Strategic geometric graphs through mean field games
Résumé
We exploit the structure of geometric graphs on Riemannian manifolds to analyze strategic
dynamic graphs at the limit, when the number of nodes tends to infinity. This framework
allows to preserve intrinsic geometrical information about the limiting graph structure, such
as the Ollivier curvature. After introducing the setting, we derive a mean field game system,
which models a strategic equilibrium between the nodes. It has the usual structure with
the distinction of being set on a manifold. Finally, we establish existence and uniqueness
of solutions to the system when the Hamiltonian is quadratic for a class of non-necessarily
compact Riemannian manifolds, referred to as manifolds of bounded geometry.
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