Right, I understand why you want to make it a function. But as I see it your practical options are, 1) make a gross generalization from insufficient data that might have no relation to the function of information to power in the future and hope that you get close enough to reality that your model has at least some accuracy in its predictions OR 2) come up with 4-5 plausible but as-different-as-possible functions relating information to power and model with each of them. The result 4-5 times more predictions to sort through and instead of conclusions like "Starting conditions x,y,z, lead to a singleton" you'll get conclusions like "Starting conditions x,y,z, given assumptions a,b,c about the relation of information to power, lead to a singleton." The second option is harder and less conclusive. But it is also less wrong.

One more thing about the offense/defense distinction. One implication of the theory is that technological advancement can actually undermine an agents position in a multi-polar system. If Agent A develops an offensive weapon that guarantees victory if Agent A strikes first then other agents are basically forced to attack preemptively and likely gang up on Agent A. Given this particular input of more information, the function of information to power seems to output less power.