Abstract: In this talk, we discuss the role of boundary conditions in first-order MFGS. First, we review prior results on the existence of a solution to the Dirichlet problem. Next, looking at one-dimensional examples, we examine the motivation for Dirichlet-Neumann type boundary conditions. Finally, we examine the role of monotonicity and variational techniques on the uniqueness, existence of solutions, and on the construction of numerical methods.