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

2. 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
Mike Shor

3. “Mistakes are the portals of discovery”
Sample Auction
“Mistakes are the portals of discovery”
- James Joyce
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4. Going Once, Going Twice, …
Bidding starts at $1 Who will make the first bid?
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5. 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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6. Private Value Auction
Dinner
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7. Common Value Auction
Unproven oil fields
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8. 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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9. 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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10. 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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11. 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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12. Sample Dutch Auction Minimum Bid: $10
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13. Sealed-Bid First Price Auctions
All buyers submit bids
Buyer submitting the highest bid wins and pays the price he or she bid
$700
$400
$500
$300
WINNER! Pays $700
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14. Sealed-Bid Second Price Auctions
All buyers submit bids
Buyer submitting the highest bid wins and pays the second highest bid
$700
$400
$500
$300
WINNER! Pays $500
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15. Why Second Price? It is strategically equivalent to an English Auction
$300
$400
$500
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16. Why Second Price? Bidding strategy is easy Intuition:
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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17. 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)
Mike Shor

18. 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!
Mike Shor

19. Which is Better? In a second price auction In a first 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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20. 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
Mike Shor

21. Revenue Equivalence in the Real World
Risk Aversion
Does not influence 2nd price auctions
Risk averse bidders are more aggressive in first price auctions
Risk aversion  1st price or Dutch are better
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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22. 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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23. 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?
Mike Shor

24. 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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25. Summary Bidding: Designing: Bid true valuation in 2nd price auctions
Shade bids in 1st price auctions
Designing:
Take advantage of inexperience
Take advantage of risk aversion
Do sweat the little stuff
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26. 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!
Mike Shor

27. 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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28. Hypothetical Oil Field Auction1 2 3 4 5
Bidder 1
Bidder 2
Bidder 3
Bidder 4 6 7 8 9 10
10 tracts for sale
each with four bidders
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29. 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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30. Oil Field Auction
How much do you bid?
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31. The Winner’s Curse $60 $40 $70 $50 $80 $60
The estimates are correct, on average
What happens if everyone bids his or her estimate?
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32. 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
Mike Shor

33. 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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34. Avoiding the Winner’s Curse
Bidding for a company of uncertain value
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35. 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!
Mike Shor

36. 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
Mike Shor

37. 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
Mike Shor

38. “The greatest auction in history”
Extra Low Frequency (ELF)
LF HF UHF EHF
MF VHF SHF
Infrared Visible Ultraviolet XRay Gamma Cosmic
Ray Ray
3 x 10-8 m / 0 Hz
3 x 10-7 Å / 1025 Hz
“The greatest auction in history”
- New York Times, March 16, 1995, p.A17

39. 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?
Mike Shor

40. 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
Mike Shor

41. 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
Mike Shor

42. Number of Bidders
Assume more generally that valuations are drawn uniformly from [20,40]:
Example:
New Zealand 1993 UHF License Auction
Second price auction
Four lots won by Sky Network:
Number of Bidders
Expected Price
Lot
High Bid (k$)
Second Bid (k$)
price/high 1
2,371
401
17% 2
2,273
18% 3 4
1,121
36%
Mike Shor

43. Importance of Rules FCC Spectrum Auctions…
Want to encourage minority and female-owned 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?
Mike Shor

44. “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
Mike Shor