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Game Theory

Game Theory. Mike Shor Lecture 12. “The greatest auction in history”. - New York Times , March 16, 1995, p.A17. Sources of Uncertainty. Private Value Auction Difficult to lose money Do not bid more than your value (or less than your cost)

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Game Theory

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  1. Game Theory Mike ShorLecture 12 “The greatest auction in history” - New York Times, March 16, 1995, p.A17

  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!

  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

  4. Bidder 2 Bidder 1 Bidder 4 Bidder 3 Hypothetical Oil Field Auction 5 4 3 2 1 10 9 8 7 6 10 tracts for sale each with four bidders

  5. Hypothetical Oil Field Auction

  6. Oil Field Auction • How much do you bid?

  7. The Winner’s Curse • The estimates are correct, on average What happens if everyone bids his or her estimate? $40 $70 $50 $60 $80 $60

  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

  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!

  10. Avoiding the Winner’s Curse • Bidding for a company of uncertain value

  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

  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)

  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

  14. Independent Multi-Unit Multiple works of art May be auctioned off separately

  15. Dependent Multi-Unit PCS Spectrum Auctions (FCC) Design of combinatorial auctions is very complicated

  16. Very Low Frequency (VLF) LF HF UHF EHF MF VHF SHF Infrared Visible Ultraviolet XRay Gamma Cosmic Ray Ray 3 x 10-8 m / 0 Hz 3 x 10-7Å / 1025 Hz

  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

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