A posteriori probabilistic feasibility guarantees for Nash equilibria in uncertain multi-agent games

On the robustness of equilibria in generalized aggregative games

“…Remark 3: The result in Proposition 1 implies that, given the same K-multisample δ K ∈ ∆ K , (6) provides tighter bounds compared to [17,Cor. 7], since we focus on the set of equilibria rather than on the entire feasibility set.…”

“…Now, let Ω δ be the set of equilibria induced by δ ∈ ∆. In the spirit of [17,Def. 4], we investigate the violation probability of the set of equilibria of a scenario-based GNEP, according to the definition given next.…”

“…a recent development of data-driven (or distribution-free) robust approaches, see, e.g., [15], [16], [17].…”

“…• Along the direction of [17], we focus on the entire set of equilibria, implicitly relaxing the assumption on the uniqueness of the equilibrium postulated in [16]; • We extend the results in [15], [17] providing a-posteriori robustness certificates for the set of GNE rather than for the feasible set or Nash equilibria without coupling constraints. We also show that the resulting bounds are less conservative ( §III); • The obtained probabilistic guarantees rely on the notion of support subsample, a key concept of the scenario approach theory.…”

Probabilistic feasibility guarantees for solution sets to uncertain variational inequalities

“…Remarkably, the family of VIs we consider is quite large, encompassing practical applications in several domains. Indeed, Nash equilibrium problems (NEPs) and generalized Nash equilibrium problems (GNEPs) can be modelled as VIs [18,17], whose popular robust version falls in the class investigated in this paper [1,19,36,16]. As a static assignment problem, an optimal network flow in traffic networks can also be computed via solution to an associated VI [37,Th.…”