Distributed Nash Equilibrium Seeking in Merely Monotone Games Using an Event- and Switching-Activated Communication Scheme

This article is concerned with distributed dynamic event-triggered Nash equilibrium seeking in merely monotone games under switching communication topologies. Based on a regularization algorithm, a gradient play and a leader-following consensus protocol, a distributed Nash equilibrium seeking strategy incorporating an event- and switching-activated communication scheme is established. More specifically, the regularization algorithm is involved to compensate for the absence of strict/strong monotonicity of game mapping and the gradient play is utilized to optimize players' objectives. The event-triggered leader-following consensus protocol is introduced to achieve distributed estimation of all players' actions, where communication transmissions among neighbors occur only when the preset event-triggering conditions are satisfied and communication topologies are switching. It is shown that the proposed seeking strategy can asymptotically steer players' actions to the least-norm Nash equilibrium of merely monotone games with reduced communication resources. An illustrative example on least-distance formation control for a network of unicycle-type mobile vehicles is given to validate the effectiveness of the proposed method.