Topic 8
Auctions
“Everything is worth what its purchaser will pay for it.”
Publilius Syrus (Maxim 847, 42 B.C.)

Mike Shor
What is an Auction?
 Definition:
 A market institution with rules governing resource allocation on the basis of bids from participants
 Over 30% of US GDP moves through auctions:


IPOs
Emissions permits


Wine
Art


Radio Spectrum
Import quotas


Flowers
Fish
 Mineral rights  Electric power
 Procurement  Treasury bills
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Sample Auction
Mike Shor
“Mistakes are the portals of discovery”
- James Joyce
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Going Once, Going Twice, …
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Mike Shor
Overview of Auctions
 Auctions are a tricky business
 Different auction mechanisms
 sealed vs. open auctions
 first vs. second price
 optimal bidding & care in design
 Different sources of uncertainty
 private vs. common value auctions
 the winner’s curse
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Mike Shor
Private Value Auction
 Dinner
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Common Value Auction
 Unproven oil fields
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Mike Shor
Sources of Uncertainty
 Private Value Auction
 Each bidder knows his or her value for the object
 Bidders differ in their values for the object
 e.g., memorabilia, consumption items
 Common Value Auction
 The item has a single though unknown value
 Bidders differ in their estimates of the true value
 e.g., FCC spectrum, drilling, disciplinary corporate takeovers
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Mike Shor
Basic Auction Types
 Open Auctions (sequential)
 English Auctions
 Dutch Auctions
 Japanese Auctions
 Sealed Auctions (simultaneous)
 First Price Sealed Bid
 Second Price Sealed Bid
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Mike Shor
English Auctions
(Ascending Bid)
 Bidders call out prices (outcry)
 Auctioneer calls out prices (silent)
 Bidders hold down button (Japanese)
 Highest bidder gets the object
 Pays a bit over the next highest bid
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Mike Shor
Dutch (Tulip) Auction
Descending Bid

“Price Clock” ticks down the price

First bidder to “buzz in” and stop the clock is the winner
 Pays price on clock
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Mike Shor
Sample Dutch Auction
Minimum Bid: $10
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Mike Shor
Sealed-Bid
First Price Auctions
 All buyers submit bids
 Buyer submitting the highest bid wins and pays the price he or she bid
WINNER!
Pays $700
$700 $500
$400 $300
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Mike Shor
Sealed-Bid
Second Price Auctions
 All buyers submit bids
 Buyer submitting the highest bid wins and pays the second highest bid
WINNER!
Pays $500
$700 $500
$400 $300
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Mike Shor
Why Second Price?
 It is strategically equivalent to an English Auction
$500
$400
$300
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Mike Shor
Why Second Price?
 Bidding strategy is easy

Bidding one’s true valuation is a (weakly) dominant strategy
 Intuition:
 The amount a bidder pays is not dependent on her bid
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Mike Shor
Bidding True Valuation
Say your value is $100
 Why not bid $500?
 If others all bid under $100, no difference
 If someone bids > $500, no difference
 If someone bids $300, you overpay!
 Why not bid $50?
 If someone bids $80, you lose (but would have made money bidding $100)
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Mike Shor
First Price Auction
 First price auction presents tradeoffs
 If bidding your valuation –no surplus
 Lower your bid below your valuation
 Smaller chance of winning, lower price
 Bid shading
 Depends on the number of bidders
 Depends on your information
 Optimal bidding strategy is complicated!
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Mike Shor
Which is Better?
 In a second price auction
 bidders bid their true value
 auctioneer receives the second highest bid
 In a first price auction
 bidders bid below their true value
 auctioneer receives the highest bid
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Mike Shor
Revenue Equivalence
 All common auction formats yield the same expected revenue (in theory)
Any auctions in which:
 The prize always goes to the person with the highest valuation
 A bidder with the lowest possible valuation expects zero surplus yield the same expected revenue
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Mike Shor
Revenue Equivalence in the Real World
 Risk Aversion
 Does not influence 2 nd price auctions
 Risk averse bidders are more aggressive in first price auctions
 Risk aversion  1 st price or Dutch are better
 Non-familiarity with auctions
 More overbidding in second-price auctions
 More overbidding in sealed-bid auctions
 Inexperience  2 nd price sealed bid is better
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Mike Shor
Designing Auction Rules
 Every rule may have unintended consequences
 What is the minimum bid for a new bidder?
 How much must bids be beaten by?
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Mike Shor
Importance of Rules eBay …
 Three laptops for sale
 Top three bidders pay the third highest bid
 Opening bid: $1
 Current high bids:
 $50, $80, $400
 How high should the next bid be?
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Mike Shor
Importance of Rules
FCC Spectrum Auctions…
 Discouraging Collusion
 Do not identify highest bidders
 Capturing Surplus
 Do not set a bidding increment
“I bid $8,000,483”
“I bid $3,000,395”
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Mike Shor
Summary
 Bidding:
 Bid true valuation in 2 nd price auctions
 Shade bids in 1 st price auctions
 Designing:
 Take advantage of inexperience
 Take advantage of risk aversion
 Do sweat the little stuff
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Mike Shor
Sources of Uncertainty
 Private Value Auction
 Difficult to lose money
 Do not bid more than your value
(or less than your cost)
 Common Value Auction
 The item has a single though unknown value
 Bidders differ in their estimates
 The winner might be wrong!
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Mike Shor
Common Value Auctions
 Example: Offshore oil leases
 Value of oil is roughly the same for every participant
 No bidder knows value for sure
 Each bidder has some information
 Auction formats are not equivalent
 Oral auctions provide information
 Sealed-bid auctions do not
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Mike Shor
Hypothetical Oil Field Auction
1 2 3 4 5
6 7 8 9 10
10 tracts for sale
Bidder 1 Bidder 2 each with four bidders
Bidder 3 Bidder 4
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Mike Shor
Hypothetical Oil Field Auction
Bidder 1 Bidder 2
Bidder 3 Bidder 4



