We examine the routing problem for self-interested vehicles using stochastic decision strategies. By approximating the road latency functions and a non-linear variable transformation, we frame the problem as an aggregative game. We characterize the approximation error and we derive a new monotonicity condition for a broad category of games that encompasses the problem under consideration. Next, we propose a semi-decentralized algorithm to calculate the routing as a variational generalized Nash equilibrium and demonstrate the solution's benefits with numerical simulations. In the particular case of potential games, which emerges for linear latency functions, we explore a receding-horizon formulation of the routing problem, showing asymptotic convergence to destinations and analysing closed-loop performance dependence on horizon length through numerical simulations.

A fundamental open problem in monotone game theory is the computation of a specific generalized Nash equilibrium (GNE) among all the available ones, e.g. the optimal equilibrium with respect to a system-level objective. The existing GNE seeking algorithms have in fact convergence guarantees toward an arbitrary, possibly inefficient, equilibrium. In this paper, we solve this open problem by leveraging results from fixed-point selection theory and in turn derive distributed algorithms for the computation of an optimal GNE in monotone games. We then extend the technical results to the time-varying setting and propose an algorithm that tracks the sequence of optimal equilibria up to an asymptotic error, whose bound depends on the local computational capabilities of the agents.

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.

To optimally select a generalized Nash equilibrium, in this paper, we consider a semi-decentralized algorithm based on a double-layer Tikhonov regularization algorithm. Technically, we extend the Tikhonov method for equilibrium selection to generalized games. Next, we couple such an algorithm with the preconditioned forward-backward splitting, which guarantees linear convergence to a solution of the inner layer problem and allows for a semi-decentralized implementation. We then establish a conceptual connection and draw a comparison between the considered algorithm and the hybrid steepest descent method, the other known distributed approach for solving the equilibrium selection problem.

We study generalized games with full row rank equality coupling constraints and we provide a strikingly simple proof of strong monotonicity of the associated KKT operator. This allows us to show linear convergence to a variational equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we propose a fully-distributed algorithm with linear convergence guarantee for aggregative games under partial-decision information. Based on these results, we establish stability properties for online GNE seeking in games with time-varying cost functions and constraints. Finally, we illustrate our findings numerically on an economic dispatch problem for peer-to-peer energy markets.

Monotone aggregative games may admit multiple (variational) generalized Nash equilibria, yet currently there is no algorithm able to provide an a-priori characterization of the equilibrium solution actually computed. In this paper, we formulate for the first time the problem of selecting a specific variational equilibrium that is optimal with respect to a given objective function. We then propose a semi-decentralized algorithm for optimal equilibrium selection in linearly coupled aggregative games and prove its convergence.

We study a particular class of online quadratic optimization problems, where the objective function linearly depends on some time-varying parameters. In the context of prediction-correction algorithms, that is, algorithms that combine a prediction of the future cost function and a correction on the observation of the past one, we explore the effect of a stochastic disturbance in the prediction. We then propose an algorithm that leverages the information on the prediction uncertainty and on the problem structure to approximate the optimal combination between prediction and correction.