  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 semi-decentralized Nash equilibrium
seeking algorithm. In the proposed two-layer scheme, a coordinator iteratively
integrates the (possibly noisy and sporadic) agents' feedback to learn the
pseudo-gradients 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 ridehailing
service provided by several companies with mobility as a service orchestration,
necessary to both handle competition among firms and avoid traffic congestion,
which is also adopted to run numerical experiments verifying our results.
