Learning generalized Nash equilibria in monotone games: A hybrid adaptive extremum seeking control approach

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