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Distributed Finite-Time Nash Equilibrium Seeking for Non-Cooperative Games

Distributed Finite-Time Nash Equilibrium Seeking for Non-Cooperative Games
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Year:    2021

Author:    Xiao Fang, Jinhu Lü, Guanghui Wen

CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 1 : pp. 162–174

Abstract

The paper aims to design a distributed algorithm for players in games such that the players can learn Nash equilibriums of non-cooperative games in finite time. We first consider the quadratic non-cooperative games and design estimate protocols for the players such that they can estimate all the other players' actions in distributed manners. In order to make the players track all the other players' real actions in finite time, a bounded gradient dynamics is designed for players to update their actions by using the estimate information. Then the algorithm is extended to more general non-cooperative games and it is proved that players' estimates can converge to all the other players' real actions in finite time and all players can learn the unique Nash equilibrium in finite time under mild assumptions. Finally, simulation examples are provided to verify the validity of the proposed finite-time distributed Nash equilibrium seeking algorithms.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/csiam-am.2020-0028

CSIAM Transactions on Applied Mathematics, Vol. 2 (2021), Iss. 1 : pp. 162–174

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Nash equilibrium non-cooperative game distributed algorithm finite-time convergence.

Author Details

Xiao Fang

Jinhu Lü

Guanghui Wen

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