An excellent Search Engine Watch thread named How To Get Out Of Bid Wars A Winner? This advertiser says that, "in position 1 we get a lot more clicks than in position 2 - about 50% drop and that is why we need to be on top."
Moderator David Wallace offers sage advice:
Yes, stop fighting that battle. Lay back for awhile and find other keywords that you can focus on that are not part of a bidding war. You may find that the person you are battling settles down as well, eventually lowering their bid and then you can start the whole crazy madness once again! In the meantime you may discover new keywords you have never thought of before that produce excellent ROI for you.
But what is interesting is that everyone agrees that with Yahoo! the "sweet spot" is position number two.
But what if you need to have the number one position. Moderator Haplo says:
Only way I know of to actually "win" a bidding war is to have the bigger budget (or cheat).
However, you can win *during* a bidding war simply through maintaining your profitability.
Don't know what your market is, but if the profit margin is similar between competitors -- immediately move to your upper limit so you get the most traffic you can while maintaining profitability. If competitors pay more to get higher in the results, then it's likely they won't be profitable and will eventually fall back to earth. If they have a "war chest" for this sort of thing, then it may take a while before they figure out they're spending too much for too little. As long as you're spending ad money on generating business, let your competitors spend their money on ranking #1.
The thread goes on discussing the various methods, check it out.