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 | |||||||||
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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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