# On the Characterization of Local Nash Equilibria in Continuous Games

arXiv: https://arxiv.org/abs/1411.2168 · HTML: https://mlsanity.com/paper/1411.2168/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Nov 2014.

## Built on by (most cited first, 22 of 22)

- [Faster Single-loop Algorithms for Minimax Optimization without Strong Concavity](https://mlsanity.com/paper/2112.05604/) (2021)
- [Multiplayer Performative Prediction: Learning in Decision-Dependent Games](https://mlsanity.com/paper/2201.03398/) (2022)
- [Modeling Content Creator Incentives on Algorithm-Curated Platforms](https://mlsanity.com/paper/2206.13102/) (2022)
- [A unified stochastic approximation framework for learning in games](https://mlsanity.com/paper/2206.03922/) (2022)
- [Neuro-Symbolic Causal Reasoning Meets Signaling Game for Emergent Semantic Communications](https://mlsanity.com/paper/2210.12040/) (2022)
- [On the convergence of policy gradient methods to Nash equilibria in general stochastic games](https://mlsanity.com/paper/2210.08857/) (2022)
- [Minimax Optimization with Smooth Algorithmic Adversaries](https://mlsanity.com/paper/2106.01488/) (2021)
- [Zero-shot Meta-learning for Tabular Prediction Tasks with Adversarially Pre-trained Transformer](https://mlsanity.com/paper/2502.04573/) (2025)
- [Domain Adversarial Training: A Game Perspective](https://mlsanity.com/paper/2202.05352/) (2022)
- [For Learning in Symmetric Teams, Local Optima are Global Nash Equilibria](https://mlsanity.com/paper/2207.03470/) (2022)
- [Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Games](https://mlsanity.com/paper/2505.19537/) (2025)
- [Riemannian stochastic approximation algorithms](https://mlsanity.com/paper/2206.06795/) (2022)
- [Robust Forecasting for Robotic Control: A Game-Theoretic Approach](https://mlsanity.com/paper/2209.10802/) (2022)
- [Human adaptation to adaptive machines converges to game-theoretic equilibria](https://mlsanity.com/paper/2305.01124/) (2023)
- [A Robust Adversary Detection-Deactivation Method for Metaverse-oriented Collaborative Deep Learning](https://mlsanity.com/paper/2401.01895/) (2023)
- [A Framework for Finding Local Saddle Points in Two-Player Zero-Sum Black-Box Games](https://mlsanity.com/paper/2503.18224/) (2025)
- [Generative Adversarial Networks with Limited Data: A Survey and Benchmarking](https://mlsanity.com/paper/2504.05456/) (2025)
- [Uncoupled Learning of Differential Stackelberg Equilibria with Commitments](https://mlsanity.com/paper/2302.03438/) (2023)
- [Adversarial Reinforcement Learning Framework for ESP Cheater Simulation](https://mlsanity.com/paper/2509.24274/) (2025)
- [LLM-Empowered Agentic MAC Protocols: A Dynamic Stackelberg Game Approach](https://mlsanity.com/paper/2510.10895/) (2025)
- [Learning Coordinated Preference for Multi-Objective Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2606.14693/) (2026)
- [Cordial Learning: Distributed Training with Correlated Data](https://mlsanity.com/paper/2610.03330/) (2026)

## Abstract (arXiv)

We present a unified framework for characterizing local Nash equilibria in continuous games on either infinite-dimensional or finite-dimensional non-convex strategy spaces. We provide intrinsic necessary and sufficient first- and second-order conditions ensuring strategies constitute local Nash equilibria. We term points satisfying the sufficient conditions differential Nash equilibria. Further, we provide a sufficient condition (non-degeneracy) guaranteeing differential Nash equilibria are isolated and show that such equilibria are structurally stable. We present tutorial examples to illustrate our results and highlight degeneracies that can arise in continuous games.