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

Abstract

We analyse 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 that it converges R-linearly to a generalized Nash equilibrium. To this end, we extend the available results on asymmetric projection algorithms to our setting. Finally, we show that the proposed scheme can be implemented in a decentralized fashion and it is suitable for 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.

Distributed algorithm design for aggregative games of disturbed multiagent systems over weight‐balanced digraphs

“…The exogenous disturbance results that most of existing distributed algorithms cannot ensure the multiagent system converge to the GNE of the game. Moreover, the communication among players is depicted by weight‐balanced digraphs, which extend undirected graphs considered by most of existing results about aggregative games . Besides, unlike the differential games that are known as dynamic games (see the work of Başar and Olsder for details), the aggregative games considered here are static games, where the cost functions of all players are independent of the derivatives of decisions and the transient trajectories given by algorithms, though exogenous disturbances are involved for players.…”

“…The following standard assumptions are about the cost functions, which were widely used (eg, see other works 11,14,16,18,20 ).…”

“…Remark 1. Different from most of aggregative games, 11,[15][16][17][18][19][20] our formulation involves exogenous disturbances for players. The exogenous disturbance results that most of existing distributed algorithms cannot ensure the multiagent system (7) converge to the GNE of the game.…”

“…Moreover, Gharesifard and Cortés 27 pointed out that a convergent algorithm over undirected graphs may be divergent for some digraphs. It is worthwhile mentioning that many distributed GNE seeking algorithms depend on the undirected graphs such as those in other works, 11,[15][16][17][18][19][20] while there are few results about aggregative games over directed graphs.…”

“…(i) We formulate the aggregative games of multiagent systems with linear coupling constraints and weight-balanced digraphs, where all players have first-order dynamics and are influenced by exogenous disturbances. The considered problem can be viewed as extensions of some well-known problems, including the aggregative games discussed in other works 11,[15][16][17][18][19][20] by adding disturbed multiagent systems over weight-balanced digraphs and distributed control and optimization of multiagent system investigated in the works of Lin and Ren 6 and Deng et al 8 by considering game concerns. Without involving exogenous disturbances and weight-balanced digraphs, many existing distributed GNE seeking algorithms cannot be applied to our problem.…”