Criminals Can Be Leaders: An Endogenous Timing Approach to Security Games

Security Games traditionally assume sequential interactions, with the defender acting as the leader and the attacker as the follower. In this paper, we challenge such an assumption by showing that security interactions can also be simultaneous or that even the attacker might be the leader. Specifically, we consider a simple security game framework consisting of two possible targets, one attacker and one defender. Then, we extend that basic interaction using a well-known endogenous timing framework (the Game with Observable Delay) to endogenously obtain the timing of the game as part of the equilibrium outcome. Our results show that, for the same set of general assumptions, the interaction can be simultaneous or sequential (with either the defender or attacker being the leader). Although the simultaneous case could be discarded using payoff dominance, it is impossible to compare the two sequential configurations using the same criterion. The risk dominance criterion also turns out to be helpless in this case. Thus, we argue that considering attackers as leaders in Security Games is a plausible scenario that merits further consideration, not only from a theoretical point of view but also due to its alignment with certain types of real-world crime.