Why? Do you really consider it worth $100 to you just to prevent someone else from getting $9900, or do you just value $100 so little that you are willing to round it down to $0?
I can imagine real-world scenarios in which I might spend $100 worth of my time to try to address a problem, especially if I think that problem might affect others. (Scenarios involving an actual $100 seem even less likely, but plausible for a sufficiently egregious wrong.)
However, as a game, I'd call it free money no matter the amount; neither player did anything in particular to earn the money other than taking their time to play the game, and I don't see it as even slightly unfair of the first player to offer less money to the second, so I don't see any value in "punishing" the first player. The first player happened to get the better opportunity, and the second player gets to choose between having something or having nothing. In the game version, I'd place zero value on how much the first player gets.
Now, if I thought I could bluff the first player via advance communication into believing that I'd reject the offer if less than a certain amount, I'd certainly do it; however, if they called the bluff, I'll take what I can get.