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Game Theory “A cynic knows the price of everything and the value of nothing” - Oscar Wilde, Lady Windemere’s Fan Mike Shor Lecture 11

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Mike Shor Game Theory & Business Strategy 2 What is an Auction? auc tion 1. A public sale in which property or merchandise are sold to the highest bidder. 2. A market institution with explicit rules determining resource allocation and prices on the basis of bids from participants. 3. Games: The bidding in bridge [Latin: auctiō, auctiōn – from auctus, past participle of augēre, to increase]

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Mike Shor Game Theory & Business Strategy 3 Examples of Auctions Definition: A market institution with rules governing resource allocation on the basis of bids from participants Over 30% of US GDP moves through auctions: Wine Art Flowers Fish Electric power Treasury bills IPOs Emissions permits Radio Spectrum Import quotas Mineral rights Procurement

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Mike Shor Game Theory & Business Strategy 4 Sample Auction “Mistakes are the portals of discovery” - James Joyce

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Mike Shor Game Theory & Business Strategy 5 Going Once, Going Twice, … Bidding starts at $1 Who will make the first bid?

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Mike Shor Game Theory & Business Strategy 6 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

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Mike Shor Game Theory & Business Strategy 7 Private Value Auction Dinner

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Mike Shor Game Theory & Business Strategy 8 Common Value Auction Unproven oil fields

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Mike Shor Game Theory & Business Strategy 9 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 of the object e.g., FCC spectrum, drilling, disciplinary corporate takeovers

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Mike Shor Game Theory & Business Strategy 10 Basic Auction Types Open Auctions (sequential) English Auctions Dutch Auctions Japanese Auctions Sealed Auctions (simultaneous) First Price Sealed Bid Second Price Sealed Bid

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Mike Shor Game Theory & Business Strategy 11 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

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Mike Shor Game Theory & Business Strategy 12 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

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Mike Shor Game Theory & Business Strategy 13 Sample Dutch Auction Minimum Bid: $10

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Mike Shor Game Theory & Business Strategy 14 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

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Mike Shor Game Theory & Business Strategy 15 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

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Mike Shor Game Theory & Business Strategy 16 Why Second Price? It is strategically equivalent to an English Auction $300 $400 $500

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Mike Shor Game Theory & Business Strategy 17 Why Second Price? Bidding strategy is easy Bidding one’s true valuation is a dominant strategy Intuition: The amount a bidder pays is not dependent on her bid

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Mike Shor Game Theory & Business Strategy 18 Optimal Bidding Strategy in Second Price Auctions You Lose You Win higher Your bid Others’ bids Your value

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Mike Shor Game Theory & Business Strategy 19 Bidding Higher Than My Valuation Case 1Case 2Case 3 No difference Lose money

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Mike Shor Game Theory & Business Strategy 20 Bidding Lower Than My Valuation Case 1Case 2Case 3 No difference Lose money

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Mike Shor Game Theory & Business Strategy 21 Second Price Auction In a second price auction, always bid your true valuation Winning bidder’s surplus Difference between the winner’s valuation and the second highest valuation Surplus decreases with more bidders

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Mike Shor Game Theory & Business Strategy 22 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! Rule of thumb: bid (N-1)/N of your value

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Mike Shor Game Theory & Business Strategy 23 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

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Mike Shor Game Theory & Business Strategy 24 Which is Better? Draw 4 keep highest Draw 4 keep 2 nd highest

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Mike Shor Game Theory & Business Strategy 25 Revenue Equivalence All common auction formats yield the same expected revenue (in theory) In fact, any auction satisfying: 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

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Mike Shor Game Theory & Business Strategy 26 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

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Mike Shor Game Theory & Business Strategy 27 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?

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Mike Shor Game Theory & Business Strategy 28 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

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Mike Shor Game Theory & Business Strategy 29 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

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Mike Shor Game Theory & Business Strategy 30 Number of Bidders Assume more generally that valuations are drawn uniformly from [20,40]: Number of Bidders Expected Price

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Mike Shor Game Theory & Business Strategy 31 Designing Auction Rules Every rule may have unintended consequences What is the minimum bid for a new bidder? What kind of financing can bidders present? How much must bids be beaten by?

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Mike Shor Game Theory & Business Strategy 32 “Tweaking the Rules” I 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?

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Mike Shor Game Theory & Business Strategy 33 “Tweaking the Rules” II 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?

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Mike Shor Game Theory & Business Strategy 34 “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

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Mike Shor Game Theory & Business Strategy 35 “Tweaking the Rules” III 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”

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Mike Shor Game Theory & Business Strategy 36 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

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