{"ID":2849845,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.23851","arxiv_id":"2510.23851","title":"On the Sampling-based Computation of Nash Equilibria under Uncertainty via the Nikaido-Isoda Function","abstract":"We consider the computation of an equilibrium of a stochastic Nash equilibrium problem, where the player objectives are assumed to be $L_0$-Lipschitz continuous and convex given rival decisions with convex and closed player-specific feasibility sets. To address this problem, we consider minimizing a suitably defined value function associated with the Nikaido-Isoda function. Such an avenue does not necessitate either monotonicity properties of the concatenated gradient map or potentiality requirements on the game but does require a suitable regularity requirement under which a stationary point is a Nash equilibrium. We design and analyze a sampling-enabled projected gradient descent-type method, reliant on inexact resolution of a player-level best-response subproblem. By deriving suitable Lipschitzian guarantees on the value function, we derive both asymptotic guarantees for the sequence of iterates as well as rate and complexity guarantees for computing a stationary point by appropriate choices of the sampling rate and inexactness sequence.","short_abstract":"We consider the computation of an equilibrium of a stochastic Nash equilibrium problem, where the player objectives are assumed to be $L_0$-Lipschitz continuous and convex given rival decisions with convex and closed player-specific feasibility sets. To address this problem, we consider minimizing a suitably defined va...","url_abs":"https://arxiv.org/abs/2510.23851","url_pdf":"https://arxiv.org/pdf/2510.23851v1","authors":"[\"Luke Marrinan\",\"Farzad Yousefian\",\"Uday V. Shanbhag\"]","published":"2025-10-27T20:48:04Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}