Distributed equilibrium seeking in aggregative games: linear convergence under singular perturbations lens
We present a fully-distributed algorithm for Nash equilibrium seeking in aggregative games over networks. The proposed scheme endows each agent with a gradient-based scheme equipped with a tracking mechanism to locally reconstruct the aggregative variable, which is not available to the agents. We sh...
| Main Authors: | , , , , |
|---|---|
| Format: | Conference item |
| Language: | English |
| Published: |
2024
|
| _version_ | 1811140276917370880 |
|---|---|
| author | Carnevale, G Fabiani, F Fele, F Margellos, K Notarstefano, G |
| author_facet | Carnevale, G Fabiani, F Fele, F Margellos, K Notarstefano, G |
| author_sort | Carnevale, G |
| collection | OXFORD |
| description | We present a fully-distributed algorithm for Nash equilibrium seeking in aggregative games over networks. The proposed scheme endows each agent with a gradient-based scheme equipped with a tracking mechanism to locally reconstruct the aggregative variable, which is not available to the agents. We show that our method falls into the framework of singularly perturbed systems, as it involves the interconnection between a fast subsystem – the global information reconstruction dynamics – with a slow one concerning the optimization of the local strategies. This perspective plays a key role in analyzing the scheme with a constant stepsize, and in proving its linear convergence to the Nash equilibrium in strongly monotone games with local constraints. By exploiting the flexibility of our aggregative variable definition (not necessarily the arithmetic average of the agents’ strategy), we show the efficacy of our algorithm on a realistic voltage support case study for the smart grid. |
| first_indexed | 2024-09-25T04:19:25Z |
| format | Conference item |
| id | oxford-uuid:c08b9f32-2f37-45ea-b95b-8dd441805d31 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-09-25T04:19:25Z |
| publishDate | 2024 |
| record_format | dspace |
| spelling | oxford-uuid:c08b9f32-2f37-45ea-b95b-8dd441805d312024-07-26T10:07:56ZDistributed equilibrium seeking in aggregative games: linear convergence under singular perturbations lensConference itemhttp://purl.org/coar/resource_type/c_5794uuid:c08b9f32-2f37-45ea-b95b-8dd441805d31EnglishSymplectic Elements2024Carnevale, GFabiani, FFele, FMargellos, KNotarstefano, GWe present a fully-distributed algorithm for Nash equilibrium seeking in aggregative games over networks. The proposed scheme endows each agent with a gradient-based scheme equipped with a tracking mechanism to locally reconstruct the aggregative variable, which is not available to the agents. We show that our method falls into the framework of singularly perturbed systems, as it involves the interconnection between a fast subsystem – the global information reconstruction dynamics – with a slow one concerning the optimization of the local strategies. This perspective plays a key role in analyzing the scheme with a constant stepsize, and in proving its linear convergence to the Nash equilibrium in strongly monotone games with local constraints. By exploiting the flexibility of our aggregative variable definition (not necessarily the arithmetic average of the agents’ strategy), we show the efficacy of our algorithm on a realistic voltage support case study for the smart grid. |
| spellingShingle | Carnevale, G Fabiani, F Fele, F Margellos, K Notarstefano, G Distributed equilibrium seeking in aggregative games: linear convergence under singular perturbations lens |
| title | Distributed equilibrium seeking in aggregative games: linear convergence under singular perturbations lens |
| title_full | Distributed equilibrium seeking in aggregative games: linear convergence under singular perturbations lens |
| title_fullStr | Distributed equilibrium seeking in aggregative games: linear convergence under singular perturbations lens |
| title_full_unstemmed | Distributed equilibrium seeking in aggregative games: linear convergence under singular perturbations lens |
| title_short | Distributed equilibrium seeking in aggregative games: linear convergence under singular perturbations lens |
| title_sort | distributed equilibrium seeking in aggregative games linear convergence under singular perturbations lens |
| work_keys_str_mv | AT carnevaleg distributedequilibriumseekinginaggregativegameslinearconvergenceundersingularperturbationslens AT fabianif distributedequilibriumseekinginaggregativegameslinearconvergenceundersingularperturbationslens AT felef distributedequilibriumseekinginaggregativegameslinearconvergenceundersingularperturbationslens AT margellosk distributedequilibriumseekinginaggregativegameslinearconvergenceundersingularperturbationslens AT notarstefanog distributedequilibriumseekinginaggregativegameslinearconvergenceundersingularperturbationslens |