On the Sampling-Based Computation of Nash Equilibria Under Uncertainty via the Nikaido–Isoda Function

Marrinan, L.; Shanbhag, U. V.; Yousefian, F.

doi:10.1007/s10013-025-00770-x

On the Sampling-Based Computation of Nash Equilibria Under Uncertainty via the Nikaido–Isoda Function

Journal Article · Wed Sep 17 00:00:00 EDT 2025 · Vietnam Journal of Mathematics

DOI:https://doi.org/10.1007/s10013-025-00770-x· OSTI ID:3009732

Marrinan, L. ^[1]; Shanbhag, U. V. ^[2]; Yousefian, F. ^[3]

Pennsylvania State University, Centre County, PA (United States)
University of Michigan, Ann Arbor, MI (United States)
Rutgers University, Piscataway, NJ (United States)

We consider the computation of an equilibrium of a stochastic Nash equilibrium problem, where the player objectives are assumed to be L₀-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 defined using 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-response method, reliant on inexact resolution of a player-level best-response subproblem. Here, by deriving suitable Lipschitzian guarantees on the value function, we derive both asymptotic guarantees for the sequence of generated iterates as well as rate and complexity guarantees for computing a stationary point by appropriate choices of the sampling rate and inexactness sequence.

View Accepted Manuscript (DOE)

Research Organization:: Pennsylvania State University, University Park, PA (United States); Rutgers University, Piscataway, NJ (United States); University of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: Air Force Office of Scientific Research (AFOSR); Office of Naval Research (ONR); USDOE

Grant/Contract Number:: SC0023303

OSTI ID:: 3009732

Report Number(s):: DOE-Rutgers--23303

Journal Information:: Vietnam Journal of Mathematics, Journal Name: Vietnam Journal of Mathematics Journal Issue: 4 Vol. 53; ISSN 2305-2228; ISSN 2305-221X

Publisher:: Springer Science and Business Media LLCCopyright Statement

Country of Publication:: United States

Language:: English

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Nikaido-Isoda function
Non-monotone games
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Stochastic approximation

On the Sampling-Based Computation of Nash Equilibria Under Uncertainty via the Nikaido–Isoda Function

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