Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917686025388032 |
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| author | Zhou, Fuzhong Zhang, Chenyu Chen, Xu Di, Xuan |
| author_facet | Zhou, Fuzhong Zhang, Chenyu Chen, Xu Di, Xuan |
| contents | We propose a discrete time graphon game formulation on continuous state and action spaces using a representative player to study stochastic games with heterogeneous interaction among agents. This formulation admits both philosophical and mathematical advantages, compared to a widely adopted formulation using a continuum of players. We prove the existence and uniqueness of the graphon equilibrium with mild assumptions, and show that this equilibrium can be used to construct an approximate solution for finite player game on networks, which is challenging to analyze and solve due to curse of dimensionality. An online oracle-free learning algorithm is developed to solve the equilibrium numerically, and sample complexity analysis is provided for its convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_08005 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm Zhou, Fuzhong Zhang, Chenyu Chen, Xu Di, Xuan Optimization and Control Artificial Intelligence Computer Science and Game Theory Machine Learning We propose a discrete time graphon game formulation on continuous state and action spaces using a representative player to study stochastic games with heterogeneous interaction among agents. This formulation admits both philosophical and mathematical advantages, compared to a widely adopted formulation using a continuum of players. We prove the existence and uniqueness of the graphon equilibrium with mild assumptions, and show that this equilibrium can be used to construct an approximate solution for finite player game on networks, which is challenging to analyze and solve due to curse of dimensionality. An online oracle-free learning algorithm is developed to solve the equilibrium numerically, and sample complexity analysis is provided for its convergence. |
| title | Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm |
| topic | Optimization and Control Artificial Intelligence Computer Science and Game Theory Machine Learning |
| url | https://arxiv.org/abs/2405.08005 |