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You searched for +publisher:"King Abdullah University of Science and Technology" +contributor:("Fusco, Nicola"). One record found.

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King Abdullah University of Science and Technology

1. Evangelista, David. Stationary Mean-Field Games with Congestion.

Degree: Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division, 2019, King Abdullah University of Science and Technology

Mean-field games (MFG) are models of large populations of rational agents who seek to optimize an objective function that takes into account their state variables and the distribution of the state variable of the remaining agents. MFG with congestion model problems where the agents’ motion is hampered in high-density regions. First, we study radial solutions for first- and second-order stationary MFG with congestion on Rd. The radial case, which is one of the simplest non one-dimensional MFG, is relatively tractable. As we observe, 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. For the first case, we use our approach to compute numerical approximations to the solutions of the corresponding MFG systems. Next, we consider second-order stationary MFG with congestion and prove the existence of stationary solutions. Because moving in congested areas is difficult, agents prefer to move in non-congested areas. As a consequence, the model becomes singular near the zero density. The existence of stationary solutions was previously obtained for MFG with quadratic Hamiltonians thanks to a very particular identity. Here, we develop robust estimates that give the existence of a solution for general subquadratic Hamiltonians. Additionally, we study first-order stationary MFG with congestion with quadratic or power-like Hamiltonians. Using explicit examples, we illustrate two key difficulties: the lack of classical solutions and the existence of areas with vanishing densities. Our main contribution is a new variational formulation for MFG with congestion. With this formulation, we prove the existence and uniqueness of solutions. Finally, we devise a discretization that is combined with optimization algorithms to numerically solve various MFG with congestion. Advisors/Committee Members: Gomes, Diogo A. (advisor), Tempone, Raul (committee member), Santamarina, Carlos (committee member), Fusco, Nicola (committee member).

Subjects/Keywords: mean-field games; congestion problems; stationary problems; calculus f variations

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Evangelista, D. (2019). Stationary Mean-Field Games with Congestion. (Thesis). King Abdullah University of Science and Technology. Retrieved from http://hdl.handle.net/10754/655679

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Evangelista, David. “Stationary Mean-Field Games with Congestion.” 2019. Thesis, King Abdullah University of Science and Technology. Accessed April 11, 2021. http://hdl.handle.net/10754/655679.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Evangelista, David. “Stationary Mean-Field Games with Congestion.” 2019. Web. 11 Apr 2021.

Vancouver:

Evangelista D. Stationary Mean-Field Games with Congestion. [Internet] [Thesis]. King Abdullah University of Science and Technology; 2019. [cited 2021 Apr 11]. Available from: http://hdl.handle.net/10754/655679.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Evangelista D. Stationary Mean-Field Games with Congestion. [Thesis]. King Abdullah University of Science and Technology; 2019. Available from: http://hdl.handle.net/10754/655679

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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