Distributed algorithms for Nash equilibrium seeking in aggregative games with state-dependent cost functions

Authors

Jingyi Zhao, Yongxin Wu, Zhenhua Zhang, Yuhu Wu

Abstract

Recently, the aggregative game in cyber-physical systems has gained significant attention from researchers. In this work, we employ the port Hamiltonian (PH) framework to model the multi-agent systems, providing an accurate representation of the physical dynamics for each player (agent). Then, taking into account the impact imposed by the physical dynamics of the multi-agent systems, we investigate the Nash equilibrium seeking problem of the aggregative game with two types of state-dependent cost functions. Next, two distributed Nash equilibrium seeking algorithms are proposed for aggregative games with these cost functions, respectively. Furthermore, we demonstrate that the multi-agent systems with the proposed distributed algorithm exponentially converge to the Nash equilibrium of the aggregative game with the corresponding cost function. Finally, two simulation examples are provided to show the effectiveness of the proposed algorithms.

Keywords

aggregative game, distributed control, nash equilibrium, port-hamiltonian system

Citation

• Journal: Journal of the Franklin Institute
• Year: 2026
• Volume: 363
• Issue: 1
• Pages: 108266
• Publisher: Elsevier BV
• DOI: 10.1016/j.jfranklin.2025.108266

BibTeX

@article{Zhao_2026,
  title={{Distributed algorithms for Nash equilibrium seeking in aggregative games with state-dependent cost functions}},
  volume={363},
  ISSN={0016-0032},
  DOI={10.1016/j.jfranklin.2025.108266},
  number={1},
  journal={Journal of the Franklin Institute},
  publisher={Elsevier BV},
  author={Zhao, Jingyi and Wu, Yongxin and Zhang, Zhenhua and Wu, Yuhu},
  year={2026},
  pages={108266}
}

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