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Title: Nash equilibrium seeking in N-coalition games via a gradient-free method
Authors: Pang, Yipeng
Hu, Guoqiang
Keywords: Engineering::Electrical and electronic engineering
Issue Date: 2022
Source: Pang, Y. & Hu, G. (2022). Nash equilibrium seeking in N-coalition games via a gradient-free method. Automatica, 136, 110013-.
Project: RG180/17(2017-T1-002-158)
Journal: Automatica
Abstract: This paper studies an N-coalition non-cooperative game problem, where the players in the same coalition cooperatively minimize the sum of their local cost functions under a directed communication graph, while collectively acting as a virtual player to play a non-cooperative game with other coalitions. Moreover, it is assumed that the players have no access to the explicit functional form but only the function value of their local costs. To solve the problem, a discrete-time gradient-free Nash equilibrium seeking strategy, based on the gradient tracking method, is proposed. Specifically, a gradient estimator is developed locally based on Gaussian smoothing to estimate the partial gradients, and a gradient tracker is constructed locally to trace the average sum of the partial gradients among the players within the coalition. With a sufficiently small constant step-size, we show that all players’ actions approximately converge to the Nash equilibrium at a geometric rate under a strongly monotone game mapping condition. Numerical simulations are conducted to verify the effectiveness of the proposed algorithm.
ISSN: 0005-1098
DOI: 10.1016/j.automatica.2021.110013
Schools: School of Electrical and Electronic Engineering 
Rights: © 2021 Elsevier Ltd. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
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