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Distributed Nash Equilibrium Seeking for Non-Cooperative Games with a Coupled Inequality Constraint

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Advances in Guidance, Navigation and Control

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 644))

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Abstract

In this paper, the Nash equilibrium seeking issue for non-cooperative games with a coupled inequality constraint is investigated. In particular, there exists coupling between distinct decision variables of players in every cost function and the constrained inequality function. A distributed seeking algorithm with local information interaction is proposed. Specifically, a distributed observer with projection is first proposed such that the decision variables of all the other players can be estimated by every player. Next, by implementing these estimates, a seeking algorithm with projection is developed. In terms of a time-scale separation method, the stability analysis is performed. It is first shown that the distributed observer, as the fast dynamics, guarantees the estimation errors converging to an arbitrarily small neighborhood of the origin in finite time and maintaining within it afterwards. With this result, it is then shown that the seeking algorithm, as the slow dynamics, guarantees the strategy profiles converging to a neighborhood of the concerned generalized Nash equilibrium.

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Acknowledgements

The work has been in part supported by the Fundamental Research Funds for the Central Universities under Grant FRF-TP-19-006B1, in part by Scientific and Technological Innovation Foundation of Shunde Graduate School, University of Science and Technology Beijing, in part by the National Natural Science Foundation of China under Grants 61933001 and 62073028, in part by Scientific and Technological Innovation Foundation of Shunde Graduate School, USTB under Grant BK19AE014, and in part by Beijing Top Discipline for Artificial Intelligent Science and Engineering, University of Science and Technology Beijing.

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Authors and Affiliations

  1. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, 100083, People’s Republic of China

    Yao Zou

  2. Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing, 100083, People’s Republic of China

    Wei He

Authors
  1. Yao Zou
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  2. Wei He
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Correspondence to Yao Zou .

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Editors and Affiliations

  1. Beihang University, Beijing, China

    Liang Yan

  2. Beihang University, Beijing, China

    Haibin Duan

  3. Beihang University, Beijing, China

    Xiang Yu

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Zou, Y., He, W. (2022). Distributed Nash Equilibrium Seeking for Non-Cooperative Games with a Coupled Inequality Constraint. In: Yan, L., Duan, H., Yu, X. (eds) Advances in Guidance, Navigation and Control . Lecture Notes in Electrical Engineering, vol 644. Springer, Singapore. https://doi.org/10.1007/978-981-15-8155-7_72

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