Distributed Nash Equilibrium Searching via Fixed-Time Consensus-Based Algorithms

Li, Zhongguo; Ding, Zhengtao

doi:10.23919/acc.2019.8815076

Cited by 10 publications

(8 citation statements)

References 29 publications

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“…In some special cases, the feasible strategy sets of agents are in the form of linear inequality constraints. For example, the following shared linear constraint was considered [58] .…”

Section: Ifmentioning

confidence: 99%

“…For example, Refs. [51,52,58] considered the case where each agent has only access to its local block matrices in the shared linear coupling constraint (Eq. ( 5)) instead of the global shared constraint, that is to say, agent only knows in the constraint (Eq.…”

Section: Distributed Information and Communication Structure Settingsmentioning

confidence: 99%

“…This kind of information structures was discussed in Refs. [58,81]. Nevertheless, the interference graph of a multi-agent game can be dense in many cases, such as aggregative games discussed later.…”

Section: Distributed Information and Communication Structure Settingsmentioning

confidence: 99%

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A Survey on Noncooperative Games and Distributed Nash Equilibrium Seeking over Multi-Agent Networks

Lei

et al. 2022

CAAI Artificial Intelligence Research

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The work gives a review on the distributed Nash equilibrium seeking of noncooperative games in multi-agent networks, which emerges as one of the frontier research topics in the area of systems and control community. Firstly, we give the basic formulation and analysis of noncooperative games with continuous action spaces, and provide the motivation and basic setting for distributed Nash equilibrium seeking. Then we introduce both the gradient-based algorithms and best-response based algorithms for various type of games, including zero-sum games, aggregative games, potential games, monotone games, and multi-cluster games. In addition, we provide some applications of noncooperative games.

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“…In some special cases, the feasible strategy sets of agents are in the form of linear inequality constraints. For example, the following shared linear constraint was considered [58] .…”

Section: Ifmentioning

confidence: 99%

Section: Distributed Information and Communication Structure Settingsmentioning

confidence: 99%

See 1 more Smart Citation

A Survey on Noncooperative Games and Distributed Nash Equilibrium Seeking over Multi-Agent Networks

Lei

et al. 2022

CAAI Artificial Intelligence Research

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“…Remark 6: The addressed prescribed-time NE seeking is partially inspired by some existing finite-/fixed/appointed-time works on consensus and optimization (e.g., [17]- [26]). However, those works encounter certain design limitations such as the dependence of known initial states [17], [22], [23], [25], the control parameters [24], [26], and unavailable settling time by homogeneity analysis [18]. The appointed-time design in [21] heavily relies on motionplanning-based samplings.…”

Section: Prescribed-time and Fully Distributed Ne Seeking Design On J...mentioning

confidence: 99%

Prescribed-Time Fully Distributed Nash Equilibrium Seeking in Noncooperative Games

Feng,

2020

Preprint

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In this paper, we investigate a prescribed-time and fully distributed Nash Equilibrium (NE) seeking problem for continuoustime noncooperative games. By exploiting pseudo-gradient play and consensus-based schemes, various distributed NE seeking algorithms are presented over either fixed or switching communication topologies so that the convergence to the NE is reached in a prescribed time. In particular, a prescribed-time distributed NE seeking algorithm is firstly developed under a fixed graph to find the NE in a prior-given and user-defined time, provided that a static controller gain can be selected based on certain global information such as the algebraic connectivity of the communication graph and both the Lipschitz and monotone constants of the pseudo-gradient associated with players' objective functions. Secondly, a prescribed-time and fully distributed NE seeking algorithm is proposed to remove global information by designing heterogeneous dynamic gains that turn on-line the weights of the communication topology. Further, we extend this algorithm to accommodate jointly switching topologies. It is theoretically proved that the global convergence of those proposed algorithms to the NE is rigorously guaranteed in a prescribed time based on a time function transformation approach. In the last, numerical simulation results are presented to verify the effectiveness of the designs.The advantages of the proposed NE seeking algorithm include: 1) the convergence time is user-defined according to task requirements, which is neither dependent on any initial states or the parameters of the algorithm; 2) the proposed algorithm is fully distributed without requiring any global information on the graph's algebraic connectivity, the pseudo-gradient's Lipschitz and monotone constants, and the number of players; and 3) the communication graph is allowed to be jointly switching. The aforementioned requirements can improve the practical relevance of the problem to be addressed and meanwhile, it poses some technical challenges to the algorithm design and stability analysis, which makes that the NE seeking algorithms in the existing literature cannot be directly applied.

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“…Nash equilibrium searching over distributed networks has been widely studied using both discrete‐ and continuous‐time algorithms, for example, References [19–26]. In Reference [22], aggregative games with global constraints are studied using projected gradient methods.…”

Section: Introductionmentioning

confidence: 99%

On the game‐theoretic analysis of distributed generative adversarial networks

Dong

Chen

et al. 2021

Int J Intell Syst

Self Cite

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In this paper, a distributed method is proposed for training multiple generative adversarial networks (GANs) with private data sets via a game‐theoretic approach. To facilitate the requirement of privacy protection, distributed training algorithms offer a promising solution to learn global models without sample exchanges. Existing studies have mainly concentrated on training neural networks using pure cooperation strategies, which are not suitable for GANs. This paper develops a new framework for distributed GANs, where two groups of discriminators and generators are involved in a zero‐sum game. Under connected graphs, such a framework is reformulated as a constrained minmax optimisation problem. Then, a fully distributed training algorithm is proposed without exchanging any private data samples. The convergence of the proposed algorithm is established via advanced consensus and optimisation techniques. Simulation studies are presented to validate the effectiveness of the proposed framework and algorithm.

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Distributed Nash Equilibrium Searching via Fixed-Time Consensus-Based Algorithms

Cited by 10 publications

References 29 publications

A Survey on Noncooperative Games and Distributed Nash Equilibrium Seeking over Multi-Agent Networks

A Survey on Noncooperative Games and Distributed Nash Equilibrium Seeking over Multi-Agent Networks

Prescribed-Time Fully Distributed Nash Equilibrium Seeking in Noncooperative Games

On the game‐theoretic analysis of distributed generative adversarial networks

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