Presentation is loading. Please wait.

Presentation is loading. Please wait.

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

Similar presentations


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

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

2 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: Mike Shor 2  Wine  Art  Flowers  Fish  Electric power  Treasury bills  IPOs  Emissions permits  Radio Spectrum  Import quotas  Mineral rights  Procurement

3 Sample Auction Mike Shor 3 “Mistakes are the portals of discovery” - James Joyce

4 Going Once, Going Twice, … Bidding starts at $1 Who will make the first bid? Mike Shor 4

5 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 5

6 Private Value Auction Dinner Mike Shor 6

7 Common Value Auction Unproven oil fields Mike Shor 7

8 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 8

9 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 9

10 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 10

11 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 11

12 Sample Dutch Auction Minimum Bid: $10 Mike Shor 12

13 Sealed-Bid First Price Auctions All buyers submit bids Buyer submitting the highest bid wins and pays the price he or she bid Mike Shor 13 $700 $400 $500 $300 WINNER! Pays $700

14 Sealed-Bid Second Price Auctions All buyers submit bids Buyer submitting the highest bid wins and pays the second highest bid Mike Shor 14 $700 $400 $500 $300 WINNER! Pays $500

15 Why Second Price? It is strategically equivalent to an English Auction Mike Shor 15 $300 $400 $500

16 Why Second Price? Bidding strategy is easy  Bidding one’s true valuation is a (weakly) dominant strategy Intuition:  The amount a bidder pays is not dependent on her bid Mike Shor 16

17 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 17

18 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 18

19 Which is Better? In a second 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 19

20 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 20

21 Revenue Equivalence in the Real World Risk Aversion  Does not influence 2 nd price auctions  Risk averse bidders are more aggressive in first price auctions  Risk aversion  1 st price or Dutch are better Non-familiarity with auctions  More overbidding in second-price auctions  More overbidding in sealed-bid auctions  Inexperience  2 nd price sealed bid is better Mike Shor 21

22 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 22

23 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 23

24 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 24

25 Summary Bidding:  Bid true valuation in 2 nd price auctions  Shade bids in 1 st price auctions Designing:  Take advantage of inexperience  Take advantage of risk aversion  Do sweat the little stuff Mike Shor 25

26 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 26

27 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 27

28 Hypothetical Oil Field Auction Mike Shor tracts for sale each with four bidders Bidder 1 Bidder 2 Bidder 3 Bidder 4

29 Hypothetical Oil Field Auction Mike Shor 29 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

30 Oil Field Auction How much do you bid? Mike Shor 30

31 The Winner’s Curse The estimates are correct, on average What happens if everyone bids his or her estimate? Mike Shor 31 $80 $70 $50 $40 $60

32 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 32

33 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 33

34 Avoiding the Winner’s Curse Bidding for a company of uncertain value Mike Shor 34

35 Avoiding the Winner’s Curse Mike Shor 35 The expected value of the object is irrelevant. To bid: Consider only the value of the object if you win!

36 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 36

37 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 37

38 Extra Low Frequency (ELF) LF HF UHF EHF MF VHF SHF Infrared Visible Ultraviolet XRay Gamma Cosmic Ray Ray 3 x m / 0 Hz 3 x Å / Hz  “The greatest auction in history” - New York Times, March 16, 1995, p.A17

39 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 39

40 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 40

41 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 41

42 Number of Bidders Assume more generally that valuations are drawn uniformly from [20,40]: Mike Shor 42 Number of Bidders Expected Price Example: New Zealand 1993 UHF License Auction  Second price auction  Four lots won by Sky Network: LotHigh Bid (k$)Second Bid (k$)price/high 12, % 22, % 32, % 41, %

43 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 43

44 “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 44


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

Similar presentations


Ads by Google