A Machine Learning Method for Stackelberg Mean Field Games
We propose a single-level numerical approach to solve Stackelberg mean field game (MFG) problems. In the Stackelberg MFG, an infinite population of agents plays a noncooperative game and chooses their controls to optimize their individual objectives while interacting with the principal and other age...
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| Published in | Mathematics of operations research |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
02.12.2024
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| Online Access | Get full text |
| ISSN | 0364-765X 1526-5471 |
| DOI | 10.1287/moor.2023.0065 |
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| Abstract | We propose a single-level numerical approach to solve Stackelberg mean field game (MFG) problems. In the Stackelberg MFG, an infinite population of agents plays a noncooperative game and chooses their controls to optimize their individual objectives while interacting with the principal and other agents through the population distribution. The principal can influence the mean field Nash equilibrium at the population level through policies, and she optimizes her own objective, which depends on the population distribution. This leads to a bilevel problem between the principal and mean field of agents that cannot be solved using traditional methods for MFGs. We propose a reformulation of this problem as a single-level mean field optimal control problem through a penalization approach. We prove convergence of the reformulated problem to the original problem. We propose a machine learning method based on (feed-forward and recurrent) neural networks and illustrate it on several examples from the literature. We also give a modified example to show the scalability of the proposed method and show its efficiency by comparing its performance with an alternative bilevel approach. |
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| AbstractList | We propose a single-level numerical approach to solve Stackelberg mean field game (MFG) problems. In the Stackelberg MFG, an infinite population of agents plays a noncooperative game and chooses their controls to optimize their individual objectives while interacting with the principal and other agents through the population distribution. The principal can influence the mean field Nash equilibrium at the population level through policies, and she optimizes her own objective, which depends on the population distribution. This leads to a bilevel problem between the principal and mean field of agents that cannot be solved using traditional methods for MFGs. We propose a reformulation of this problem as a single-level mean field optimal control problem through a penalization approach. We prove convergence of the reformulated problem to the original problem. We propose a machine learning method based on (feed-forward and recurrent) neural networks and illustrate it on several examples from the literature. We also give a modified example to show the scalability of the proposed method and show its efficiency by comparing its performance with an alternative bilevel approach. |
| Author | Laurière, Mathieu Dayanıklı, Gökçe |
| Author_xml | – sequence: 1 givenname: Gökçe orcidid: 0000-0002-4984-7574 surname: Dayanıklı fullname: Dayanıklı, Gökçe organization: Department of Statistics, University of Illinois at Urbana-Champaign, Champaign, Illinois 61820 – sequence: 2 givenname: Mathieu orcidid: 0000-0002-4380-1399 surname: Laurière fullname: Laurière, Mathieu organization: Shanghai Frontiers Science Center of Artificial Intelligence and Deep Learning, NYU-ECNU Institute of Mathematical Sciences, NYU Shanghai, Shanghai 200126, People’s Republic of China |
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