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A Classical Search Game In Discrete Locations

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published
<mark>Journal publication date</mark>31/05/2023
<mark>Journal</mark>Mathematics of Operations Research
Issue number2
Volume48
Number of pages21
Pages (from-to)687-707
Publication StatusPublished
Early online date1/07/22
<mark>Original language</mark>English

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 i = 1,...,n. The hider aims to maximize the expected time until detection, while the searcher aims to minimize it. We prove the existence of an optimal strategy for each player. In particular, any optimal mixed hiding strategy hides in each location with a nonzero probability, and there exists an optimal mixed search strategy which can be constructed with up to n simple search sequences.