game theory “everything is worth what its purchaser will pay for it.” - publilius syrus (maxim...
TRANSCRIPT
Game Theory
“Everything is worth what its purchaser will pay for it.”
- Publilius Syrus (Maxim 847, 42 B.C.)
Mike ShorLecture 12
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 leasesValue of oil is roughly the same
for every participantNo bidder knows value for sureEach bidder has some information
Auction formats are not equivalentOral auctions provide informationSealed-bid auctions do not
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Hypothetical Oil Field Auction
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10 tracts for sale
1 2 3 4 5
6 7 8 9 10
each with four bidders
Bidder 1 Bidder 2
Bidder 3 Bidder 4
Hypothetical Oil Field Auction
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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
Oil Field Auction
How much do you bid?
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The Winner’s Curse
The estimates are correct, on average
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$80
$70$50
$40
$60
$60
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
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COMMANDMENTCOMMANDMENT
The expected value of the object is irrelevant.
To bid: Consider only the value of the object
if you win!
Avoiding the Winner’s Curse
Bidding for a company of uncertain value
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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 that as the basis of your bidMike ShorGame Theory & Business Strategy
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Private or Common Value?
Most Auctions are not purely private value or purely common value
Private ValueResale component (art)Reputation / conspicuous consumption
Public ValueDiffering 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
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Independent Multi-Unit
Multiple works
of art
May be auctioned off separately
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Dependent Multi-Unit
PCS Spectrum Auctions (FCC)
Design of
combinatorial auctions
is very complicatedMike ShorGame Theory & Business Strategy
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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
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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