Each tract has four bidders
Each bidder knows the amount of oil in his or her quadrant
Each quarter’s value is evenly distributed between
$200,000 and $800,000
 Total value of oil field:
Sum of the values of the four quarters
 Type of auction:
First price sealed bid
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Mike Shor
Oil Field Auction
 How much do you bid?
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Mike Shor
The Winner’s Curse
$40
$50
$60
$60
$70
 The estimates are correct, on average
What happens if everyone bids his or her estimate?
$80
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Mike Shor
The Winner’s Curse Defined


If the average estimate is generally correct, the highest estimate is usually too high
If bids are based on estimates, the highest bidder overpays

To avoid the winner’s curse, estimate the average of the object conditional on winning the auction
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Mike Shor
Avoiding the Winner’s Curse

Given that I win an auction …
All others bid less than me …
Thus the object’s value must be lower than I thought

Winning the auction is “bad news”
One must incorporate this into one’s bid
Assume that your estimate is the most optimistic
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Mike Shor
Avoiding the
Winner’s Curse
 Bidding for a company of uncertain value
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Mike Shor
Avoiding the Winner’s Curse
The expected value of the object is irrelevant.
To bid:
Consider only the value of the object
if you win!
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Mike Shor
Avoiding the Winner’s Curse
 Bidding with no regrets:
 Since winning means you have the most optimistic signal, always bid as if you have the highest signal
 If your estimate is the most optimistic – what is the object worth?
 Use that as the basis of your bid
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Mike Shor
Summary
 Average value of an object is irrelevant
 Consider only the value if you win
 In common value auctions, assume that you have the most optimistic estimate
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Extra Low
Frequency
(ELF)
3 x 10 -8 m / 0 Hz
LF HF UHF EHF
MF VHF SHF
Infrared Visible Ultraviolet XRay Gamma Cosmic
Ray Ray
3 x 10 -7 Å / 10 25 Hz
 “The greatest auction in history”
New York Times , March 16, 1995, p.A17

Mike Shor
More Bidders
 More bidders lead to higher prices
 Example
 Second price auction
 Each bidder has a valuation of either
$20 or $40, each with equal probability
 What is the expected revenue?
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Number of Bidders
 Two bidders
 Each has a value of 20 or 40
 There are four value combinations:
Pr{20, 20 }=Pr{ 20 ,40}=Pr{40, 20 }=Pr{40, 40 }= ¼
Mike Shor
Expected price = ¾ ( 20 )+ ¼ ( 40 ) = 25
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Mike Shor
Number of Bidders
 Three bidders
 Each has a value of 20 or 40
 There are eight value combinations:
Pr{20,20, 20 }=Pr{ 20 ,20,40}=Pr{20,40, 20 }
= Pr{20,40, 40 }=Pr{40,20, 20 }=Pr{40,20, 40 }
= Pr{ 40 ,40,20}=Pr{40,40, 40 }= 1/8
Expected price = ½ ( 20 )+ ½ ( 40 ) = 30
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Number of Bidders
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 Second price auction

40
Four lots won by Sky Network:
High Bid (k$) Second Bid (k$) Lot
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1
30
2
25
3
20
4
1
2,371
2,273
2,273
1,121
10
401
401
401
401
100
Number of Bidders price/high
17%
18%
18%
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Mike Shor
Importance of Rules
FCC Spectrum Auctions…
 Want to encourage minority and femaleowned firms to bid but licenses are very expensive.
 Reserve several frequency blocks for smaller bidders.
 Allow 10% down, low interest, remaining principal owed in 7 years.
 What happens?
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Mike Shor
“Tweaking the Rules” II
(continued)
 Bid high!
 If licenses end up being worth less, default!
 Of the four largest winners,
 one went bankrupt and defaulted
 one had $1B reduced to $66M in bankruptcy court
 one was a front for Qualcomm
 one was sold to Siemens
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