability αi, for [Formula: see text]. The hider aims to maximize the expected time until detection, whereas the searcher aims to minimize it. We present an algorithm to compute an optimal strategy for each player. We demonstrate the algorithm’s efficiency in a numerical study, in which we also study the characteristics of the optimal hiding strategy. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: J. Clarkson is grateful for the support of the Engineering & Physical Sciences Research Council STOR-i Centre for Doctoral Training at Lancaster University [Grant EP/L015692/1]. Supplemental Material: The software that supports the findings of this study is available within the paper as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0155 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .