Game on! Seminars

Game theory. Control. Intelligent systems.

Participation is open to everyone with no registration required.
The talks are typically held on Tuesdays at 16:00 CET.

Upcoming seminars

26-May-2026, 16:00 CET

__ Filippo Fabiani__
IMT Lucca

Data-based certificates in stochastic Nash games

Many modern systems in smart grids and smart cities rely on the interaction of multiple decision-makers whose choices affect one another. These interactions can be naturally described using game-theoretic models, but in practice they are often influenced by uncertainty (e.g., fluctuating demand or renewable generation) whose statistical properties are unknown. From a mathematical perspective, this complicates enormously the evaluation of the expected cost of each agent. Most existing approaches rely on large amounts of data and guarantee convergence only in the limit of infinite samples, an assumption that is unrealistic in many real-world and safety-critical settings. This talk asks a more practical question: what can be guaranteed when only a finite amount of data is available?

Building on recent advances in stability analysis and stochastic approximation, we will introduce a data-based framework that provides computable certificates measuring how close one can get from a Nash or generalized Nash equilibrium using finite samples. The approach leverages the monotonicity property and variational inequality structure of the stochastic game at hand, together with standard Nash equilibrium seeking schemes based on operator theory, thereby enabling reliable assessment of convergence even when part of the game model is unknown and shall be approximated in a data-driven fashion. Our results thus offer finite-sample certificates that bound equilibrium residuals and stability margins directly from available uncertainty realizations, without knowing the underlying probability distribution. As such, the proposed framework provides a unifying view of learning dynamics and equilibrium verification in stochastic multi-agent systems, with implications for data-driven control, economic modeling, and large-scale learning in games. Numerical illustrations demonstrate how the proposed certificates track equilibrium quality in practice.