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dc.contributor.authorGomes, Diogo A.
dc.contributor.authorNurbekyan, Levon
dc.contributor.authorSedjro, Marc
dc.date.accessioned2017-01-02T08:42:39Z
dc.date.available2017-01-02T08:42:39Z
dc.date.issued2016-11-01
dc.identifier.citationGomes DA, Nurbekyan L, Sedjro M (2016) One-Dimensional Forward–Forward Mean-Field Games. Applied Mathematics & Optimization 74: 619–642. Available: http://dx.doi.org/10.1007/s00245-016-9384-y.
dc.identifier.issn0095-4616
dc.identifier.issn1432-0606
dc.identifier.doi10.1007/s00245-016-9384-y
dc.identifier.urihttp://hdl.handle.net/10754/622228
dc.description.abstractWhile the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
dc.description.sponsorshipThe authors were supported by KAUST baseline and start-up funds.
dc.publisherSpringer Nature
dc.relation.urlhttp://link.springer.com/article/10.1007%2Fs00245-016-9384-y
dc.subjectMean-field games
dc.subjectSystems of conservation laws
dc.subjectConvergence to equilibrium
dc.subjectHamilton–Jacobi equations
dc.subjectTransport equations
dc.subjectFokker-Planck equation
dc.titleOne-Dimensional Forward–Forward Mean-Field Games
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalApplied Mathematics & Optimization
dc.identifier.arxividarXiv:1606.09064
kaust.personGomes, Diogo A.
kaust.personNurbekyan, Levon
kaust.personSedjro, Marc
dc.date.published-online2016-11-01
dc.date.published-print2016-12


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