A Novel Single-Time Scale Distributed Attack-Resilient Algorithm for Multi-Cluster Games

In this paper, the multi-cluster game with Denial-of-Service (DoS) attacks is first investigated, which cannot be solved by existing distributed algorithms due to the presence of DoS attacks that can disrupt the connectivity of the network. Specifically, each cluster consists of some agents that aim to collaboratively minimize the sum of their local cost functions depending on the decisions of all the game participants. The clusters are competitive with each other, and each cluster is considered to be a virtual player aiming to find its own Nash equilibrium (NE). A new single-time scale distributed attack-resilient algorithm requiring only partial-decision information is designed. With the help of the hybrid system method and Lyapunov stability analysis, rigorous analysis is performed to demonstrate that the algorithm achieves exponential convergence under certain bounded conditions on the frequency and duration of attacks. Finally, the numerical simulation is given to corroborate the effectiveness of the algorithm.