A Feedback Control Algorithm to Steer Networks to a Cournot–Nash Equilibrium

In this paper, we propose distributed feedback control that steers a dynamical network to a prescribed equilibrium corresponding to the so-called Cournot-Nash equilibrium. The network dynamics considered here are a class of passive nonlinear second-order systems, where production and demands act as external inputs to the systems. While productions are assumed to be controllable at each node, the demand is determined as a function of local prices according to the utility of the consumers. Using reduced information on the demand, the proposed controller guarantees the convergence of the closed-loop system to the optimal equilibrium point dictated by the Cournot-Nash competition.