Bidding War
  
Two or more people who really want to buy the same thing, shamelessly raising their offers. That's a bidding war.
This can happen in an auction setting. Imagine two people furiously waving their paddles in the air, trying to secure a rare painting or a discontinued bottle of wine. "Do I hear one million...a million...do I hear two million...five million...ten million!"
Bidding wars often break out in hot real estate markets as well.
In a corporate setting, a bidding war can break out for an acquisition. Two pharma giants get interested in a smaller drug developer who just figured out the next best cure for baldness. They keep upping their offer to shareholders, usually until one finally reaches the end of its financial rope.
A bidding war almost always ends with someone overpaying for the asset. It's marked by a break down in reason, with people getting more interested in "winning the bidding war" in the sense of eventually obtaining the asset than "winning the bidding war" in the sense of getting out of the situation in a better financial position than when they started.