mlsanityData to 7 Oct 2026

On the Characterization of Local Nash Equilibria in Continuous Games

arXiv 1411.2168 ↗First posted 8 Nov 2014math.OCcited by 21

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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.

Key facts. Cited by 21 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Nov 2014.

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Citing papers per year: 2021: 2; 2022: 9; 2023: 3; 2024: 0; 2025: 6; 2026: 1.

21 papers.

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  1. 2021Faster Single-loop Algorithms for Minimax Optimization without Strong Concavitycited by 47
  2. 2022Multiplayer Performative Prediction: Learning in Decision-Dependent Gamescited by 42
  3. 2022Modeling Content Creator Incentives on Algorithm-Curated Platformscited by 35
  4. 2022A unified stochastic approximation framework for learning in gamescited by 22
  5. 2022Neuro-Symbolic Causal Reasoning Meets Signaling Game for Emergent Semantic Communicationscited by 20
  6. 2022On the convergence of policy gradient methods to Nash equilibria in general stochastic gamescited by 13
  7. 2021Minimax Optimization with Smooth Algorithmic Adversariescited by 8
  8. 2025Zero-shot Meta-learning for Tabular Prediction Tasks with Adversarially Pre-trained Transformercited by 8
  9. 2022Domain Adversarial Training: A Game Perspectivecited by 7
  10. 2022For Learning in Symmetric Teams, Local Optima are Global Nash Equilibriacited by 6
  11. 2025Continuous-Time Analysis of Heavy Ball Momentum in Min-Max Gamescited by 3
  12. 2022Riemannian stochastic approximation algorithmscited by 2
9 more
  1. 2022Robust Forecasting for Robotic Control: A Game-Theoretic Approachcited by 2
  2. 2023Human adaptation to adaptive machines converges to game-theoretic equilibriacited by 2
  3. 2023A Robust Adversary Detection-Deactivation Method for Metaverse-oriented Collaborative Deep Learningcited by 1
  4. 2025A Framework for Finding Local Saddle Points in Two-Player Zero-Sum Black-Box Gamescited by 1
  5. 2025Generative Adversarial Networks with Limited Data: A Survey and Benchmarkingcited by 1
  6. 2023Uncoupled Learning of Differential Stackelberg Equilibria with Commitmentscited by 0
  7. 2025Adversarial Reinforcement Learning Framework for ESP Cheater Simulationcited by 0
  8. 2025LLM-Empowered Agentic MAC Protocols: A Dynamic Stackelberg Game Approachcited by 0
  9. 2026Learning Coordinated Preference for Multi-Objective Multi-Agent Reinforcement Learningcited by 0