Monday, March 24, 2008

And the winning bidder is . . .?

You want to sell at auction an antique dining-room suite. There are five people who want it, and they're willing to pay $8,000, $9,500, $6,500, $11,000, and $7,500, respectively. Your reservation price (the price above which the bidding must go before you sell it) is $7,000. No one in the room has any information about the value of the suite to anyone else. At about what price will the suite be sold and to whom? Explain.

Congratulations to Yang Di on his back-to-back wins (and third overall). Di was the first to correctly deduce that the winning price will be approximately equal to the value of the second highest bidder. Though auctions can be organized in many different fashions, the most commonly used mechanism is known as the English Auction.

3 comments:

yangdi said...

I think the suite will be sold to the one who is willing to pay $11,000, and price will be just a little bit higher than $9,500. In an auction, the bidders will continue to raise the price until the price goes above their willingness to pay. Thus, in this situation, the price will go up until it reaches the point a little bit higher than $9,500. All the other four bidders give up one by one, and whoever willing to pay $11,000 wins.

Celia Brockway said...

The two highest bidders at the auction are willing to pay $9,500 and $11,000, respectively. Since there is a $1,500 gap between these two prices, the $11,000 bidder will buy the suite, however it will be for a price closer to $10,000 since this bidder is the only one willing to go over $9,500.

Yaoguang Li said...

The reservation price is $7000, and the highest pay is $11,000, $4000 higher than the reservation price. So this suite will be sold to who want to pay $11000.