I agree that it shouldn't be possible to figure out exactly how much budget space everyone has left, but at least in my case (as one of the two other bidders) that wasn't what happened.
I still had a few million left that I could have used to go higher, but once the bidding got to that level, I also came to the conclusion that he was being overpaid. I figured it was better to transfer money out of my prospect budget so that I could offer a max contract to my #1 choice (who's also being overpaid) than to go higher on my #4 choice.