Non-Coherent Over-the-Air Decentralized Method for Non-Cooperative Games in Multi-Agent Systems

Distributed non-cooperative games are prevalent in emerging applications such as traffic control, vehicle charging, and smart grid management. In distributed systems without central coordinators, agents must share and retrieve information locally to seek a Nash equilibrium (NE). However, this extensive data exchange can lead to significant communication bottlenecks. To address this challenge, over-the-air computing provides a promising solution by exploiting the superposition property of wireless multiple access channels (MAC), allowing for substantial bandwidth savings. In this paper, we propose an over-the-air framework for general distributed non-cooperative games. Specifically, we introduce an algorithm based on non-coherent over-the-air computing, AirNES, to find an NE in distributed non-cooperative games. Our algorithm accounts for noisy channels and non-coherent transmission, eliminating the need for channel state information. We demonstrate that, with properly tuned decreasing consensus and gradient stepsizes, AirNES guarantees almost sure convergence to the exact NE, even in the presence of channel fading and additive noise. Additionally, we extend our analysis to scenarios with fixed stepsizes, where linear convergence can be achieved at the expense of reduced accuracy. Finally, we provide numerical simulations to demonstrate the effectiveness of the proposed protocol.