A Classical Search Game in Discrete Locations

Consider a two-person zero-sum search game between hider and searcher. The hides among n discrete locations, the searcher successively visits individual locations until finding hider. Known to both players, at location i takes t time units detects hider—if hidden there—independently with probability [Formula: see text] for text]. aims maximize expected detection, whereas minimize it. We prove existence of an optimal strategy each player. In particular, any mixed hiding in nonzero probability, there exists that can be constructed up simple sequences. Funding: This work was supported by Engineering Physical Sciences Research Council [Grant EP/L015692/1] STOR-i Centre Doctoral Training.