A Classical Search Game in Discrete Locations

Jake Clarkson (), Kyle Y. Lin () and Kevin D. Glazebrook ()
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Jake Clarkson: STOR-i Centre for Doctoral Training, Lancaster University, Lancaster LA1 4YR, United Kingdom
Kyle Y. Lin: Operations Research Department, Naval Postgraduate School, Monterey, California 93943
Kevin D. Glazebrook: Department of Management Science, Lancaster University, Lancaster LA1 4YX, United Kingdom

Mathematics of Operations Research, 2023, vol. 48, issue 2, 687-707

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 t i time units and detects the hider—if hidden there—independently with probability α i for i = 1 , … , n . The hider aims to maximize the expected time until detection, whereas 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 that can be constructed with up to n simple search sequences.

Keywords: Primary: 91A05; 91A10; search games; Gittins index; semifinite games; search and surveillance (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:48:y:2023:i:2:p:687-707

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