1 Teck-Hua Ho April 18, 2006 Auction Design I. Economic and Behavioral Foundations of Pricing II. Innovative Pricing Concepts and Tools III. Internet Pricing.
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April 18, 2006
1
Teck-Hua Ho
Auction Design
I. Economic and Behavioral Foundations of Pricing
II. Innovative Pricing Concepts and Tools
III. Internet Pricing Models
April 18, 2006
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Teck-Hua Ho
OutlineOutline
Choice of Price Format
Auction Formats
Strategic and Revenue Equivalence
A Field Test
An In-Class Experiment on Common-Value Auction
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Choice of Price FormatChoice of Price Format
Seller Buyer Seller & Buyer
Price Setting Party
Pri
ce O
ver
Tim
e / P
rice
For
mat
ion
Stat
icD
ynam
ic
www.priceline.com
www.landsend.com www.freemarkets.com
www.ebay.com
www.letsbuyit.com
Financial markets
www.amazon.com
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ObservationsObservations
Buyer versus seller: Ample (limited and unique) supply Seller (buyer) set prices
High (low) knowledge of buyer WTPs Seller (buyer) set prices
Static versus Dynamic High (low) product perishability Dynamic (static) pricing
models
Price fairness is (not) an issue Static (dynamic) pricing models
High information asymmetry between buyers and sellers Dynamic pricing (auction)
Higher efficiency Dynamic pricing
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Design of AuctionDesign of AuctionPrice Setting Party
Seller Buyer Seller & Buyer
Pri
ce O
ver
Tim
e Stat
icD
ynam
ic - Dutch - English - 1st Price Sealed-bid - 2nd Price Sealed-bid
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Promises of Internet AuctionPromises of Internet Auction
Increased convenience (temporal, geographical)
Asynchronous bidding is possible
Larger markets for the seller
Increased ability to search (for the buyer)
Removes the need to choose a price for a product
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Design of Auction: Auction Design of Auction: Auction FormatsFormatsDutch auction (D) (e.g, www.landsend.com;
http://www.vbn.nl/en/overvbn/index.asp )
First-price sealed-bid auction (F) (e.g., US Treasury bills, supply contracts; government procurement (10% GDP))
Second-price sealed-bid (Vickrey) auction (S) (e.g., www.sandafayre.com; NZ’s communication spectrum rights)
English auction (E) (e.g., www.ebay.com ; www.yahoo.com )
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Two Fundamental QuestionsTwo Fundamental Questions
Which auction pairs are strategically equivalent?Types A and B are strategically equivalent if an
identical bidder would follow the same strategy
Which auction pairs are revenue equivalent?Types A and B are revenue equivalent if they yield
the same expected revenue
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William VickreyWilliam Vickrey
WILLIAM VICKREY 1996 Nobel Laureate in Economics
for fundamental contributions to the economic theory of incentives under asymmetric information.
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Independent Private-ValueIndependent Private-Value AuctionAuctionBuyers are risk-neutral
Buyers WTPs are independent of each other and drawn from a uniform distribution
What will be the optimal bidding strategies in the following auction formats:Open English auction?Second-price sealed bid (or the so-called Vickrey
auction)?
),0( WTP
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Strategic Equivalence TheoremStrategic Equivalence Theorem Buyers’ bidding strategies are identical in open English and
second-price sealed-bid auction (except for the winner)
Second-price sealed bid auction
Optimal bid for all bidders =
English auction
Optimal bid for all bidders except the winner =
Optimal bid for the winner =
Revenue =
Buyers’ bidding strategies are identical in Dutch and first-price sealed-bid auction
Optimal bid for bidder i =
Revenue =
iWTPn
n
1
iWTP
)(
1nWTP
n
n
)1( nWTP)1( nWTP
iWTP
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Expected KExpected Kthth Highest Value Highest ValueLet buyer WTPs (independently drawn from an uniform
distribution) are denoted by WTP1, WTP2, …, WTPn-1,
WTPn
Arrange them in an ascending order and denote ranked bids by WTP(1), WTP(2), …, WTP(n-1), WTP(n). That is, we have WTP(1) < WTP(2) < …< WTP(n-1) < WTP(n)
Expected Kth Highest Value: WTP
n
kWTPE k
1)( )(
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Revenue Equivalence Revenue Equivalence TheoremTheorem
Expected revenue is identical in open English and second-price sealed-bid auctions Expected Revenue =
Expected revenue is identical in Dutch and first-price sealed-bid auctions Expected Revenue =
Expected revenue is identical in Dutch, English, first-price, and second-price sealed-bid auctions IPV Rational, risk-neutral bidders
WTPn
nWTPE n
1
1)( )1(
WTPn
n
n
nWTP
n
nE n
1
1)
1( )(
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What Happen When Assumptions Fail?What Happen When Assumptions Fail?
