Distributed best response dynamics for Nash equilibrium seeking in potential games
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Control Theory and Technology http://link.springer.com/journal/11768
Distributed best response dynamics for Nash equilibrium seeking in potential games Shijie HUANG 1,2 , Peng YI 3,4† 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 Received 26 December 2019; revised 14 May 2020; accepted 15 May 2020
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. Keywords: 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
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Introduction
With decision-making problems on large-scale multiagent networks receiving more and more research attention, distributed Nash equilibrium (NE) seeking becomes an emerging research frontier, motivated by numerous applications including autonomous vehicle-
target assignment [1], power control in wireless communication networks [2–4], resource allocation in cloud computation [5, 6], and opinion dynamics in social networks [7]. In these noncooperative games, each agent has its own cost function (usually dependent on the actions of other agents) and feasible action set. NE is a resonable solution for noncooperative games, since
† Corresponding author. E-mail: [email protected]. This work was supported by the Shanghai Sailing Program (No. 20YF1453000) and the Fundamental Research Funds for the Central Universities (No. 22120200048).
© 2020 South China University of Technology, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature
S. Huang, P. Yi / Control Theory Tech, Vol.
no agent can further decrease its cost by unilaterally changing its action. Various distributed algorithms for Nash equilibrium seeking have been proposed in recent years [8–15]. Potential game is a very important type of games due to its wide applications and elegant theoretical properties. In a potential game, there exists a potential function characterizi
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