Equilibrium Seeking in Learning-Based Noncooperative Nash Games

Traditionally, based on convexity, multi-agent decision-making models can hardly handle scenarios where agents’ cost functions defy this assumption, which is specifically required to ensure the existence of several equilibrium concepts. More recently, the advent of machine learning (ML), with its inherent non-convexity, has changed the conventional approach of pursuing convexity at all costs. This paper explores and integrates the robustness of game theoretic frameworks in managing conflicts among agents with the capacity of ML approaches, such as deep neural networks (DNNs), to capture complex agent behaviors. Specifically, we employ feed-forward DNNs to characterize agents’ best response actions rather than modeling their goals with convex functions. We introduce a technical assumption on the weight of the DNN to establish the existence and uniqueness of Nash equilibria and present two distributed algorithms based on fixed-point iterations for their computation. Finally, we demonstrate the practical application of our framework to a noncooperative community of smart energy users under a dynamic time-of-use energy pricing scheme.