“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.)

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

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

Hypothetical Oil Field Auction 1 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

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

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

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

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

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

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

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

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

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

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

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

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

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