Answer
The team that pushes hardest on the ground wins.
Work Step by Step
If team A pulls to the right on the rope, exerting a force on team B, Newton's third law shows that the rope exerts an equal and opposite force on team A, pulling them to the left.
The winning team pushes harder against the ground. By Newton's third law, the ground pushes harder on them, producing a net force away from the other team, and resulting in victory!
This is shown on page 81.