On optimal strategies of the border patrol
In this paper we consider the optimal usage of some detection tool for border patrol needs. The effectiveness of the tool depends on a moment of its application. To describe an interaction between a border trespasser and a border patrol we introduce a zero-sum game, which in cases of practical interest has no saddle points in pure strategies. To find an equilibrium in mixed strategies we obtain a maximin problem, which is solved using the equalization principle.