Date 28^th October 2002-Monday

AUCTION THEORY

Authors:

Ravi Kumar

Shivam Anand

 

The word auction comes from Latin root auctio which means to increase.

 

Applications:

 

·        Government disinvestments (Sealed Bid Auctions)

·         Offshore oil leases

·         Internet auctions (e.g. bazee.com)

·         Scrap metal auctions.

·         Timber rights.

·        Flower Market in Netherlands: The Dutch auction derives its name from the wholesale flower market in Holland, the largest exporter of cut flowers. Since a primary concern is damage and exposure to the flowers, this auction technique is chosen because it provides the most time efficient scheme of getting the cut flowers to market. In the Dutch auction, a seller (auction house) sets a price. Using a clock, the price falls until a buyer bids (presses a button to stop the clock). The first bid is the winning bid.

·        Various Investment procedures.

·        Reverse auctions (purchasing from suppliers): In this firm invites bid for purchasing products & services from suppliers.  Supplier having the lowest bid is the winner.

 

 

Types of auctions:

 

There are four main types of auctions. They are:

 

• The English  or open ascending price  auction
• The Dutch or  Open descending price auction
• The First-price sealed bid auction
• The Second-price sealed bid auction (or the Vickrey auction).

 

The English auction is the most familiar type of auction. It is an ascending price auction, where a minimum bid is specified by the Auctioneer. Bidders then publicly offer successively higher bids to the Auctioneer, sometimes at the auctioneer’s prompting. This continues until no one else will offer a higher bid. The item is then sold to the highest bidder. Most EBay (online) auctions work this way.

 

 

The Dutch auction is a descending-price auction. An auctioneer will start bidding at a very high price, and then will lower it until someone offers to buy the good at the price offered. The Dutch auction, like the English auction, is done in an open format. Sale of flowers in the Netherlands is done using this type of auction.

 

 

The First-price sealed bid auction has bidders submit bids over a specified period. Their bids are hidden from other bidders, in contrast to the English and Dutch auctions. The auctioneer sees the bids after they have all been submitted, and the winner is the highest bidder.

 

 

 

The Second-price sealed bid auction is also called the Vickrey auction. William Vickrey was the economist who defined this type of auction in the 1960’s. This auction works just like the First-price sealed bid auction i.e., highest bidder wins but the winning bidder pays an amount equal to the bid of the second-highest bidder. The winner therefore pays less than the highest bid, his bid.

 

 

Problems with auctions:

Traditionally, auctions are difficult to conduct. This as a matter of fact involves inviting various bidders at one place and then organizing a fair Auction.

Another problem is that the auction might be rigged e.g., in case of second price auction, seller can put a dummy bid higher than the second highest bidder so that winner has to pay more. Nowadays Internet auctions are becoming more and more popular and various Internet sites are completely devoted to conduct the same in fair and justified manner.

 

 

 

Assumptions

 

Private Value Assumptions (PVA):

 

•             Each bidder knows the value of the object to himself.
•             No bidder knows with certainty the value attached by the other bidder.
•             These values do not affect his value.

 

 

Common Value Assumption:

 

                        The value, although unknown at the time of bidding, is same for all        bidders. This topic will not be covered in this course.

 

 

 

 

 

Equivalent Auctions

 

                        OPEN CRY                                                                SEALED BID

 

 

	DUTCH DESCENDING PRICE AUCTION				FIRST PRICE AUCTION

 

 

 

 

 

	ENGLISH ASCENDING PRICE AUCTION				SECOND PRICE AUCTION

 

 

 

 

 

 

 

In both Dutch descending price auction and first price auction the bidder will always quote an amount equal to his private valuation. While in English ascending price and second price auction bidders will quote an amount equal to their private valuations but the highest bidder pays an amount almost equal to the second highest bid (under Private value assumption).

 

 

 

Revenue Vs Efficiency

 

Consider an auction involving only two bidders A & B. Assume seller’s value of the object to be X_o. let the two bidders A & B associate values  V₁ & V₂ respectively such that V₁ > V₂.

 

If item is sold to A at a price = R

 

Total gain = seller’s gain + A’s gain = (R- X_o) + (V₁ – R) = G_A

 

If item is sold to B at a price = R

 

Total gain = seller’s gain + A’s gain = (R- X_o) + (V₂ – R) = G_B

 

As V₁ > V₂ therefore G_A > G_B

 

So we can see that trade is efficient if the object goes to the bidder who values it more.