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dc.contributor.advisorGomes, Diogo A.
dc.contributor.authorEvangelista, David
dc.date.accessioned2019-06-23T08:59:12Z
dc.date.available2019-06-23T08:59:12Z
dc.date.issued2019-06-23
dc.identifier.citationEvangelista, D. (2019). Stationary Mean-Field Games with Congestion. KAUST Research Repository. https://doi.org/10.25781/KAUST-79GH9
dc.identifier.doi10.25781/KAUST-79GH9
dc.identifier.urihttp://hdl.handle.net/10754/655679
dc.description.abstractMean-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.
dc.language.isoen
dc.subjectmean-field games
dc.subjectcongestion problems
dc.subjectstationary problems
dc.subjectcalculus f variations
dc.titleStationary Mean-Field Games with Congestion
dc.typeDissertation
dc.contributor.departmentComputer, Electrical and Mathematical Science and Engineering (CEMSE) Division
thesis.degree.grantorKing Abdullah University of Science and Technology
dc.contributor.committeememberTempone, Raul
dc.contributor.committeememberSantamarina, Carlos
dc.contributor.committeememberFusco, Nicola
thesis.degree.disciplineApplied Mathematics and Computational Science
thesis.degree.nameDoctor of Philosophy
refterms.dateFOA2019-06-23T08:59:13Z
kaust.request.doiyes


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