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arXiv · 2510.23851

On the Sampling-based Computation of Nash Equilibria under Uncertainty via the Nikaido-Isoda Function

Luke Marrinan·Farzad Yousefian·Uday V. Shanbhag
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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.

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Luke Marrinan, Farzad Yousefian, Uday V. Shanbhag. 2025-10-27. On the Sampling-based Computation of Nash Equilibria under Uncertainty via the Nikaido-Isoda Function. https://arxiv.org/abs/2510.23851

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