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SUMMARY:A variational approach to mean field games with control on the acc
 eleration - Megan Griffin-Pickering (Durham University)
DTSTART:20220222T133000Z
DTEND:20220222T141500Z
UID:TALK170138@talks.cam.ac.uk
DESCRIPTION:The theory of mean field games aims to describe the limits of 
 Nash equilibria for differential games as the number of players tends to i
 nfinity. If players control their state by choosing their acceleration\, t
 hen the mean field games system describing this equilibrium includes a kin
 etic transport term. Previous results on the well-posedness theory of mean
  field games of this type assume either that the running and final costs a
 re regularising functionals of the density variable\, or the presence of n
 oise - that is\, a second-order system. I will present recently obtained r
 esults in which we construct global-in-time weak solutions for a determini
 stic `kinetic&rsquo\; mean field game with local (hence non-regularising) 
 couplings\, under suitable convexity and monotonicity conditions. Our appr
 oach is based on a characterisation of the solutions through two optimisat
 ion problems in duality. Furthermore\, under stronger monotonicity/convexi
 ty assumptions\, we obtain Sobolev regularity estimates on the solutions. 
 This talk is based on joint work with Alp&aacute\;r M&eacute\;sz&aacute\;r
 os.
LOCATION:Seminar Room 2\, Newton Institute
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