Article
Mathematics, Applied
Jinlong Lei, Uday Shanbhag
Summary: This paper proposes a proximal gradient algorithm for stochastic Nash equilibrium problems involving n players and demonstrates its convergence speed and complexity through theoretical analysis. Additionally, a distributed protocol scheme is introduced to address aggregative stochastic NEP problems while reducing communication complexity.
SIAM JOURNAL ON OPTIMIZATION
(2022)
Article
Automation & Control Systems
Wicak Ananduta, Sergio Grammatico
Summary: We propose a distributed Nash equilibrium seeking method based on the Bregman forward-backward splitting, which utilizes a mirror mapping instead of the standard projection as the backward operator. Our main contribution is to demonstrate convergence to a Nash equilibrium when the game has cocoercive pseudogradient mapping. Additionally, when the feasible sets of the agents are simplices, choosing a suitable Legendre function results in an exponentiated pseudogradient method that outperforms the standard projected pseudogradient and dual averaging methods in our numerical experiments.
EUROPEAN JOURNAL OF CONTROL
(2022)
Article
Automation & Control Systems
Sijie Chen, Chengke Xu, Zheng Yan, Xinping Guan, Xinyi Le
Summary: This article introduces a distributed strategy update algorithm (DSUA) to address strategic players in distributed power dispatch algorithms (DPDAs). The DSUA considers the behavior deviation of strategic suppliers optimizing their bids, and analyzes the closeness of their bids to the Nash equilibrium.
IEEE TRANSACTIONS ON CYBERNETICS
(2022)
Article
Engineering, Electrical & Electronic
Maojiao Ye, Qing-Long Han, Lei Ding, Shengyuan Xu
Summary: This article provides a survey on distributed Nash equilibrium seeking in games with partial decision information. It introduces the fundamental problem descriptions and related results, and explains representative continuous and discrete-time methods. Two practical applications demonstrate the applicability of distributed Nash equilibrium seeking strategies, and future research directions are suggested.
PROCEEDINGS OF THE IEEE
(2023)
Article
Computer Science, Information Systems
Himanshu Agrawal, Krishna Asawa
Summary: Dynamic spectrum access using cognitive radio has various applications, and the objective is to minimize regret by selecting the best channel. An adaptive sequencing strategy has been proposed to achieve logarithmic order of regret with time.
JOURNAL OF KING SAUD UNIVERSITY-COMPUTER AND INFORMATION SCIENCES
(2022)
Article
Computer Science, Artificial Intelligence
Zhenhua Deng, Yangyang Liu
Summary: This article studies the multicluster games over weight-balanced digraphs where the cost functions of players are nonsmooth. A distributed algorithm based on subgradient descent, differential inclusions, and projection operations is designed to seek the Nash equilibrium of the game, and a distributed learning strategy is embedded for players to estimate the decisions of other players. The article also presents a numerical simulation to illustrate the effectiveness of the proposed algorithm.
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
(2023)
Article
Automation & Control Systems
Shijie Huang, Jinlong Lei, Yiguang Hong
Summary: This article discusses the distributed Nash equilibrium (NE) seeking of strongly monotone aggregative games over a multiagent network. A distributed algorithm is proposed, which involves multiple rounds of communication and achieves convergence to the NE with a linear convergence rate. Furthermore, a single-round communication version of the algorithm is studied, which also achieves linear convergence rate under certain conditions. Numerical simulations are provided to verify the results.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2023)
Article
Automation & Control Systems
Bin Du, Kun Qian, Christian Claudel, Dengfeng Sun
Summary: This article presents a novel Jacobi-style iteration algorithm for solving the problem of distributed submodular maximization. The algorithm is based on the multilinear extension of the submodular function and uses unbiased estimation of the gradient of multilinear extension function obtained by sampling the agents' local strategies. It enables simultaneous updates among all individual agents and guarantees convergence to a desirable equilibrium solution. The algorithm is further enhanced by handling communication delays among the agents.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2022)
Article
Automation & Control Systems
Basilio Gentile, Dario Paccagnan, Bolutife Ogunsula, John Lygeros
Summary: This article introduces a novel concept of inertial Nash equilibrium to account for switching costs in practical situations, defining it as a distribution over action space where no agent benefits from switching actions. The set of inertial Nash equilibria contains all Nash equilibria, is nonconvex, and can be characterized as a solution to a variational inequality. Classical algorithms for computing Nash equilibria are not applicable in the presence of switching costs, while a better-response dynamics algorithm is proposed and proven to converge to an inertial Nash equilibrium.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2021)
Article
Automation & Control Systems
Zhenhua Deng
Summary: This paper investigates nonsmooth aggregative games and develops a distributed algorithm for seeking the generalized Nash equilibrium. The algorithm uses dynamic average consensus to estimate the approximate subgradients of the decisions' aggregate, leading to convergence to the variational GNE. Simulation examples are provided to illustrate the algorithm.
