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

arXiv: https://arxiv.org/abs/2304.05308 · HTML: https://mlsanity.com/paper/2304.05308/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2023.

## Built on by (most cited first, 3 of 3)

- [Adversarially and Distributionally Robust Virtual Energy Storage Systems via the Scenario Approach](https://mlsanity.com/paper/2511.09427/) (2025)
- [Wasserstein Distributionally Robust Nash Equilibrium Seeking with Heterogeneous Data: A Lagrangian Approach](https://mlsanity.com/paper/2511.14048/) (2025)
- [Scenario Approach with Post-Design Certification of User-Specified Properties](https://mlsanity.com/paper/2602.15568/) (2026)

## Abstract (arXiv)

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.