Distributed convergence to Nash equilibria in network and average aggregative games

Parise, Francesca; Grammatico, Sergio; Gentile, B. De; Lygeros, John

doi:10.1016/j.automatica.2020.108959

Cited by 38 publications

(22 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is unrealistic that these participants will adopt any centralized methods that require cooperation among them. Because of this, there is an enduring research interest in distributing the computation of Nash equilibria [15], [16], especially through the avenue of operator splitting technique [17], [18]. In addition to the distributed computation, under most circumstances, participants can only have access to the local information and decisions of their neighbors, which constitutes a partialdecision information setting [19]- [21].…”

Section: Imentioning

confidence: 99%

Distributed Computation of Stochastic GNE with Partial Information: An Augmented Best-Response Approach

Huang

2021

Preprint

View full text Add to dashboard Cite

In this paper, we focus on the stochastic generalized Nash equilibrium problem (SGNEP) which is an important and widely-used model in many different fields. In this model, subject to certain global resource constraints, a set of self-interested players aim to optimize their local objectives that depend on their own decisions and the decisions of others and are influenced by some random factors. We propose a distributed stochastic generalized Nash equilibrium seeking algorithm in a partialdecision information setting based on the Douglas-Rachford operator splitting scheme, which significantly relaxes assumptions on co-coercivity and contractiveness in the existing literature. The proposed algorithm updates players' local decisions through boxconstrained augmented best-response schemes and subsequent projections onto the local feasible sets, which occupy most of the computational workload. The projected stochastic subgradient method is applied to provide approximate solutions to the augmented best-response subproblems for each player. The Robbins-Siegmund theorem is leveraged to establish the main convergence results to a true Nash equilibrium and sufficient conditions to be satisfied by the inexact solver used. Finally, we illustrate the validity of the proposed algorithm through two numerical examples, i.e., a stochastic Nash-Cournot distribution game and a multi-product assembly problem with the two-stage model.

show abstract

Section: Imentioning

confidence: 99%

Distributed Computation of Stochastic GNE with Partial Information: An Augmented Best-Response Approach

Huang

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Our proposed solution to the above problem is inspired by some recent work in non-cooperative games on networks, i.e., the generalized Nash equilibrium problem (GNEP) [12], which has attracted increasing research interest, especially through the avenue of operator splitting [13], [14], [15]. For example, the algorithms proposed in [16], [17] carry out multiple rounds of communication within each iteration. With sufficient rounds of information exchange, the proposed This work was supported by the National Science Foundation under Grant No.…”

Section: Imentioning

confidence: 99%

A Primal Decomposition Approach to Globally Coupled Aggregative Optimization over Networks

Huang¹,

Hu²

2021

Preprint

View full text Add to dashboard Cite

We consider a class of multi-agent optimization problems, where each agent has a local objective function that depends on its own decision variables and the aggregate of others, and is willing to cooperate with other agents to minimize the sum of the local objectives. After associating each agent with an auxiliary variable and the related local estimates, we conduct primal decomposition to the globally coupled problem and reformulate it so that it can be solved distributedly. Based on the Douglas-Rachford method, an algorithm is proposed which ensures the exact convergence to a solution of the original problem. The proposed method enjoys desirable scalability by only requiring each agent to keep local estimates whose number grows linearly with the number of its neighbors. We illustrate our proposed algorithm by numerical simulations on a commodity distribution problem over a transport network.

show abstract

“…In the second class of aggregative games (partial-information case), there is no population coordinator. Instead, the agents exchange information with each other through a network [14], where the aggregative term can be defined either as local [15] or global [16]. Recently, the authors in [17] proposed a fully-distributed algorithm for seeking a generalized Nash equilibrium that exploits an interconnection of dynamic tracking of the aggregate term, projected-pseudo-gradient dynamics and Krasnoselskij-Mann (KM) iterations.…”

Section: Introductionmentioning

confidence: 99%

Multipopulation Aggregative Games:Equilibrium Seeking via Mean-Field Control and Consensus

Kebriaei

Sadati-Savadkoohi

Shokri

et al. 2021

IEEE Trans. Automat. Contr.

Self Cite

View full text Add to dashboard Cite

In this paper, we extend the theory of deterministic mean-field/aggregative games to multi-population games. We consider a set of populations, each managed by a population coordinator (PC), of selfish agents playing a global non-cooperative game, whose cost functions are affected by an aggregate term across all agents from all populations. In particular, we impose that the agents cannot exchange information between themselves directly; instead, only a PC can gather information on its own population and exchange local aggregate information with the neighboring PCs. To seek an equilibrium of the resulting (partialinformation) game, we propose an iterative algorithm where each PC broadcasts a mean-field signal, namely, an estimate of the overall aggregative term, to its own population only. In turn, we let the local agents react with a best response and the PCs cooperate for estimating the aggregative term. Our main technical contributions are to cast the proposed scheme as a fixed-point iteration with errors, namely, the interconnection of a Krasnoselskij-Mann iteration and a linear consensus protocol, and, under a non-expansiveness condition, to show convergence towards an ε-Nash equilibrium, where ε is inversely proportional to the population size.

show abstract

Distributed convergence to Nash equilibria in network and average aggregative games

Cited by 38 publications

References 16 publications

Distributed Computation of Stochastic GNE with Partial Information: An Augmented Best-Response Approach

Distributed Computation of Stochastic GNE with Partial Information: An Augmented Best-Response Approach

A Primal Decomposition Approach to Globally Coupled Aggregative Optimization over Networks

Multipopulation Aggregative Games:Equilibrium Seeking via Mean-Field Control and Consensus

Contact Info

Product

Resources

About