Learning equilibria with personalized incentives in a class of nonmonotone games

Filippo Fabiani, Andrea Simonetto and Paul J. Goulart

@inproceedings{FSG:2022,
  author = {Fabiani, Filippo and Simonetto, Andrea and Goulart, Paul J.},
  title = {Learning equilibria with personalized incentives in a class of nonmonotone games},
  booktitle = {2022 European Control Conference (ECC)},
  year = {2022},
  pages = {2179-2184},
  url = {https://ieeexplore.ieee.org/abstract/document/9838083},
  doi = {10.23919/ECC55457.2022.9838083}
}

We consider quadratic, nonmonotone generalized Nash equilibrium problems with symmetric interactions among the agents. Albeit this class of games is known to admit a potential function, its formal expression can be unavailable in several real-world applications. For this reason, we propose a two-layer Nash equilibrium seeking scheme in which a central coordinator exploits noisy feedback from the agents to design personalized incentives for them. By making use of those incentives, the agents compute a solution to an extended game, and then return feedback measures to the coordinator. We show that our algorithm returns an equilibrium if the coordinator is endowed with standard learning policies, and corroborate our results on a numerical instance of a hypomonotone game.