Auctions

Question 1

Why use auctions?

Answer 1

Under normal selling conditions, buyers may not reveal their preferences. Even if they do reveal preferences, they have an incentive to lie and manipulate to get a cheaper price.
Auctions are designed so that buyers are motivated to reveal their true preferences.

Question 2

What are the four types of auction?

Answer 2

“Open cry”: English Auction; Dutch Auction

“Sealed bid auctions”: 1st price (pay your bid); 2nd price (Vickery)

Question 3

What is an English auction?

Answer 3

• Auctions begin with an opening bid
• Other participants sequentially raise the bid, until no one is willing to increase further.
• The item is sold to the highest bidder, who pays his last offer.

Question 4

Do bidders have access to information under an English auction?

Answer 4

Yes. Although initially bidders don’t have information about the other bidders, they continually gain information as the auction proceeds. Thus, they continue to bid only if they value the item more than the current bid. Outcome: The bidder who values the item the highest, wins!

Question 5

What is a Dutch auction?

Answer 5

• The auctioneer starts the bidding at a very high price.
• He then sequentially lowers the price until a buyer is willing to purchase the item.
• The winner pays the last price that was offered.

Question 6

Do bidders have access to information under a Dutch auction?

Answer 6

No. Information is only revealed once the auction is over (ie. when the winner makes his/her bid)

Question 7

What is a 1st price sealed bid auction?

Answer 7

• Bidders all write their bid on a piece of paper, which is then sealed.
• The auctioneer collects these bids, and awards the item to whoever has bid the highest.
• The winner pays his bid.

Question 8

How do 1st price sealed auctions differ from English auctions?

Answer 8

• In both cases, the winner pays his bid.
• However, bidders do not know information about other bidders. The info available to bidders in a 1st price auction is identical to that under a Dutch auction.

Question 9

What is a 2nd price sealed bid auction?

Answer 9

• Bidders all write their bids on a piece of paper, which is then sealed.
• The auctioneer collects the bids, and allocates the item to the highest bidder.
• However, the winner pays the 2nd highest bid, not his own.

Question 10

Which auctions are strategically equivalent?

Answer 10

• 1st Price and Dutch!!

- 2nd Price and English - optimal strategy is to bid truthfully.

Question 11

What is independent private values?

Answer 11

An auction environment where each bidder knows his/her valuation, but doesn’t know other bidders’ valuations.
Also, valuations are independent, meaning that one persons valuation would not be affected, even if they had knowledge of other people’s valuations.

Question 12

What is affiliated (correlated) value estimates?

Answer 12

Where bidders don’t know their own valuation, or the valuation of others.
- Bidders try and research the true value of the item, and this value estimates are affiliated (ie. If you value the item highly, it is likely that fellow bidders also value it highly.)

Question 13

What is a common-value auction?

Answer 13

A special auction scenario where the value of the item is the same for all bidders, but they can only estimate this value by trying to obtain information about it.

Question 14

What is the optimal bidding strategy for an English auction, with independent private values?

Answer 14

• Bid until the price exceeds the bidder’s valuation of the item.
• The winner of the auction simply has to pay the second highest valuation (“plus a penny”).

Question 15

What is the optimal bidding strategy for a 2nd price (Vickery) auction, with independent private values?

Answer 15

• Bid your valuation of the item!
• If you bid less, you stand less chance of winning.
  If you bid more, chances are you could end up paying more than your valuation.

Question 16

Is bidding your valuation a dominant strategy under 2nd price auctions?

Answer 16

YES! Regardless of what other bidders do, you gain nothing from lying. This is why Vickery auctions are socially efficient - the auction allocates goods to the person with the highest value.

Question 17

What is the optimal bidding strategy for 1st price auctions and Dutch auctions, with independent private values?

Answer 17

• “Shade” your bid.
• If you bid your valuation, you may win, but you will always gain zero surplus.
• Thus, you should try and bid lower than your valuation, by trading off the probability of winning, with the amount of surplus gained if you win.

Question 18

Mathematically, what is the optimal bid for 1st price auctions and Dutch auctions, with independent private values?

Answer 18

If bids are uniformly distributed, and range between H (highest bid) and L (the lowest bid) then:
b = v - [(v-L)/n]
Where v = your valuation, and n = the number of bidders in the auction.

Question 19

What is the “Winner’s Curse”?

Answer 19

When the value of the item is not known (for example, under a common-value auction), each firm will try and use information to obtain an estimate as to it’s value. The person with the highest value estimate is likely to win the auction. However, because the value estimates of all firms is assumed to be fairly evenly distributed, the likelihood is that the winner has paid a price that exceeds the true value if the item - this is the winner’s curse.

Question 20

How should a firm avoid the winner’s curse?

Answer 20

Try and revise his bid downwards to account for the fact he may have overvalued it. Note: The winner’s curse is likely to be greater under sealed bid auctions, because bidder’s do not gain information about others’ valuation during the auction.

Question 21

What is revenue equivalence in independent private value auctions?

Answer 21

English auction: Winner pays 2nd highest valuation (plus a penny)
2nd-Price: Winner (of course) pays the second highest valuation.
1st Price: Winner trys to shade his bid. Will try and shrink it so that it is very slightly above the second highest valuation. Hence, on average, the winner pays the second highest valuation.
Dutch: Same logic as 1st price.
HENCE, in terms of revenue received by the auctioneer: English = 2nd-Price = 1st Price = Dutch.

Question 22

Does the revenue equivalence theorem hold under affiliated (correlated) values?

Answer 22

NO! Player’s ability to shrink his bid depends on the information available to him.
English auction: Max possible information, so less shrinking, and hence more revenue for auctioneers.
1st Price and Dutch: No information available, so no bid shrinking, so winner pays his valuation.
2nd Price: No info is gained during the auction, but winner still pays the second highest valuation. Thus, he will shrink his bid, but not to the extent seen in English auctions.
In terms of revenue: English > 2nd Price > 1st Price = Dutch.