Game Theory
Mike Shor
Lecture 12
“Everything is worth what its
purchaser will pay for it.”
- Publilius Syrus (Maxim 847, 42 B.C.)
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
Game Theory & Business Strategy
2
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
Mike Shor
Game Theory & Business Strategy
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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
Mike Shor
Game Theory & Business Strategy
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
Mike Shor
Game Theory & Business Strategy
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Oil Field Auction
How much do you bid?
Mike Shor
Game Theory & Business Strategy
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The Winner’s Curse
$40
$70
$50
$60
$60
$80
The estimates are correct, on average
Mike Shor
Game Theory & Business Strategy
7
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
Mike Shor
Game Theory & Business Strategy
8
Avoiding the Winner’s Curse
COMMANDMENT
The expected value of the object
is irrelevant.
To bid:
Consider only the value of the object
if you win!
Mike Shor
Game Theory & Business Strategy
9
Avoiding the
Winner’s Curse
Bidding for a company
of uncertain value
Mike Shor
Game Theory & Business Strategy
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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
If
your estimate is the most optimistic –
what is the object worth?
Use
Mike Shor
Game Theory & Business Strategy
that as the basis of your bid
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Private or Common Value?
Most Auctions are not purely private
value or purely common value
Private Value
Resale
component (art)
Reputation / conspicuous consumption
Public Value
Differing
Mike Shor
Game Theory & Business Strategy
abilities (mining)
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Multi-Unit Auctions
What if you have multiple items to sell?
Depends on whether the items are …
Independent
in value
Dependent on each other
Mike Shor
Game Theory & Business Strategy
13
Independent Multi-Unit
Multiple works
of art
May be auctioned
off separately
Mike Shor
Game Theory & Business Strategy
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Dependent Multi-Unit
PCS Spectrum
Auctions (FCC)
Design of
combinatorial
auctions
is very complicated
Mike Shor
Game Theory & Business Strategy
15
Extra Low
LF
HF
UHF
EHF
Frequency
MF
VHF
SHF
(ELF)
3 x 10-8 m / 0 Hz
Mike Shor
Game Theory & Business Strategy
Infrared
Visible
Ultraviolet
Cosmic
XRay
Gamma
Ray
Ray
3 x 10-7 Å / 1025 Hz
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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
Mike Shor
Game Theory & Business Strategy
17