Seeking Nash Equilibrium in Non-cooperative Quadratic Games Under Delayed Information Exchange

Fuente: arXiv
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Autori principali: Jiang, Kaichen, Yan, Yuyue, Yue, Mingda, Wu, Yuhu
Natura: Preprint
Pubblicazione: 2026
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author Jiang, Kaichen
Yan, Yuyue
Yue, Mingda
Wu, Yuhu
author_facet Jiang, Kaichen
Yan, Yuyue
Yue, Mingda
Wu, Yuhu
contents In this paper, we investigate the seeking of Nash equilibrium (NE) in a non-cooperative quadratic game where all agents exchange their delayed strategy information with their neighbors. To extend best-response algorithms to the delayed information setting, an estimation mechanism for each agent to estimate the current strategy profile is designed. Based on the best-response strategy to the estimations, the strategy profile dynamics of all agents is established, which is revealed to converge asymptotically to the NE when agents exchange multi-step-delay information via the Lyapunov-Krasovskii functional approach. In the scenario where agents exchange one-step-delay information, the exponential convergence of the strategy profile dynamics to the NE can be guaranteed by restricting the learning rate to less than an upper bound. Moreover, a lower bound on the learning rate for instability of the NE is proposed. Numerical simulations are provided for verifying the developed results.
format Preprint
id arxiv_https___arxiv_org_abs_2602_18751
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Seeking Nash Equilibrium in Non-cooperative Quadratic Games Under Delayed Information Exchange
Jiang, Kaichen
Yan, Yuyue
Yue, Mingda
Wu, Yuhu
Systems and Control
In this paper, we investigate the seeking of Nash equilibrium (NE) in a non-cooperative quadratic game where all agents exchange their delayed strategy information with their neighbors. To extend best-response algorithms to the delayed information setting, an estimation mechanism for each agent to estimate the current strategy profile is designed. Based on the best-response strategy to the estimations, the strategy profile dynamics of all agents is established, which is revealed to converge asymptotically to the NE when agents exchange multi-step-delay information via the Lyapunov-Krasovskii functional approach. In the scenario where agents exchange one-step-delay information, the exponential convergence of the strategy profile dynamics to the NE can be guaranteed by restricting the learning rate to less than an upper bound. Moreover, a lower bound on the learning rate for instability of the NE is proposed. Numerical simulations are provided for verifying the developed results.
title Seeking Nash Equilibrium in Non-cooperative Quadratic Games Under Delayed Information Exchange
topic Systems and Control
url https://arxiv.org/abs/2602.18751