An asynchronous, forward-backward, distributed generalized Nash equilibrium seeking algorithm

Abstract

In this paper, we propose an asynchronous distributed algorithm for the computation of generalized Nash equilibria in noncooperative games, where the players interact via an undirected communication graph. Specifically, we extend the paper "Asynchronous distributed algorithm for seeking generalized Nash equilibria" by Yi and Pavel: we redesign the asynchronous update rule using auxiliary variables over the nodes rather than over the edges. This key modification renders the algorithm scalable for highly interconnected games. The derived asynchronous algorithm is robust against delays in the communication and it eliminates the idle times between computations, hence modeling a more realistic interaction between players with different update frequencies. We address the problem from an operator-theoretic perspective and design the algorithm via a preconditioned forward-backward splitting. Finally, we numerically simulate the algorithm for the Cournot competition in networked markets.

Towards Time-Varying Proximal Dynamics in Multi-Agent Network Games

“…The scaling factors α i describe how the burden of satisfying the constraints are divided between the agents, hence N i=1 α i = 1. If α i = 1 /N, for all i ∈ N , then the effort to satisfy the couplying constraints is fairly splitted between the agents, this case is considered in several works, e.g., [5], [15], [24]. This class of problems was introduced for the first time in the seminal work by Rosen [25], where the author formulates the concept of normalized equilibrium.…”

Online distributed tracking of generalized Nash equilibrium on physical networks

“…In reference [9], a Nesterov-based algorithm was proposed to seek the GNE of an energy sharing game among prosumers, where the proposed algorithm showed better convergence performance than two classical distributed methods: the alternating direction method of multipliers (ADMM) and the gradient descent method. References [10,11] separately studied the distributed forwardbackward algorithm for GNE seeking. The former studied a stochastic GNG, while the latter formulated an asynchronous algorithm paradigm.…”

“…Theorem 1 Suppose Assumption A1 holds. If the step size satisfies 0 < α < 2M/L 2 , then the gap between the fixed point of the offline algorithm (11) and the GNE of (2) is presented as…”

Multi-agent network games with applications in smart electric mobility

“…Solutions for nooncoperative games over networks subject to local convex constraints have been developed, e.g., in [141], under strongly convex quadratic costs and time-invariant communication graphs; in [110] [155], with differentiable cost functions with Lipschitz continuous gradients, strictly convex cost functions, and undirected, possibly time-varying, communication graphs; and in [47], where the communication is ruled by a possibly time-varying digraph and the cost functions are assumed to be convex. In some recent works, researchers have developed algorithms to solve games over networks subject to asynchronous updates of the agents: among others, in [177,40], the game is subject to affine coupling constraints, and the cost functions are differentiable, while the communication graph is assumed to be undirected.…”

“…The problem of noncooperative multi-agent games, subject to coupling constrains, was firstly studied in [79], under the assumptions of continuously differentiable cost functions and no network structure between the agents. In the past years, several researchers focused on this class of problems providing a range of results for games over networks, e.g., in [176,20,40] where the communication network is always assumed to be undirected, while the cost functions are chosen either differentiable or continuously differentiable. Moreover, some researchers also focused on the class of noncooperative games over time-varying communication networks, in particular on the unconstrained case.…”