An observation on pure strategies in Security Games

Security Games have been used in several different fields to randomise the division of limited resources and thus maximise the possibility of securing a set of targets. For this very practical purpose it is natural to consider primarily mixed strategies, but such focus omits some theoretical properties of the games discussed. In this paper we discuss the existence and properties of pure Nash equilibria in security games. We give an overview of the basic observations that can be made in this setting. We also recognize an interesting problem in a case with multiple players playing a security game asynchronously, propose an algorithm for finding a strategy for any given player in the mentioned case and prove that the strategy profile resulting from the algorithm is in fact a Nash equilibrium and, even stronger, a subgame perfect equilibrium. We think that these findings are a nice supplement of the practical approach to Security Games and allow to form new research questions.