“Everything is worth what its purchaser will pay for it.” Game Theory Topic 8 Auctions “Everything is worth what its purchaser will pay for it.” - Publilius Syrus (Maxim 847, 42 B.C.)

What is an Auction? Definition: A market institution with rules governing resource allocation on the basis of bids from participants Over 30% of US GDP moves through auctions: IPOs Emissions permits Radio Spectrum Import quotas Mineral rights Procurement Wine Art Flowers Fish Electric power Treasury bills Mike Shor

“Mistakes are the portals of discovery” Sample Auction “Mistakes are the portals of discovery” - James Joyce Mike Shor

Going Once, Going Twice, … Bidding starts at $1 Who will make the first bid? Mike Shor

Overview of Auctions Auctions are a tricky business Different auction mechanisms sealed vs. open auctions first vs. second price optimal bidding & care in design Different sources of uncertainty private vs. common value auctions the winner’s curse Mike Shor

Private Value Auction Dinner Mike Shor

Common Value Auction Unproven oil fields Mike Shor

Sources of Uncertainty Private Value Auction Each bidder knows his or her value for the object Bidders differ in their values for the object e.g., memorabilia, consumption items Common Value Auction The item has a single though unknown value Bidders differ in their estimates of the true value e.g., FCC spectrum, drilling, disciplinary corporate takeovers Mike Shor

Basic Auction Types Open Auctions (sequential) English Auctions Dutch Auctions Japanese Auctions Sealed Auctions (simultaneous) First Price Sealed Bid Second Price Sealed Bid Mike Shor

English Auctions (Ascending Bid) Bidders call out prices (outcry) Auctioneer calls out prices (silent) Bidders hold down button (Japanese) Highest bidder gets the object Pays a bit over the next highest bid Mike Shor

Dutch (Tulip) Auction Descending Bid “Price Clock” ticks down the price First bidder to “buzz in” and stop the clock is the winner Pays price on clock Mike Shor

Sample Dutch Auction Minimum Bid: $10 Mike Shor

Sealed-Bid First Price Auctions All buyers submit bids Buyer submitting the highest bid wins and pays the price he or she bid $700 $400 $500 $300 WINNER! Pays $700 Mike Shor

Sealed-Bid Second Price Auctions All buyers submit bids Buyer submitting the highest bid wins and pays the second highest bid $700 $400 $500 $300 WINNER! Pays $500 Mike Shor

Why Second Price? It is strategically equivalent to an English Auction $300 $400 $500 Mike Shor

Why Second Price? Bidding strategy is easy Intuition: Bidding one’s true valuation is a (weakly) dominant strategy Intuition: The amount a bidder pays is not dependent on her bid Mike Shor

Bidding True Valuation Say your value is $100 Why not bid $500? If others all bid under $100, no difference If someone bids > $500, no difference If someone bids $300, you overpay! Why not bid $50? If someone bids $80, you lose (but would have made money bidding $100) Mike Shor

First Price Auction First price auction presents tradeoffs If bidding your valuation – no surplus Lower your bid below your valuation Smaller chance of winning, lower price Bid shading Depends on the number of bidders Depends on your information Optimal bidding strategy is complicated! Mike Shor

Which is Better? In a second price auction In a first price auction bidders bid their true value auctioneer receives the second highest bid In a first price auction bidders bid below their true value auctioneer receives the highest bid Mike Shor

Revenue Equivalence All common auction formats yield the same expected revenue (in theory) Any auctions in which: The prize always goes to the person with the highest valuation A bidder with the lowest possible valuation expects zero surplus yield the same expected revenue Mike Shor

Revenue Equivalence in the Real World Risk Aversion Does not influence 2nd price auctions Risk averse bidders are more aggressive in first price auctions Risk aversion  1st price or Dutch are better Non-familiarity with auctions More overbidding in second-price auctions More overbidding in sealed-bid auctions Inexperience  2nd price sealed bid is better Mike Shor

Designing Auction Rules Every rule may have unintended consequences What is the minimum bid for a new bidder? How much must bids be beaten by? Mike Shor

Importance of Rules eBay … Three laptops for sale Top three bidders pay the third highest bid Opening bid: $1 Current high bids: $50, $80, $400 How high should the next bid be? Mike Shor

Importance of Rules FCC Spectrum Auctions… Discouraging Collusion Do not identify highest bidders Capturing Surplus Do not set a bidding increment “I bid $8,000,483” “I bid $3,000,395” Mike Shor

Summary Bidding: Designing: Bid true valuation in 2nd price auctions Shade bids in 1st price auctions Designing: Take advantage of inexperience Take advantage of risk aversion Do sweat the little stuff Mike Shor

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

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

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

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

Oil Field Auction How much do you bid? Mike Shor

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

The Winner’s Curse Defined If the average estimate is generally correct, the highest estimate is usually too high If bids are based on estimates, the highest bidder overpays To avoid the winner’s curse, estimate the average of the object conditional on winning the auction Mike Shor

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

Avoiding the Winner’s Curse Bidding for a company of uncertain value Mike Shor

Avoiding the Winner’s Curse The expected value of the object is irrelevant. To bid: Consider only the value of the object if you win! Mike Shor

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

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

“The greatest auction in history” 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 “The greatest auction in history” - New York Times, March 16, 1995, p.A17

More Bidders More bidders lead to higher prices Example Second price auction Each bidder has a valuation of either $20 or $40, each with equal probability What is the expected revenue? Mike Shor

Number of Bidders Two bidders Each has a value of 20 or 40 There are four value combinations: Pr{20,20}=Pr{20,40}=Pr{40,20}=Pr{40,40}= ¼ Expected price = ¾ (20)+ ¼ (40) = 25 Mike Shor

Number of Bidders Three bidders Each has a value of 20 or 40 There are eight value combinations: Pr{20,20,20}=Pr{20,20,40}=Pr{20,40,20} = Pr{20,40,40}=Pr{40,20,20}=Pr{40,20,40} = Pr{40,40,20}=Pr{40,40,40}= 1/8 Expected price = ½ (20)+ ½ (40) = 30 Mike Shor

Number of Bidders Assume more generally that valuations are drawn uniformly from [20,40]: Example: New Zealand 1993 UHF License Auction Second price auction Four lots won by Sky Network: Number of Bidders Expected Price Lot High Bid (k$) Second Bid (k$) price/high 1 2,371 401 17% 2 2,273 18% 3 4 1,121 36% Mike Shor

Importance of Rules FCC Spectrum Auctions… Want to encourage minority and female-owned firms to bid but licenses are very expensive. Reserve several frequency blocks for smaller bidders. Allow 10% down, low interest, remaining principal owed in 7 years. What happens? Mike Shor

“Tweaking the Rules” II (continued) Bid high! If licenses end up being worth less, default! Of the four largest winners, one went bankrupt and defaulted one had $1B reduced to $66M in bankruptcy court one was a front for Qualcomm one was sold to Siemens Mike Shor