Abstract
A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE seeking algorithms have in fact convergence guarantees toward an arbitrary, possibly inefficient, equilibrium. In this paper, we solve this open problem by leveraging results from fixed-point selection theory and in turn derive distributed algorithms for the computation of an optimal GNE in monotone games. We then extend the technical results to the time-varying setting and propose an algorithm that tracks the sequence of optimal equilibria up to an asymptotic error, whose bound depends on the local computational capabilities of the agents.
| Original language | English |
|---|---|
| Pages (from-to) | 7644-7659 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 68 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 2023 |
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.
Keywords
- Convergence
- Couplings
- Games
- Heuristic algorithms
- Multi-agent systems
- Nash equilibrium
- Nash equilibrium seeking
- Optimization
- Peer-to-peer computing