Distributed Edge-Based Nash Equilibrium Seeking With Event-Triggered Quantized Communication

This article investigates a noncooperative game of multiagent systems in incomplete information scenarios. To cooperatively seek the Nash equilibrium (NE), each agent aims to minimize its own cost function by interacting with its neighbors over undirected communication networks. While existing distributed NE seeking methods alleviate the computational burden, they also entail higher communication costs. To reduce communication frequency and bandwidth, we propose a class of distributed edge-based NE seeking methods by leveraging the advantages of event-triggered mechanisms and quantization techniques. In the proposed framework, a buffer is equipped on every communication channel, thereby reducing the workload of both agents at either end. It is shown that the convergence error can be made arbitrarily small by tuning a constant threshold, and it can asymptotically converge to zero by setting an exponentially decaying threshold or a dynamic threshold. Moreover, in the case of unawareness of any global information, we further provide a fully distributed event-triggered quantized algorithm, by which the convergence error is ultimately uniformly bounded. Finally, two numerical examples are utilized to illustrate the effectiveness of the proposed algorithms.