| Abstract: |
| Mean field games (MFG) systems have been introduced to describe Nash
equilibria in differential games with infinitely many players. In some
simple cases, the model collapses into a system consisting on a
backward Hamilton-Jacobi equation coupled with a forward Fokker-Plank equation.
The starting point of the current study is that in some cases the MFG
system can be understood as the optimality system of two convex
optimization problems in duality. This leads to a variational analysis
strategy to study the well-posedness of the PDE system. Following this
methodology, we will discuss first the existence and uniqueness of
weak solutions of some possibly degenerated Mean Field Games and then the
existence of solutions of a modified problem prescribing the final
distribution of the agents. |
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