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M. Ye, Q.-L. Han, L. Ding, S. Xu, and G. Jia, “Distributed Nash Equilibrium Seeking Strategies Under Quantized Communication,” IEEE/CAA J. Autom. Sinica,. doi: 10.1109/JAS.2022.105857
Citation: M. Ye, Q.-L. Han, L. Ding, S. Xu, and G. Jia, “Distributed Nash Equilibrium Seeking Strategies Under Quantized Communication,” IEEE/CAA J. Autom. Sinica,. doi: 10.1109/JAS.2022.105857

Distributed Nash Equilibrium Seeking Strategies Under Quantized Communication

doi: 10.1109/JAS.2022.105857
Funds:  This work was supported by the National Natural Science Foundation of China (NSFC) (62222308, 62173181, 62073171), the Natural Science Foundation of Jiangsu Province (BK20200744, BK20220139), Jiangsu Specially-Appointed Professor (RK043STP19001), the Young Elite Scientists Sponsorship Program by CAST (2021QNRC001), 1311 Talent Plan of Nanjing University of Posts and Telecommunications, and the Fundamental Research Funds for the Central Universities (30920032203)
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  • This paper is concerned with distributed Nash equilibrium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization of players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized information flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respectively. Through Lyapunov stability analysis, it is shown that players’ actions can be steered to a neighborhood of the Nash equilibrium with logarithmic and uniform quantizers, and the quantified convergence error depends on the parameter of the quantizer for both undirected and directed cases. A numerical example is given to verify the theoretical results.

     

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