High-Order Decentralized Pricing Dynamics for Congestion Games: Harnessing Coordination to Achieve Acceleration

We introduce a class of decentralized high-order pricing dynamics (HOPD) for the solution of optimal incentive problems in affine congestion games with full resource utilization. The dynamics incorporate momentum and decentralized coordinated resets to achieve better transient performance compared to traditional first-order gradient-based pricing algorithms. The proposed dynamics are studied using tools from graph theory, game theory, and hybrid dynamical systems theory. Our main results establish suitable stability and convergence properties with respect to the set of incentives that generate Nash flows that also maximize the social welfare function of the game. The theoretical results are illustrated via numerical examples in two different types of communication graphs, highlighting the effect of the communication topology and the coordination between players on the transient performance of the HOPD.