Game theoretical security detection strategy for networked systems

In this paper, a game theoretical analysis method is presented to provide the optimal security detection strategies for heterogeneous networked systems. A two-stage game model is firstly established, in which the attacker and defender are considered as two players. In the first stage, the two players make decisions on whether to execute the attack/monitoring actions or to keep silence for each network unit. In the second stage, two important strategic varibles, i.e. the attack intensity and detection threshold, are cautiously determined. The necessary and sufficient conditions to ensure the existence of the Nash equilibriums for the game with complete information are rigorously analyzed. The results reflect that with limited resources and capacities, the defender (attacker) tends to perform defense (attack) actions and further allocate more defense (less attack) resources to the units with larger assets. Besides, Bayesian and robust Nash equilibrium analysis is provided for the game with incomplete information. Finally, a sampling based Nash equilibrium verification and calculation approach is proposed for the game model with continuous kernels. Thus the convexity restrictions can be relaxed and the computational complexity is effectively reduced, with comparison to the existing recursive calculation methods. Numerical examples are given to validate our theoretical results