Gradient-tracking-based distributed Nesterov accelerated algorithms for multiple cluster games over time-varying unbalanced digraphs

This paper studies the design of accelerated distributed algorithms for seeking the Nash Equilibrium (NE) of multiple cluster games over time-varying unbalanced digraphs, where players in the same cluster cooperatively minimize the summation of the local cost function and do not concern the interest of other clusters. In this game, the players have limited access to others’ decisions, while they can communicate with others over the inter-cluster and intra-cluster topologies. Accelerated distributed algorithms are proposed based on the decision estimation, Nesterov acceleration, and pseudo gradient estimation to seek the NE of multiple cluster games. We prove that the proposed algorithm linearly converges to the NE using the multistep contraction and linear systems of inequalities. Moreover, three variants of the proposed algorithm are also given for dealing with cases where only partial communication topologies are time-varying and gossip-type. Lastly, the effectiveness of proposed algorithms and the acceleration effect are verified by solving the intrusion–interception confrontation problem of Unmanned Vehicle (UV) swarms in simulations.