Search for the optimal initial distribution of players' location in a patrolling game

A patrolling game with two players, a patroller and an attacker, is considered in the paper. The aim of the former is to protect an object from intruders and catch the attacker. The aim of the latter is to cause damage to the protected object without being caught. Cellular base stations are viewed as protected objects. A game-theoretic model is constructed to find an initial distribution of players on base stations. When the transition matrix of players among the stations is known, an optimal strategy of players and the value of the game are calculated. An inverse problem of searching for optimal transition matrices with known initial distribution of players is studied. The Nash equilibrium with the attacker making two attacks is found for the considered problem.