A Classical Search Game In Discrete Locations

Clarkson, Jake and Lin, Kyle and Glazebrook, Kevin (2023) A Classical Search Game In Discrete Locations. Mathematics of Operations Research, 48 (2). pp. 687-707. ISSN 0364-765X

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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.