  In this paper, we solve the problem of learning a generalized Nash
equilibrium (GNE) in merely monotone games. First, we propose a novel
continuous semi-decentralized solution algorithm without projections that uses
first-order information to compute a GNE with a central coordinator. As the
second main contribution, we design a gain adaptation scheme for the previous
algorithm in order to alleviate the problem of improper scaling of the cost
functions versus the constraints. Third, we propose a data-driven variant of
the former algorithm, where each agent estimates their individual
pseudogradient via zeroth-order information, namely, measurements of their
individual cost function values. Finally, we apply our method to a perturbation
amplitude optimization problem in oil extraction engineering.
