1. “Everything is worth what its purchaser will pay for it.”
Game Theory
Mike Shor Lecture 12
“Everything is worth what its purchaser will pay for it.”
- Publilius Syrus (Maxim 847, 42 B.C.)

2. 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

3. 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

4. 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
Mike Shor
Game Theory & Business Strategy

5. 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

6. Oil Field Auction How much do you bid? Mike Shor
Game Theory & Business Strategy

7. The Winner’s Curse $60 $40 $70 $50 $80 $60
The estimates are correct, on average
Mike Shor
Game Theory & Business Strategy

8. 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

9. 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

10. Avoiding the Winner’s Curse
Bidding for a company of uncertain value
Mike Shor
Game Theory & Business Strategy

11. 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
Game Theory & Business Strategy

12. 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 abilities (mining)
Mike Shor
Game Theory & Business Strategy

13. 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

14. Independent Multi-Unit
Multiple works of art May be auctioned off separately
Mike Shor
Game Theory & Business Strategy

15. Dependent Multi-Unit
PCS Spectrum Auctions (FCC) Design of combinatorial auctions is very complicated
Mike Shor
Game Theory & Business Strategy

16. 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
Mike Shor
Game Theory & Business Strategy

17. 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
Game Theory & Business Strategy