Radially symmetric mean-field games with congestion

David Evangelista; Diogo A. Gomes; Levon Nurbekyan

doi:10.1109/CDC.2017.8264121

Radially symmetric mean-field games with congestion

David Evangelista, Diogo A. Gomes, Levon Nurbekyan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

Here, we study radial solutions for first-and second-order stationary Mean-Field Games (MFG) with congestion on R^d. MFGs with congestion model problems where the agents' motion is hampered in high-density regions. The radial case, which is one of the simplest non one-dimensional MFG, is relatively tractable. As we observe in this paper, the Fokker-Planck equation is integrable with respect to one of the unknowns. Consequently, we obtain a single equation substituting this solution into the Hamilton-Jacobi equation. For the first-order case, we derive explicit formulas; for the elliptic case, we study a variational formulation of the resulting equation. In both cases, we use our approach to compute numerical approximations to the solutions of the corresponding MFG systems.

Original language	English (US)
Title of host publication	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3158-3163
Number of pages	6
ISBN (Electronic)	9781509028733
DOIs	https://doi.org/10.1109/CDC.2017.8264121
State	Published - Jun 28 2017
Event	56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia Duration: Dec 12 2017 → Dec 15 2017

Publication series

Name	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume	2018-January

Conference

Conference	56th IEEE Annual Conference on Decision and Control, CDC 2017
Country/Territory	Australia
City	Melbourne
Period	12/12/17 → 12/15/17

ASJC Scopus subject areas

Decision Sciences (miscellaneous)
Industrial and Manufacturing Engineering
Control and Optimization

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10.1109/CDC.2017.8264121

Cite this

Evangelista, D., Gomes, D. A., & Nurbekyan, L. (2017). Radially symmetric mean-field games with congestion. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (pp. 3158-3163). (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2017.8264121

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title = "Radially symmetric mean-field games with congestion",

abstract = "Here, we study radial solutions for first-and second-order stationary Mean-Field Games (MFG) with congestion on Rd. MFGs with congestion model problems where the agents' motion is hampered in high-density regions. The radial case, which is one of the simplest non one-dimensional MFG, is relatively tractable. As we observe in this paper, the Fokker-Planck equation is integrable with respect to one of the unknowns. Consequently, we obtain a single equation substituting this solution into the Hamilton-Jacobi equation. For the first-order case, we derive explicit formulas; for the elliptic case, we study a variational formulation of the resulting equation. In both cases, we use our approach to compute numerical approximations to the solutions of the corresponding MFG systems.",

author = "David Evangelista and Gomes, {Diogo A.} and Levon Nurbekyan",

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year = "2017",

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doi = "10.1109/CDC.2017.8264121",

language = "English (US)",

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Evangelista, D, Gomes, DA & Nurbekyan, L 2017, Radially symmetric mean-field games with congestion. in 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, vol. 2018-January, Institute of Electrical and Electronics Engineers Inc., pp. 3158-3163, 56th IEEE Annual Conference on Decision and Control, CDC 2017, Melbourne, Australia, 12/12/17. https://doi.org/10.1109/CDC.2017.8264121

Radially symmetric mean-field games with congestion. / Evangelista, David; Gomes, Diogo A.; Nurbekyan, Levon.
2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 3158-3163 (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - Here, we study radial solutions for first-and second-order stationary Mean-Field Games (MFG) with congestion on Rd. MFGs with congestion model problems where the agents' motion is hampered in high-density regions. The radial case, which is one of the simplest non one-dimensional MFG, is relatively tractable. As we observe in this paper, the Fokker-Planck equation is integrable with respect to one of the unknowns. Consequently, we obtain a single equation substituting this solution into the Hamilton-Jacobi equation. For the first-order case, we derive explicit formulas; for the elliptic case, we study a variational formulation of the resulting equation. In both cases, we use our approach to compute numerical approximations to the solutions of the corresponding MFG systems.

AB - Here, we study radial solutions for first-and second-order stationary Mean-Field Games (MFG) with congestion on Rd. MFGs with congestion model problems where the agents' motion is hampered in high-density regions. The radial case, which is one of the simplest non one-dimensional MFG, is relatively tractable. As we observe in this paper, the Fokker-Planck equation is integrable with respect to one of the unknowns. Consequently, we obtain a single equation substituting this solution into the Hamilton-Jacobi equation. For the first-order case, we derive explicit formulas; for the elliptic case, we study a variational formulation of the resulting equation. In both cases, we use our approach to compute numerical approximations to the solutions of the corresponding MFG systems.

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Radially symmetric mean-field games with congestion

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