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Distributed best response dynamics for Nash equilibrium seeking in potential games
ShijieHUANG,PengYI
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(1.Key Lab of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; 2.School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China;;3.Department of Control Science & Engineering, Tongji University, Shanghai 201804, China; 4.Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai 201804, China)
摘要:
In this paper, we consider distributed Nash equilibrium (NE) seeking in potential games over a multi-agent network, where each agent can not observe the actions of all its rivals. Based on the best response dynamics, we design a distributed NE seeking algorithm by incorporating the non-smooth finite-time average tracking dynamics, where each agent only needs to know its own action and exchange information with its neighbours through a communication graph. We give a sufficient condition for the Lipschitz continuity of the best response mapping for potential games, and then prove the convergence of the proposed algorithm based on the Lyapunov theory. Numerical simulations are given to verify the result and illustrate the effectiveness of the algorithm.
关键词:  Distributed algorithms, Nash equilibrium seeking, best response dynamics, non-smooth finite-time tracking dynamics, potential games
DOI:https://doi.org/10.1007/s11768-020-9204-4
基金项目:This work was supported by the Shanghai Sailing Program (No. 20YF1453000) and the Fundamental Research Funds for the Central Universities (No. 22120200048).
Distributed best response dynamics for Nash equilibrium seeking in potential games
Shijie HUANG,Peng YI
(1.Key Lab of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; 2.School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China;;3.Department of Control Science & Engineering, Tongji University, Shanghai 201804, China; 4.Shanghai Institute of Intelligent Science and Technology, Tongji University, Shanghai 201804, China)
Abstract:
In this paper, we consider distributed Nash equilibrium (NE) seeking in potential games over a multi-agent network, where each agent can not observe the actions of all its rivals. Based on the best response dynamics, we design a distributed NE seeking algorithm by incorporating the non-smooth finite-time average tracking dynamics, where each agent only needs to know its own action and exchange information with its neighbours through a communication graph. We give a sufficient condition for the Lipschitz continuity of the best response mapping for potential games, and then prove the convergence of the proposed algorithm based on the Lyapunov theory. Numerical simulations are given to verify the result and illustrate the effectiveness of the algorithm.
Key words:  Distributed algorithms, Nash equilibrium seeking, best response dynamics, non-smooth finite-time tracking dynamics, potential games