Before revision:  The controlled dynamics under the Nash Equilibrium is derived via solving a system of free boundary problems where the boundary is "moving" in the sense that it depends on both the state of the players and the control strategies of other players.
After revision:  The controlled dynamics under the Nash Equilibrium is derived via solving a system of free boundary problems where the boundary is "moving" in the sense that it depends on both the changes of the system and the control strategies of other players.