Distributed Finite-Time and Fixed-Time Nash Equilibrium Seeking for Non-Cooperative Game with Input Saturation

Dong Wang, Zhenzhen Gao () and Long Sheng ()
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Dong Wang: College of Engineering, China University of Petroleum—Beijing at Karamay, Karamay 834000, China
Zhenzhen Gao: College of Engineering, China University of Petroleum—Beijing at Karamay, Karamay 834000, China
Long Sheng: College of Engineering, China University of Petroleum—Beijing at Karamay, Karamay 834000, China

Mathematics, 2023, vol. 11, issue 10, 1-16

Abstract: In this paper, a modified distributed Nash equilibrium seeking problem with input saturation has been investigated. The payoff function of each player is related to the communication topology, which is closer to the actual scenes. The sigmoid function is utilized to limit the range of the input. Through the network communication between players and the gradient of the players’ payoff functions, the finite-time and fixed-time distributed Nash equilibrium seeking protocols with input saturation are given. Using the Lyapunov stability analysis, it is determined that the action of each player converges to the Nash equilibrium if all the players update their action according to the proposed algorithms. The numerical simulations are also provided to testify the algorithms.

Keywords: Nash equilibrium; input saturation; finite time; sigmoid function; non-cooperative game; Lyapunov stability analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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