Differential game-based analysis of multi-attacker multi-defender interaction

Due to the increasing number of wireless terminals and progressively extensive interconnections among them, interaction between the attack group and defense group is becoming a dominant security manifestation in future wireless networks. This paper focuses on the modeling and analysis of multi-attacker to multi-defender interaction. First, considering the continuous interaction between the attack group and defense group in real-time, a differential game-based multi-attacker to multi-defender interaction model is explicated with paralysis threshold introduced to reduce the ping-pong effect in paralysis. Optimal control theory is then introduced to obtain the equilibrium strategy with Hamilton best control method and a proposed optimal strategy selection algorithm for multi-attacker to multi-defender interaction. Finally, simulations are provided to demonstrate the evolutionary trajectory of optimal attack and defensive strategies and the relationship between the paralysis threshold and the group strength evolution results. Numerical results show the attackers and defenders are aggressive to strengthen their groups initially and then gradually decrease their strength to obtain ideal cost-effectiveness ratios. Moreover, increasing the defense paralysis threshold within a certain range will be more conducive to improving the defense effectiveness.