  In this note, we extend some recent results on systems of backward stochastic
differential equations (BSDEs) with quadratic growth to the case of coupled
forward-backward stochastic differential equations (FBSDEs). We work in a
Markovian setting, and use results from the quadratic BSDE literature together
with PDE techniques to obtain a-priori estimates which lead to an existence
result. We also identify a general class of stochastic differential games whose
corresponding FBSDE systems are covered by our main existence result. This
leads to the existence of Markovian Nash equilibria for such games.
