This paper provides an existence result for solutions to fully coupled Forward Backward Stochastic Differential Equations (FBSDEs) of mean field type, which are crucial in the study of mean field games and the optimal control of McKean-Vlasov dynamics. The authors assume that the coefficients of the FBSDEs satisfy certain Lipschitz and boundedness conditions, and use Schauder's fixed point theorem to prove the existence of a solution. The proof involves transforming the FBSDE into a well-posed fixed point problem and showing that the solution map is continuous. The paper also discusses a counterexample to uniqueness and provides applications to mean-field games and the optimal control of McKean-Vlasov dynamics.This paper provides an existence result for solutions to fully coupled Forward Backward Stochastic Differential Equations (FBSDEs) of mean field type, which are crucial in the study of mean field games and the optimal control of McKean-Vlasov dynamics. The authors assume that the coefficients of the FBSDEs satisfy certain Lipschitz and boundedness conditions, and use Schauder's fixed point theorem to prove the existence of a solution. The proof involves transforming the FBSDE into a well-posed fixed point problem and showing that the solution map is continuous. The paper also discusses a counterexample to uniqueness and provides applications to mean-field games and the optimal control of McKean-Vlasov dynamics.