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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A variational approach to mean field games with co
ntrol on the acceleration - Megan Griffin-Pickerin
g (Durham University)
DTSTART;TZID=Europe/London:20220222T133000
DTEND;TZID=Europe/London:20220222T141500
UID:TALK170138AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/170138
DESCRIPTION:The theory of mean field games aims to describe th
e limits of Nash equilibria for differential games
as the number of players tends to infinity. If pl
ayers control their state by choosing their accele
ration\, then the mean field games system describi
ng this equilibrium includes a kinetic transport t
erm. Previous results on the well-posedness theory
of mean field games of this type assume either th
at the running and final costs are regularising fu
nctionals of the density variable\, or the presenc
e of noise - that is\, a second-order system. I wi
ll present recently obtained results in which we c
onstruct global-in-time weak solutions for a deter
ministic `kinetic&rsquo\; mean field game with loc
al (hence non-regularising) couplings\, under suit
able convexity and monotonicity conditions. Our ap
proach is based on a characterisation of the solut
ions through two optimisation problems in duality.
Furthermore\, under stronger monotonicity/convexi
ty assumptions\, we obtain Sobolev regularity esti
mates on the solutions. This talk is based on join
t work with Alpá\;r Mé\;szá\;ros
.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:
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