Distributed Generalized Nash Equilibria Seeking Algorithms Involving Synchronous and Asynchronous Schemes
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913230581923840 |
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| author | Li, Huaqing Ran, Liang Zheng, Lifeng Li, Zhe Hu, Jinhui Li, Jun Huang, Tingwen |
| author_facet | Li, Huaqing Ran, Liang Zheng, Lifeng Li, Zhe Hu, Jinhui Li, Jun Huang, Tingwen |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_03669 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Distributed Generalized Nash Equilibria Seeking Algorithms Involving Synchronous and Asynchronous Schemes Li, Huaqing Ran, Liang Zheng, Lifeng Li, Zhe Hu, Jinhui Li, Jun Huang, Tingwen Computer Science and Game Theory Multiagent Systems 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. |
| title | Distributed Generalized Nash Equilibria Seeking Algorithms Involving Synchronous and Asynchronous Schemes |
| topic | Computer Science and Game Theory Multiagent Systems |
| url | https://arxiv.org/abs/2402.03669 |