Distributed Generalized Nash Equilibria Seeking Algorithms Involving Synchronous and Asynchronous Schemes
<|reference_start|>Distributed Generalized Nash Equilibria Seeking Algorithms Involving Synchronous and Asynchronous Schemes: This paper considers a class of noncooperative games in which the feasible decision sets of all players are coupled together by a coupled inequality constraint. Adopting the variational inequality formulation of the game, we first introduce a new local edge-based equilibrium condition and develop a distributed primal-dual proximal algorithm with full information. Considering challenges when communication delays occur, we devise an asynchronous distributed algorithm to seek a generalized Nash equilibrium. This asynchronous scheme arbitrarily activates one player to start new computations independently at different iteration instants, which means that the picked player can use the involved out-dated information from itself and its neighbors to perform new updates. A distinctive attribute is that the proposed algorithms enable the derivation of new distributed forward-backward-like extensions. In theoretical aspect, we provide explicit conditions on algorithm parameters, for instance, the step-sizes to establish a sublinear convergence rate for the proposed synchronous algorithm. Moreover, the asynchronous algorithm guarantees almost sure convergence in expectation under the same step-size conditions and some standard assumptions. An interesting observation is that our analysis approach improves the convergence rate of prior synchronous distributed forward-backward-based algorithms. Finally, the viability and performance of the proposed algorithms are demonstrated by numerical studies on the networked Cournot competition.<|reference_end|>
@article{li2024distributed,
    title={Distributed Generalized Nash Equilibria Seeking Algorithms Involving
  Synchronous and Asynchronous Schemes},
    author={Huaqing Li, Liang Ran, Lifeng Zheng, Zhe Li, Jinhui Hu, Jun Li,
  Tingwen Huang},
    journal={arXiv preprint arXiv:2402.03669},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.03669},
    primaryClass={cs.GT cs.MA}
}