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



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


IEEE Conference on Decision and Control 2016


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.