  We propose a 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.
