Generic Properties of First-Order Mean Field Games

We consider a class of deterministic mean field games, where the state associated with each player evolves according to an ODE which is linear w.r.t. control. Existence, uniqueness, and stability solutions are studied from point view generic theory. Within suitable topological space dynamics cost functionals, we prove that, for “nearly all” games (in Baire category sense) best reply map single-valued a.e. player. As consequence, game admits strong (not randomized) solution. Examples given open sets admitting single solution, other multiple solutions. Further examples show existence set MFG having unique solution asymptotically stable map, another unstable. conclude example terminal constraints does not have any even in mild sense randomized strategies.