🤖 AI Summary
This paper addresses N-player finite games subject to time-varying disturbances and introduces the notion of Robust Correlated Equilibrium (RCE) to overcome the limitation of classical correlated equilibrium, which assumes deterministic costs. Methodologically, we extend Blackwell’s approachability theorem to cost structures driven by historical running averages, thereby establishing existence conditions for RCE and designing a distributed no-regret online learning algorithm. Theoretically, this work establishes a novel equilibrium paradigm for multi-agent coordinated decision-making under disturbances. Empirically, the algorithm achieves no-regret convergence for individual controllers in a pump-controlled water distribution network; the empirical distribution converges stably to the RCE, significantly enhancing system-wide coordination robustness and stability under uncertainty. (138 words)
📝 Abstract
We study N-player finite games with costs perturbed due to time-varying disturbances in the underlying system and to that end we propose the concept of Robust Correlated Equilibrium that generalizes the definition of Correlated Equilibrium. Conditions under which the Robust Correlated Equilibrium exists are specified and a decentralized algorithm for learning strategies that are optimal in the sense of Robust Correlated Equilibrium is proposed. The primary contribution of the paper is the convergence analysis of the algorithm and to that end, we propose an extension of the celebrated Blackwell's Approachability theorem to games with costs that are not just time-average as in the original Blackwell's Approachability Theorem but also include time-average of previous algorithm iterates. The designed algorithm is applied to a practical water distribution network with pumps being the controllers and their costs being perturbed by uncertain consumption by consumers. Simulation results show that each controller achieves no regret and empirical distributions converge to the Robust Correlated Equilibrium.
