Incomplete-Information Dynamic Stackelberg Equilibrium Seeking by A Distributed Distributionally Robust Feedback Approach

This article investigates a multileader Stackelberg game where leaders lack critical information about the follower's objective function and face random disturbances with unknown distributions. Unlike conventional approaches requiring complete follower information, we consider leaders who manipulate physical plant states while observing the follower's strategy through private tracking responders. To address distributional uncertainty in the follower's best response, we reformulate the game as a distributionally robust equilibrium-seeking problem and develop a fully distributed feedback learning algorithm. The proposed data-driven approach operates without prior knowledge of system models or disturbance distributions, enabling leaders to estimate states through neighbor communication and local gradient updates. We characterize equilibrium existence in nonconvex settings. The relationship between communication and gradient errors and the energy function of the dynamic system is established. The upper bound of the regret based on the proposed algorithm is rigorously analyzed. A case study demonstrates the framework's effectiveness in achieving distributionally robust solutions against uncertain stochastic perturbations.