In artificial intelligence literature there is a rising interest in studying strategic interaction situations. In these situations a number of rational agents act strategically, being in competition, and their analysis is carried out by employing game theoretical tools. One of the most challenging strategic interaction situation is the strategic patrolling: a guard patrols a number of houses in the attempt to catch a rob, which, in its turn, chooses a house to rob in the attempt to be not catched by the guard. Our contribution in this paper is twofold. Firstly, we provide a critique concerning the models presented in literature and we propose a model that is game theoretical satisfactory. Secondly, by exploit the game theoretical analysis to design a solving algorithm more efficient than state-of-the-art's ones.