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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&#x0027; 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.

Personalized Incentives as Feedback Design in Generalized Nash Equilibrium Problems