  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.
