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Local Nash Equilibria are Isolated, Strict Local Nash Equilibria in ‘Almost All’ Zero-Sum Continuous Games

Mazumdar, Eric and Ratliff, Lillian J. (2019) Local Nash Equilibria are Isolated, Strict Local Nash Equilibria in ‘Almost All’ Zero-Sum Continuous Games. In: 2019 IEEE 58th Conference on Decision and Control (CDC). IEEE , Piscataway, NJ, pp. 6899-6904. ISBN 978-1-7281-1398-2. https://resolver.caltech.edu/CaltechAUTHORS:20210903-222215800

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Abstract

We prove that differential Nash equilibria are generic amongst local Nash equilibria in continuous zero-sum games. That is, there exists an open-dense subset of zero-sum games for which local Nash equilibria are nondegenerate differential Nash equilibria. The result extends previous results to the zero-sum setting, where we obtain even stronger results; in particular, we show that local Nash equilibria are generically hyperbolic critical points. We further show that differential Nash equilibria of zero-sum games are structurally stable. The purpose for presenting these extensions is the recent renewed interest in zero-sum games within machine learning and optimization. Adversarial learning and generative adversarial network approaches are touted to be more robust than the alternative. Zero-sum games are at the heart of such approaches. Many works proceed under the assumption of hyperbolicity of critical points. Our results justify this assumption by showing `almost all' zero-sum games admit local Nash equilibria that are hyperbolic.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/cdc40024.2019.9030203DOIArticle
https://arxiv.org/abs/2002.01007arXivDiscussion Paper
ORCID:
AuthorORCID
Mazumdar, Eric0000-0002-1815-269X
Ratliff, Lillian J.0000-0001-8936-0229
Additional Information:© 2019 IEEE.
DOI:10.1109/CDC40024.2019.9030203
Record Number:CaltechAUTHORS:20210903-222215800
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210903-222215800
Official Citation:E. Mazumdar and L. J. Ratliff, "Local Nash Equilibria are Isolated, Strict Local Nash Equilibria in ‘Almost All’ Zero-Sum Continuous Games," 2019 IEEE 58th Conference on Decision and Control (CDC), 2019, pp. 6899-6904, doi: 10.1109/CDC40024.2019.9030203
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:110736
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:07 Sep 2021 15:58
Last Modified:07 Sep 2021 19:38

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