Distributed computation of generalized Nash equilibria in quadratic aggregative games with affine coupling constraints

(Accepted)

Authors:

Dario Paccagnan, Basilio Gentile, Francesca Parise, Maryam Kamgarpour, John Lygeros

Conference:

IEEE Conference on Decision and Control 2016

Abstract:

We analyze deterministic aggregative games with large but finite number of players that are subject to both local and coupling constraints. Firstly, we derive sufficient conditions for the existence of a generalized Nash equilibrium, by using the theory of variational inequalities together with the specific structure of the objective functions and constraints. Secondly, we present a coordination scheme, belonging to the class of asymmetric projection algorithms, and we prove its convergence to a generalized Nash equilibrium. To this end, we extend the available results on asymmetric projection algorithms to our setting and we guarantee R-linear convergence. Finally, we show that the proposed scheme can be implemented in a decentralized fashion and it is thus suitable to the analysis of large populations. Our theoretical results are applied to the problem of charging a fleet of plug-in electric vehicles, in the presence of capacity constraints coupling the individual demands.