Economics 108 Workshops -- Week of September 13, 1999
Equilibrium of Supply and Demand in Auctions
A seller decides to sell a rare, signed photograph by auctioning it. Only one photo is for sale. The lowest price that the seller is willing to accept is $30. There are several potential buyers:
Buyer A values it at $50. (In other words, $50 is the highest price that A would be willing to pay for the photo. Of course, A would prefer to pay a lower price.)
Buyer B values it at $45.
Buyer C values it at $40.
Buyer D values it at $35.
Buyer E values it at $30.
Buyer F values it at $25.
Assume all bids are an integer number of dollars
(no bids with fractions of a dollar are allowed).Information Assumption 1: Suppose that no buyer knows the values that other buyers place on the photo. Each knows only his own maximum price for the photo.
Auction #1. Suppose the auction occurs today. Every second until midnight tonight, a Web site will be updated to announce the highest bid received by that time. Every bid must be at least $1 more than the current high bid. At midnight, the bidder with the highest bid wins the photo, paying the winning bid for it. (None of this is intended to be tricky.)
(1) What is likely to be the winning bid? Why?
(2) If you were one of the bidders, what kind of bidding strategy would you choose? (For example, how much would you bid initially and how would you respond to other bids?) Why? Do you have an incentive to understate (bid less than) your true value of the photo? Why or why not?
Auction #2
Suppose that, as on Ebay (www.ebay.com) and many other Internet auction sites, bidding works as follows, with a proxy:
What's Proxy Bidding?
OK, so let's say you find something on eBay that you really want.... You're willing to pay $25.00 for it, but the current bid price is only $2.25. You could take the long route and sit at your computer, outbidding each new bid until you reach $25.00. (Like you have nothing better to do...!)
Luckily, there's a better way: Let the system be your proxy and do your bidding for you. Here's how it works:
1.The seller lists an item for auction, determines the length of the auction, and opens for bidding.
2.You decide how much you're willing to pay, enter your first bid and give your proxy (the system) a confidential maximum bid.
3.You note the ending time of the auction and log off.
4.Your proxy (the system) engages in a fierce bidding war with other proxy bidders, and a few live ones—while you go about your business.
5. At the end of the auction, you check back in to see how your proxy did. If other bidders outbid your predetermined maximum, you don't get your item. But otherwise, you're the winner—and the final price might even be less than the maximum you had been willing to spend! Winning was never easier!
Assume that people can have proxies bid for them.
(3) Repeat question (1).
(4) Repeat question (2).
Auction #3.
Suppose that the seller holds a declining-price auction. The seller announces an initial price, and the first person to accept that offer wins the auction (buys the photo) at that price. If no one accepts the first price, the seller reduces the price little by little, until someone accepts the offer.
(a) Make Information Assumption 2: Every buyer knows the values that other buyers place on the photo.
(5) Repeat question (1).
(6) Repeat question (2).
(b) How would your answers to questions (5)-(6) change if we made Information Assumption 1 -- so that no buyer knows for sure what values other buyers place on the photo? Note: this is a hard problem -- you cannot give a numerical answer. Instead, see if you can think of what issues are involved.
Auction #4. Suppose that the seller holds a sealed-bid auction. The seller announces that buyers can submit only ONE bid each, anytime before midnight, and all information about
bids will be kept secret. At midnight, the bidder with highest bid wins the auction. Suppose, as in Information Assumption 2, that all buyers know the values that other buyers place on the photo.
(7) Repeat question (1).
(8) Repeat question (2).
A seller's choice. (a) If you were a seller, which auction would you prefer? Why? (b) Suppose that many other sellers are trying to sell similar photographs on other auctions, and that there are many other potential buyers like A, B, ..., F. Does competition with these other auctions affect your answer to part (a)? Explain why or why not.
Auctioning Multiple Items:
Suppose you have 4 copies of the photograph to sell. In each case, make Information Assumption 2: every buyer knows the values that everyone else places on the items.
Auction #5. Suppose you run an auction like Auction #3. After it ends, you repeat it three separate times to sell the other 3 photos.
Questions (9), (10) -- repeat questions (1) and (2).
Auction #6. Suppose you run an auction like Auction #3, except that you sell all four photos in the same auction. The 4 highest bids win, and each winner pays the lowest winning bid (so each winner pays the same bid).
Questions (11), (12) -- repeat questions (1) and (2).