Nash equilibrium seeking for a class of quadratic-bilinear Wasserstein distributionally robust games
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909692955983872 |
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| author | Pantazis, Georgios Baghbadorani, Reza Rahimi Grammatico, Sergio |
| author_facet | Pantazis, Georgios Baghbadorani, Reza Rahimi Grammatico, Sergio |
| contents | We consider a class of Wasserstein distributionally robust Nash equilibrium problems, where agents construct heterogeneous data-driven Wasserstein ambiguity sets using private samples and radii, in line with their individual risk-averse behaviour. By leveraging relevant properties of this class of games, we show that equilibria of the original seemingly infinite-dimensional problem can be obtained as a solution to a finite-dimensional Nash equilibrium problem. We then reformulate the problem as a finite-dimensional variational inequality and establish the connection between the corresponding solution sets. Our reformulation has scalable behaviour with respect to the data size and maintains a fixed number of constraints, independently of the number of samples. To compute a solution, we leverage two algorithms, based on the golden ratio algorithm. The efficiency of both algorithmic schemes is corroborated through extensive simulation studies on an illustrative example and a stochastic portfolio allocation game, where behavioural coupling among investors is modeled. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_09636 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nash equilibrium seeking for a class of quadratic-bilinear Wasserstein distributionally robust games Pantazis, Georgios Baghbadorani, Reza Rahimi Grammatico, Sergio Optimization and Control Multiagent Systems Systems and Control We consider a class of Wasserstein distributionally robust Nash equilibrium problems, where agents construct heterogeneous data-driven Wasserstein ambiguity sets using private samples and radii, in line with their individual risk-averse behaviour. By leveraging relevant properties of this class of games, we show that equilibria of the original seemingly infinite-dimensional problem can be obtained as a solution to a finite-dimensional Nash equilibrium problem. We then reformulate the problem as a finite-dimensional variational inequality and establish the connection between the corresponding solution sets. Our reformulation has scalable behaviour with respect to the data size and maintains a fixed number of constraints, independently of the number of samples. To compute a solution, we leverage two algorithms, based on the golden ratio algorithm. The efficiency of both algorithmic schemes is corroborated through extensive simulation studies on an illustrative example and a stochastic portfolio allocation game, where behavioural coupling among investors is modeled. |
| title | Nash equilibrium seeking for a class of quadratic-bilinear Wasserstein distributionally robust games |
| topic | Optimization and Control Multiagent Systems Systems and Control |
| url | https://arxiv.org/abs/2411.09636 |