Fully Distributed Event-Triggered Nash Equilibrium Seeking for Networked Mean Field Games

This article considers Nash equilibrium (NE) seeking of networked mean field games (NMFGs) with event-triggered strategies in a fully distributed manner. To simplify the formulation of distributed online decision-making problems over a network, we introduce the NMFG over a spatiotemporal domain for large-scale equilibrium computation. By merging ideas from estimation theory and consensus theory, three parallel auxiliary variables are designed to dynamically estimate the aggregative behavior of the collection, called the mean field term. The leaderless consensus of players' estimates and the optimization of local objective function need to be achieved simultaneously. In addition, the dynamic event-triggered mechanism and adaptive learning gain are introduced, which provide a natural and scalable framework for distributed communication and computation in large-scale complex networks. We further prove that convergence to NE can be guaranteed using the designed strategies. Finally, a numerical experiment is provided to validate the proposed algorithm.