Attack-Resilient Distributed Algorithms for Exponential Nash Equilibrium Seeking

This paper investigates a resilient distributed Nash equilibrium (NE) seeking problem on a directed communication network subject to malicious cyber-attacks. The considered attacks, named as Denial-of-Service (DoS) attacks, are allowed to occur aperiodically, which refers to interruptions of communication channels carried out by intelligent adversaries. In such an insecure network environment, the existence of cyber-attacks may result in undesirable performance degradations or even the failures of distributed algorithm to seek the NE of noncooperative games. Hence, the aforementioned setting can improve the practical relevance of the problem to be addressed and meanwhile, it poses some technical challenges to the distributed algorithm design and exponential convergence analysis. In contrast to the existing distributed NE seeking results over a prefect communication network, an attack-resilient distributed algorithm is presented such that the NE can be exactly reached with an exponential convergence rate in the presence of DoS attacks. Inspired by the previous works in [21]-[26], an explicit analysis of the attack frequency and duration is investigated to enable exponential NE seeking with resilience against attacks.Examples and numerical simulation results are given to show the effectiveness of the proposed design.