Abstract
We consider the Nash equilibrium problem in a partial-decision information scenario. Specifically, each agent can only receive information from some neighbors via a communication network, while its cost function depends on the strategies of possibly all agents. In particular, while the existing methods assume undirected or balanced communication, in this paper we allow for non-balanced, directed graphs. We propose a fully-distributed pseudo-gradient scheme, which is guaranteed to converge with linear rate to a Nash equilibrium, under strong monotonicity and Lipschitz continuity of the game mapping. Our algorithm requires global knowledge of the communication structure, namely of the Perron-Frobenius eigenvector of the adjacency matrix and of a certain constant related to the graph connectivity. Therefore, we adapt the procedure to setups where the network is not known in advance, by computing the eigenvector online and by means of vanishing step sizes.
| Original language | English |
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| Title of host publication | Proceedings of the 59th IEEE Conference on Decision and Control, CDC 2020 |
| Place of Publication | Piscataway, NJ, USA |
| Publisher | IEEE |
| Pages | 3555-3560 |
| ISBN (Electronic) | 978-1-7281-7447-1 |
| DOIs | |
| Publication status | Published - 2020 |
| Event | 59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of Duration: 14 Dec 2020 → 18 Dec 2020 |
Conference
| Conference | 59th IEEE Conference on Decision and Control, CDC 2020 |
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| Country/Territory | Korea, Republic of |
| City | Virtual, Jeju Island |
| Period | 14/12/20 → 18/12/20 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.