As each person pulls on the rope, the tension in the rope pulls back on the person. The pulling and the tension pulling back are a "third law action-reaction pair" and thus they must be equal and opposite., that is,the tension is equal to F.
from this, we can see that the second person is "useless" - the same tension can be achieved by having one person pull ont he rope after it has been attached to an immobile object. If twice F is required, then you need to place both people on the same end. It is easy to see that this would result in a tension of 2F.