A feedback control algorithm to steer networks to a Cournot-Nash equilibrium

TL;DR

This paper introduces a distributed feedback control method for dynamical networks with passive nonlinear systems, guiding them to a Cournot-Nash equilibrium by utilizing local price-based demand functions.

Contribution

It presents a novel control algorithm that ensures convergence to Cournot-Nash equilibrium using limited demand information in passive nonlinear network systems.

Findings

Controller guarantees convergence to equilibrium

Works with passive nonlinear second-order systems

Utilizes local prices for demand estimation

Abstract

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.