Before revision:  It establishes the existence of the solution when controls are of bounded velocity, solves explicitly the game when controls are of finite variation, and presents sensitivity analysis to compare the single-player game with the MFG . Our analysis shows that MFGs, when appropriately formulated, can demonstrate genuine gameeffects even without heterogeneity among players and additional common noise\left({\sqrt N}}\right) .
After revision:  It establishes the existence of the solution when controls are of bounded velocity, solves explicitly the game when controls are of finite variation, and presents sensitivity analysis to compare the single-player game with the MFG . Our analysis shows that MFGs, when appropriately formulated, can demonstrate genuine gameeffects even without heterogeneity among players and additional common noise\left(\frac{1{\sqrt N}}\right) .