Article
Automation & Control Systems
Bomin Huang, Yao Zou, Ziyang Meng
Summary: In this article, a distributed Nash equilibrium seeking algorithm is proposed based on a high-gain observer method for a class of distributed quadratic games over an undirected graph. The convergence is analyzed using Lyapunov stability theory, showing that each player can estimate rival players' states with errors ultimately bounded by a small bound, and the algorithm is free of chattering phenomena. The effectiveness of the algorithm is validated through a simulation of an oligopoly game in a duopoly market structure with five firms producing the same products.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2021)
Article
Computer Science, Hardware & Architecture
Syed Maaz Shahid, Sungoh Kwon
Summary: This paper proposes a cognitive radio-based spectrum assignment algorithm for IoT networks to reduce network interference and ensure connectivity. By using a conflict graph to determine potential interfering links, channels are assigned to each IoT device. Additionally, an ordered pair of channels is assigned to improve the robustness of the network topology and energy efficiency.
Article
Automation & Control Systems
Xin Cai, Feng Xiao, Bo Wei
Summary: This article proposes a distributed nonmodel based generalized Nash equilibrium (GNE) seeking algorithm for a class of constrained noncooperative games with unknown cost functions. The algorithm estimates the gradient information of auxiliary cost functions using extremum seeking control (ESC) and exact penalty method. It introduces a diminishing dither signal to remove steady-state oscillations and achieves nonlocal convergence to the GNE of the game. Numerical examples are provided to verify the effectiveness of the proposed method.
INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL
(2022)
Article
Mathematics, Applied
Chunxia Liu, Kaihong Lu, Xiaojie Chen, Attila Szolnoki
Summary: This study investigates the task allocation problem with constraints in a game-theoretical framework. It is found that when the Nash equilibrium point is feasible for the limited task allocation problem, it is the unique globally optimal solution, otherwise, the unique globally optimal solution is derived analytically. Numerical algorithms and Monte Carlo simulations are used to confirm the theoretical results.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Telecommunications
H. Sedighi, M. Abbaspour
Summary: This paper presents an optimal method for allocating frequency spectrum resources using game theory and Nash equilibrium, aiming to reduce the activities of secondary users in spectrum reallocation and decrease energy consumption in the network.
WIRELESS PERSONAL COMMUNICATIONS
(2021)
Article
Engineering, Electrical & Electronic
Ying Sun, Prabhu Babu, Daniel P. Palomar
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2015)
Article
Engineering, Electrical & Electronic
Yiyong Feng, Daniel P. Palomar
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2015)
Article
Engineering, Electrical & Electronic
Yiyong Feng, Daniel P. Palomar
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2015)
Article
Engineering, Electrical & Electronic
Yiyong Feng, Daniel P. Palomar, Francisco Rubio
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2015)
Article
Engineering, Electrical & Electronic
Junxiao Song, Prabhu Babu, Daniel P. Palomar
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2015)
Article
Engineering, Electrical & Electronic
Amir Daneshmand, Francisco Facchinei, Vyacheslav Kungurtsev, Gesualdo Scutari
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2015)
Article
Engineering, Electrical & Electronic
Francisco Facchinei, Gesualdo Scutari, Simone Sagratella
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2015)
Article
Engineering, Electrical & Electronic
Junxiao Song, Prabhu Babu, Daniel P. Palomar
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2015)
Article
Computer Science, Software Engineering
Valeria Cardellini, Vittoria De Nitto Persone, Valerio Di Valerio, Francisco Facchinei, Vincenzo Grassi, Francesco Lo Presti, Veronica Piccialli
MATHEMATICAL PROGRAMMING
(2016)
Article
Engineering, Electrical & Electronic
Licheng Zhao, Prabhu Babu, Daniel P. Palomar
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2016)
Article
Engineering, Electrical & Electronic
Tianyu Qiu, Prabhu Babu, Daniel P. Palomar
IEEE TRANSACTIONS ON SIGNAL PROCESSING
(2016)
Article
Computer Science, Software Engineering
Francisco Facchinei, Lorenzo Lampariello, Gesualdo Scutari
MATHEMATICAL PROGRAMMING
(2017)
Article
Computer Science, Software Engineering
Loris Cannelli, Francisco Facchinei, Vyacheslav Kungurtsev, Gesualdo Scutari
MATHEMATICAL PROGRAMMING
(2020)
Article
Operations Research & Management Science
Francisco Facchinei, Vyacheslav Kungurtsev, Lorenzo Lampariello, Gesualdo Scutari
Summary: This study introduces a new approach to the convergence analysis of nonconvex constrained optimization problems using penalty functions. By utilizing classical penalty functions unconventionally, the research establishes new results including analysis of diminishing stepsize methods and complexity study for sequential quadratic programming-type algorithms in nonconvex, constrained optimization.
MATHEMATICS OF OPERATIONS RESEARCH
(2021)
Article
Automation & Control Systems
Loris Cannelli, Francisco Facchinei, Gesualdo Scutari, Vyacheslav Kungurtsev
Summary: This study introduces a distributed, asynchronous algorithm for convex and nonconvex constrained optimization with a partially separable objective function. The algorithm is proven to converge at a sublinear rate in nonconvex cases and at a linear rate under specific error bound conditions. Numerical results show the effectiveness of the method in matrix completion and LASSO problems.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2021)