clever title here

The dollar auction game

I heard about this game on a game theory blog.

The game involves someone auctioning off one dollar. Bidding starts at 5 cents and bids increase by five cent increments.

There are two main components to the auction.

1. The auction ends when no one bids higher. The highest bidder pays the price of his bid and gets the dollar as a prize.
2. The second highest bidder is also forced to pay his losing bid (5 cents less than the winning bid) but gets nothing in return.

When the auction starts, you’re bidding 5 - 30 cents for $1, so you increase your bids because you’re still going to be making money. Once you hit 75c though, you start thinking about what happens if you lose. You still have to pay 75c, but you get nothing. You’re still going to get a bargain though, so you keep bidding. The thing is, the othe person is thinking the same thing, so the bids creep up to $1. You’d think that once you get to one dollar, there’s no point in continuning, but what if you’re not in the lead? You should bid more than $1 to limit your loss.

It is the incentives that dictate this weird outcome. Consider an example when the highest bid is $1.50. Since the high bid is above the prize of $1, it is clear no new bidder will enter. Hence, the second bidder faces the two choices of doing nothing and losing $1.45, or raising the bid to $1.55 to lose only 55 cents if the auction ends.

Read a more thorough explanation from mindyourdecisions.com.