The Distributed Online Algorithm for Constrained Online Cluster Game Nash Equilibrium

In this paper, we consider online multi-cluster games in which each cluster plays with each other to reach a Nash equilibrium, while all players in the cluster cooperate with each other to minimise their aggregate time-varying cost function. In addition, the actions of the players are affected by local constraints and time-varying coupling constraints. We use a leaderfollower based estimator and develop a distributed online algorithm that seeks Nash equilibrium sequences for online multi-cluster games by using the projected gradient method and the primal-dual method. We show that the designed algorithm ensures that both dynamic regret and dynamic fit are sublinearly bounded. Finally, we illustrate the effectiveness of the algorithm through an electricity market game involving multiple microgrid clusters.