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CATEGORIES:Partial Differential Equations seminar
SUMMARY:Variational Mean Field Games - Filippo Santambrogi
o (Université Paris Sud)
DTSTART;TZID=Europe/London:20170403T150000
DTEND;TZID=Europe/London:20170403T160000
UID:TALK69625AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/69625
DESCRIPTION:I will give a brief introduction to the the emergi
ng topic of Mean Field Games\, introduced some yea
rs ago (by two groups at the same time: Huang\, Ma
lhamé and Caines\, but also Lasry and Lions\, who
then devoted 6 subsequent editions of his course a
t Collège de France to its mathematical analysis)
as a model for the equilibrium of a population of
agents each selecting his own optimal paths\, acco
rding to a criterion which involves the density of
the other agents\, in the form of a congestion co
st. This gives rise to a coupled system of PDEs\,
a continuity equation where the density moves acco
rding to the gradient of a value function\, and a
Hamilton-Jacobi equation solved by the value funct
ion\, where the density also appears.\nI will main
ly deal with the case where this equilibrium probl
em may be seen as optimality conditions of a conve
x variational problem\, and give the main results
in this framework. In particular\, I will present
some easy but recent regularity results\, as well
as the connection with optimal transport theory. T
hese results are also needed to make rigorous the
connection between optimality and equilibrium and
allow for an interesting extension where instead o
f penalizing higher densities we insert a density
constraint.\nGlobally\, the talk will be based on
papers in collaborations with P. Cardaliaguet\, A.
Mészáros\, J.-D. Benamou\, G. Carlier\, A. Prosin
ski and H. Lavenant.
LOCATION:CMS\, MR13
CONTACT:Mikaela Iacobelli
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