Seeking Nash Equilibrium in Non-cooperative Quadratic Games Under Delayed Information Exchange
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911461240995840 |
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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 |