If two group in the game are exirting equal ad opposite force the rope, will the rope move?

No.

Explanation:

If the forces are acting on opposite direction, they will cancel out each other. As a result, the object will not move. This type of force is called balanced force. In this type of force the net force acting on an object is equal to 0. Hence, if two groups in the game are exerting equal and opposite force, the rope will not move.