# A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis

arXiv: https://arxiv.org/abs/1712.08277 · HTML: https://mlsanity.com/paper/1712.08277/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2017.

## Built on by (most cited first, 9 of 9)

- [Asymptotic Convergence and Performance of Multi-Agent Q-Learning Dynamics](https://mlsanity.com/paper/2301.09619/) (2023)
- [Communication-Efficient Gradient Descent-Accent Methods for Distributed Variational Inequalities: Unified Analysis and Local Updates](https://mlsanity.com/paper/2306.05100/) (2023)
- [Learning to Control Unknown Strongly Monotone Games](https://mlsanity.com/paper/2407.00575/) (2024)
- [Learning Variational Inequalities from Data: Fast Generalization Rates under Strong Monotonicity](https://mlsanity.com/paper/2410.20649/) (2024)
- [Convergence and Connectivity: Dynamics of Multi-Agent Q-Learning in Random Networks](https://mlsanity.com/paper/2503.10186/) (2025)
- [Optimization-Informed Neural Networks](https://mlsanity.com/paper/2210.02113/) (2022)
- [Stability of Multi-Agent Learning: Convergence in Network Games with Many Players](https://mlsanity.com/paper/2307.13922/) (2023)
- [Diffusion Stochastic Learning Over Adaptive Competing Networks](https://mlsanity.com/paper/2504.19635/) (2025)
- [Equilibrium Causal Games: Separation, Identification, and the Identifiability of Cyclic Latent States](https://mlsanity.com/paper/2607.19531/) (2026)

## Abstract (arXiv)

We provide a unified variational inequality framework for the study of fundamental properties of the Nash equilibrium in network games. We identify several conditions on the underlying network (in terms of spectral norm, infinity norm and minimum eigenvalue of its adjacency matrix) that guarantee existence, uniqueness, convergence and continuity of equilibrium in general network games with multidimensional and possibly constrained strategy sets. We delineate the relations between these conditions and characterize classes of networks that satisfy each of these conditions.