Seminario di Analisi e Probabilità all'Università di Padova
Martedì 29 ottobre 2019 alle ore 14:30 in aula seminario 430 del
Dipartimento di Matematica (via Trieste, 63, 35121 Padova)
Alekos Cecchin (Université de Nice Sophia-Antipolis, France)
terrà un seminario dal titolo
"Selection by vanishing common noise for potential finite state mean
field games"
Abstract:
By adding a suitable Wright-Fisher common noise in the dynamics of the
law, uniqueness is restored for finite state mean field games, for any
shape of the costs. We then focus on a class of mean field games in
which the costs admit a potential in the simplex of probability
measures. Firstly, by modifying the cost in the mean field game, we show
that the unique solution of the randomized mean field game is equal to
the unique minimizer of a suitable stochastic control problem stated in
the simplex, called potential randomized game. Thus we study the limit
as the intensity of the common noise vanishes. On the one hand, the
optimal trajectories converge to the mean field game solutions which are
minimizers of the corresponding potential game (not randomized), that is
a deterministic optimal control problem in the simplex. On the other
hand, the classical solution to the second order master equation
converges to the gradient of the value function of the related potential
game; we select a particular weak solution, in the sense of
distributions, of the master equation, which can be written as
multidimensional system of hyperbolic PDEs stated in the simplex.
Lastly, we establish uniqueness of such solution in a suitable class.
Joint work with Francois Delarue.
Tutti gli interessati sono invitati a partecipare.
Gli organizzatori
Martino Bardi, Claudio Marchi, Markus Fischer