Using drip extraction, how much caffeine is extracted from coffee as a function of the amount of water used? When using a drip coffee maker, there are basically two choices we make: the amount of water and the amount of coffee grounds.

If we use the same amount of coffee grounds but double the water, how much extra caffeine is in the resulting brew? Does all the available caffeine in the grounds get quickly liberated, so that there's not much of a difference between brewing with more water and diluting the brew with water afterwards? Or is it closer to the other extreme, where twice the water means twice the caffeine?

I saw on wikipedia that only about 20% of the caffeine is extracted for an 'optimal brew,' but I wasn't sure if that means we can extrapolate and say that the remaining 80% can be extracted just as easily.

I have the same question about the amount of coffee grounds. I only care to consider the 'normal brewing regime', that is with water at ~80-90C, 3-6 cups of water, and 1/4-1/2 a cup of grounds.

Thanks!
Caffeine has a solubility in water of 20% at 80 $^\circ$C, while the coffee has between 1 and 4% caffeine. 
That means that you have more than enough water to extract all the caffeine in the coffee. 
With the quantities you have given, I estimate that you are using from 12 to 24 mL of water per gram of coffee (bulk density 0.25 g/mL). 

So, it is not very likely that a change in volume will affect the total quantity of extracted caffeine much. Only the concentration per unit volume will be lower if more water is used. 
But then, solid-liquid extraction is not that perfect and possibly you will extract some more caffeine with more water. The main property that influences the extraction is the size of the milled coffee. The smaller the better is the extraction. 

Many other components of coffee are extracted fairly fast. 
Therefore, here we do a percolation (expresso) which extracts everything with very less water. The concentration of caffeine per unit volume seems to be higher, but the dose of coffee is much smaller.