A priori data-driven robustness guarantees on strategic deviations from generalised Nash equilibria

In this paper we focus on noncooperative games with uncertain constraints coupling the agents' decisions. We consider a setting where bounded deviations of agents' decisions from the equilibrium are possible, and uncertain constraints are inferred from data. Building upon recent advances in the so called scenario approach, we propose a randomised algorithm that returns a nominal equilibrium such that a pre-specified bound on the probability of violation for yet unseen constraints is satisfied for an entire region of admissible deviations surrounding it, thus supporting neighbourhoods of equilibria with probabilistic feasibility certificates. For the case in which the game admits a potential function, whose minimum coincides with the social welfare optimum of the population, the proposed algorithmic scheme opens the road to achieve a trade-off between the guaranteed feasibility levels of the region surrounding the nominal equilibrium, and its system-level efficiency. Detailed numerical simulations corroborate our theoretical results.