Personalized incentives as feedback design in generalized Nash equilibrium problems

We investigate both stationary and time-varying, nonmonotone-generalized Nash equilibrium problems that exhibit symmetric interactions among the agents, which are known to be potential. As may happen in practical cases, however, we envision a scenario in which the formal expression of the underlying potential function is not available, and we design a semidecentralized Nash-equilibrium-seeking algorithm. In the proposed two-layer scheme, a coordinator iteratively integrates possibly noisy and sporadic agents' feedback to learn the pseudogradients of the agents and then design personalized incentives for them. On their side, the agents receive those personalized incentives, compute a solution to an extended game, and then return feedback measurements to the coordinator. In the stationary setting, our algorithm returns a Nash equilibrium in case the coordinator is endowed with standard learning policies while it returns a Nash equilibrium up to a constant, yet adjustable, error in the time-varying case. As a motivating application, we consider the ride-hailing service provided by several competing companies with mobility as a service orchestration, necessary to both handle competition among firms and avoid traffic congestion.