Characterization and computation of local Nash equilibria in continuous games
Abstract
We present derivative-based necessary and sufficient conditions ensuring player strategies constitute local Nash equilibria in non-cooperative continuous games. Our results can be interpreted as generalizations of analogous second-order conditions for local optimality from nonlinear programming and optimal control theory. Drawing on this analogy, we propose an iterative steepest descent algorithm for numerical approximation of local Nash equilibria and provide a sufficient condition ensuring local convergence of the algorithm. We demonstrate our analytical and computational techniques by computing local Nash equilibria in games played on a finite-dimensional differentiable manifold or an infinite-dimensional Hilbert space.
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The goal of GAN optimization is to achieve Nash equilibrium.
“Namely, the goal of GAN optimization is to achieve Nash equilibrium [192].”
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- Authors
- Ratliff, L. J., Burden, S. A., & Sastry, S. S.
- Affiliations
- University of California, Berkeley (US)
- Venue
- 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- Publisher
- IEEE
- Published
- 2013-10
- Pages
- 917-924
- OpenAlex
- W2085963752
- Cited by
- 223
- References
- 24
- Citations by year
- 2026: 7 · 2025: 21 · 2024: 26 · 2023: 30 · 2022: 26 · 2021: 24 · 2020: 37 · 2019: 22 · 2018: 15 · 2017: 4 · 2016: 4 · 2015: 4 · 2014: 3
- FWCI
- 6.20
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- Allerton Conference on Communication, Control, and Computing (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Game Theory and Applications
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Optimization and Variational Analysis
- Social Sciences › Sociology and Political Science › Evolutionary Game Theory and Cooperation
- Keywords
- non-cooperative game, continuous games, second-order optimality conditions, gradient descent, local convergence, smooth manifolds, Hilbert spaces, optimal control
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