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.

Vehicle automation and connectivity bring new opportunities for safe and sustainable mobility in urban and highway networks. Such opportunities are however not directly associated with traffic flow improvements. Research on exploitation of connected and automated vehicles (CAVs) toward a more efficient traffic currently remains at a theoretical level, and/or based on simulation models with limited reliability. Furthermore, testing CAVs in the real world is still costly and very challenging from an implementation perspective. A possible alternative is to use automated robots. By designing and testing both the low-and the high-level controllers of CAVs, it is indeed possible to reach a better understanding of the challenges that future vehicles will need to face. Robotic applications can effectively test these challenges within a wide variety of research communities—for example, via robotic competitions. Along this direction, the Joint Research Centre has organized the first European robotic traffic competition for automated miniature vehicles. Each team participated with four robots and was judged based on a set of indicators that assess the collective behaviors of the vehicles. Results show the suitability of the methodology with different teams proposing completely different approaches to deal with the challenge and thus achieving different results. Future competitions may further raise awareness about the possibility of using CAVs to improve traffic and to engage with a broader community to design systems that are really capable of achieving this goal.

In the proof of [Guay and Dochain (2017), Th.1], Equation 6 is incorrect.

We propose an integral Nash equilibrium seeking control (I-NESC) law which steers the multi-agent system composed of a special class of linear agents to the neighborhood of the Nash equilibrium in noncooperative strongly monotone games. First, we prove that there exist parameters of the integral controller such that the system converges to the Nash equilibrium in the full-information case, in other words, without the parameter estimation scheme used in extremum seeking algorithms. Then we prove that there exist parameters of the I-NESC such that the system converges to the neighborhood of the Nash equilibrium in the limited information case where parameter estimation is used. We provide a simulation example that demonstrates that smaller perturbation frequencies and amplitudes are needed to attain similar convergence speed as the existing state-of-the-art algorithm.

In this paper, we consider the problem of learning a generalized Nash equilibrium (GNE) in strongly monotone games. First, we propose semi-decentralized and distributed continuous-time solution algorithms that use regular projections and first-order information to compute a GNE with and without a central coordinator. As the second main contribution, we design a data-driven variant of the former semi-decentralized algorithm where each agent estimates their individual pseudogradient via zeroth-order information, namely, measurements of their individual cost function values, as typical of extremum seeking control. Third, we generalize our setup and results for multi-agent systems with nonlinear dynamics. Finally, we apply our methods to connectivity control in robotic sensor networks and almost-decentralized wind farm optimization.