Distributed Aggregative Game Algorithm And Application

The distributed Nash equilibrium seeking problem is investigated for aggregative game.Extending existing first-order algorithms,we propose a second-order distributed heavy-ball algorithm for the aggregative Nash equilibrium seeking problem,with faster convergence being achieved.To compute the Nash equilibrium for the aggregative games in a distributed way,each player obtains an estimation of the central aggregative information in a distributed way via exchanging information only with its neighbors,and utilizes this estimated information to update its own strategy,with its privacy being protected.As an extension of existing results which only consider linear aggregative terms,the approaches reported here can deal with aggregative games with nonlinear aggregative terms.Also,by taking coupled equality constraints into account,the constrained aggregative games is also considered,and corresponding distributed Nash equilibrium seeking algorithms are designed based on the KKT condition and the variational equilibrium,with convergence being analyzed.Furthermore,the proposed distributed Nash equilibrium seeking algorithms are applied to the energy demand response model in power system and the Nash-Cournot model,with the algorithmic effectiveness being verified.