There has been significant recent interest in a class of three-player leader-follower game models in many important cybersecurity scenarios. In such a tri-level hierarchical structure, a defender usually serves as a leader, dominating the decision process by the Stackelberg equilibrium (SE) strategy. However, such a leader-follower scheme may not always work, and the Nash equilibrium (NE) strategy may provide an alternative choice. Thus, we need to reveal the consistency between SE and NE in the three-player model to help the leader evaluate its strategy impact and avoid a choice dilemma. To this end, we first provide a necessary and sufficient condition such that each SE is an NE, which not only provides access to seek a satisfactory SE but also makes a criterion for an obtained SE. Then, we apply the results for case studies with a unique SE or with at least one SE being an NE. Moreover, when the consistency condition falls short, we give an upper bound of the deviation between SE and NE to help the leader tolerably adopt an SE strategy. Finally, we apply our consistency analysis to practical scenarios, including secure wireless transmission and advanced persistent threat defense.

In this paper, we employ a hypergame framework to analyze the single-leader-multiple-followers (SLMF) Stackelberg security game with two typical misinformed situations: misperception and deception. We provide a stability criterion with the help of hyper Nash equilibrium (HNE) to investigate both strategic stability and cognitive stability of equilibria in SLMF games with misinformation. In fact, we find mild stable conditions such that the equilibria with misperception and deception can become HNE. Moreover, we discuss the robustness of the equilibria to reveal whether players have the ability to keep their profits under the influence of some misinformation.