Model Revenue Rankings
IPV and risk neutrality D = F = S = E
IPV & risk aversion D = F > S = E
Affiliated privately known WTPs and risk neutrality
D = F < S = E
Affiliated, privately unknown WTPs and risk neutrality
D = F < S < E
Privately unknown values are those where a bidder is uncertain about his own WTP until the auction is over, although he or she does have some noisy signal of his or her WTP
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Why Does Ebay Choose Why Does Ebay Choose English Auction?English Auction? In low-priced items, bidders are likely to be risk neutral
In these cases, English auction has the highest expected seller revenue
Note that Ebay’s revenue increases with seller revenue
Thus, the choice of English auction is consistent with revenue maximization for Ebay
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A Field TestA Field Test
Are Dutch and First-Price sealed-bid auctions “revenue equivalent?”
What might this imply for internet auction design?
Are English and Second-Price auctions “revenue equivalent?”
What might this imply for internet auction design?
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Dutch versus First Price Dutch versus First Price AuctionAuction
First - Dutch Dutch - First
Number of Observations
87 86
Dutch higher 63 59
Equal revenue 12 5
First-price higher 12 22
Mean Dutch-First price difference
$0.38 $0.25
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English versus Second-English versus Second-price Auctionprice Auction
English - Second Second - English
Number of Observations
66 98
English higher 20 65
Equal revenue 8 9
Second-price higher
38 24
Mean English-Second price difference
-$0.09 $0.85
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Internet Auction SitesInternet Auction Sites
Types of productsProducts in limited supply
Instances where demand is unknown to the seller
Types of revenue model80% appear to be “listing sites,” most others “merchant sites”
Types of auction format85% English auction, 14% first-price sealed bid, 1% Dutch
Why second-price sealed auction (Vickrey) is uncommon?
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Common-Value AuctionsCommon-Value AuctionsSo far, we analyze only private-value auctions
In many industrial settings, firms engage in the so-called common value auctions (e.g., oil leases, resellers)
Ex ante, bidders have different guesses about how much the item is objectively worth
Ex post, all bidders have the same ex post valuation for the good
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In-Class Experiment on In-Class Experiment on Common-Value AuctionCommon-Value Auction In-class bidding for a jar of coins
Write down your nameProvide an estimate for its worthSubmit a bid for the item
First-price sealed-bid auction: Highest bidder wins and pays what he/she bids
A prize of $10 for the person who has the most accurate estimate
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Name:__________________________
Estimate: __________________________
Bid: __________________________
Your Response on Index CardYour Response on Index Card
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Winner’s CurseWinner’s CurseWinner’s curse occurs when the winner’s bid is higher
than the true value of the object. Winning the bid but lose money!
Robust phenomenon; occurs frequently both in experiments and in real life
Optimal Bidding Strategy The less information you have compared with that your
opponents have, the lower your bid ought to be The more uncertain about the true value, the lower you should
bid The more bidders that show up for the auction, the lower you
should bid
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PunchlinePunchlineStrategic and revenue equivalence theorems
English is the most prevalent in internet auctions English auction induces truthful revelation of WTPs (i.e.,
Revelation Principle)
English auction gives the highest expected revenue when bidders are risk neutral
Beware of winner’s curse in common-value auction!
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