Is there a way to tell who you're bidding against for a FA? If I know I'm bidding against a division rival, I may stay in the bidding longer and spend more, because it's like a win-win or a lose-lose, since if you either keep him from your rival or have to face him.
In real life, it doesn't always happen, but you usually hear about the biggest players for a FA and teams generally know who they're bidding against.