Learning equilibria with personalized incentives in a class of nonmonotone games
This addresses equilibrium computation in nonmonotone games for applications like multi-agent systems, but it is incremental as it builds on existing game theory and incentive design frameworks.
The paper tackles the problem of finding equilibria in quadratic, nonmonotone generalized Nash equilibrium problems with symmetric interactions, where the potential function is often unavailable in real-world applications, by proposing a two-layer Nash equilibrium seeking scheme with personalized incentives, and shows that the algorithm returns an equilibrium when the coordinator uses standard learning policies, corroborated on a numerical hypomonotone game instance.
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.