Equilibria of Multi-level and Multi-player Stackelberg Security Games

Security games have become an effective tool for solving defense-attack problems. Generally, the leader-follower structure is used to model real-world security scenarios, where leaders predict and use possible behaviors of followers for their own decision-making to pursue Stackelberg equilibria. However, the reliability of Stackelberg equilibria strategies may be threatened due to the cognitive limitations, disturbances and uncertainties, making the dominance of leaders be weakened. In this case, pursuing Nash equilibria may be another option for leaders. In order to solve the dilemma of whether to seek Stackelberg equilibria or Nash equilibria, the coincidence of them is investigated. In this paper, Stackelberg and Nash equilibria of a kind of multi-level multi-player games, where players communicate via a tandem structure, are discussed. Sufficient and necessary conditions, under which Stackelberg equilibria strategies and Nash equilibria strategies are coincident, are derived. Finally, simulations are carried out to verify the validity of the obtained results.