Game Theory
Topic 8
Auctions
“Everything is worth what its
purchaser will pay for it.”
- Publilius Syrus (Maxim 847, 42 B.C.)
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
Radio Spectrum
Import quotas
Mineral rights
Procurement






Wine
Art
Flowers
Fish
Electric power
Treasury bills
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Sample Auction
“Mistakes are the portals
of discovery”
- James Joyce
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Going Once, Going Twice, …
Bidding starts at $1
Who will make
the first bid?
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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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Private Value Auction

Dinner
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Common Value Auction

Unproven oil fields
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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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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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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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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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Sample Dutch Auction
Minimum Bid: $10
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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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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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Why Second Price?

It is strategically equivalent
to an English Auction
$500
$400
$300
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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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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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First Price Auction
First price auction presents tradeoffs
 If bidding your valuation – no surplus

 Lower
your bid below your valuation
 Smaller
 Bid
chance of winning, lower price
shading
 Depends
on the number of bidders
 Depends on your information
 Optimal bidding strategy is complicated!
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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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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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Revenue Equivalence
in the Real World

Risk Aversion
not influence 2nd price auctions
 Risk averse bidders are more aggressive
in first price auctions
 Risk aversion  1st price or Dutch are better
 Does

Non-familiarity with auctions
 More
overbidding in second-price auctions
 More overbidding in sealed-bid auctions
 Inexperience  2nd price sealed bid is better
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Designing Auction Rules

Every rule may have unintended
consequences
 What
 How
is the minimum bid for a new bidder?
much must bids be beaten by?
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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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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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Summary

Bidding:
true valuation in 2nd price auctions
 Shade bids in 1st price auctions
 Bid

Designing:
 Take
advantage of inexperience
 Take advantage of risk aversion
 Do sweat the little stuff
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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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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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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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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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Oil Field Auction

How much do you bid?
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The Winner’s Curse
$40
$50
$70
$60
$80
$60

The estimates are correct, on average
What happens if everyone bids his or her estimate?
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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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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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Avoiding the
Winner’s Curse

Bidding for a company
of uncertain value
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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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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
your estimate is the most optimistic –
what is the object worth?
 If
 Use
that as the basis of your bid
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Summary
 Average
 Consider
value of an object is irrelevant
only the value if you win
 In
common value auctions, assume that
you have the most optimistic estimate
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Extra Low
LF
HF
UHF
EHF
Frequency
MF
VHF
SHF
(ELF)
3 x 10-8 m / 0 Hz
Infrared
Visible
Ultraviolet
XRay
Gamma
Ray
3 x 10-7 Å / 1025 Hz
“The greatest auction in history”
- New York Times, March 16, 1995, p.A17
Cosmic
Ray
More Bidders

More bidders lead to higher prices

Example
 Second
price auction
 Each bidder has a valuation of either
$20 or $40, each with equal probability
 What is the expected revenue?
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Number of Bidders

Two bidders
 Each
has a value of 20 or 40
 There are four value combinations:
Pr{20,20}=Pr{20,40}=Pr{40,20}=Pr{40,40}= ¼
Expected price = ¾ (20)+ ¼ (40) = 25
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Number of Bidders

Three bidders
 Each
has a value of 20 or 40
 There are eight value combinations:
Pr{20,20,20}=Pr{20,20,40}=Pr{20,40,20}
= Pr{20,40,40}=Pr{40,20,20}=Pr{40,20,40}
= Pr{40,40,20}=Pr{40,40,40}= 1/8
Expected price = ½ (20)+ ½ (40) = 30
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Number of Bidders


Assume
Example:more generally that valuations are drawn
uniformly
from1993
[20,40]:
New Zealand
UHF License Auction


Second price auction
Four lots won by Sky Network:
Expected Price
40
Lot
35
1
High Bid (k$)
Second Bid (k$)
price/high
2,371
401
17%
2,273
401
18%
2,273
401
18%
401100
36%
1000
30
2
25
3
20
4
1
1,121
10
Number of Bidders
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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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“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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