April 22, 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 22, 2006

2

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

April 22, 2006

3

Teck-Hua Ho

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

April 22, 2006

4

Teck-Hua Ho

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

April 22, 2006

5

Teck-Hua Ho

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

April 22, 2006

6

Teck-Hua Ho

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

April 22, 2006

7

Teck-Hua Ho

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 )

April 22, 2006

8

Teck-Hua Ho

http://www.vbn.nl/en/overvbn/veilingen/index.asp

April 22, 2006

9

Teck-Hua Ho

http://www.landsend.com/cd/ov/otc/IndexPage/0,,4_6_0_,00.html?sid=4442138515955145040

April 22, 2006

10

Teck-Hua Ho

http://www.sandafayre.com/html/aboutauc.htm

MAKE SURE YOU COVER THE PARAGRAPH ON HOW DO OUR AUCTIONS WORK

April 22, 2006

11

Teck-Hua Ho

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

April 22, 2006

12

Teck-Hua Ho

William VickreyWilliam Vickrey

WILLIAM VICKREY                                                         1996 Nobel Laureate in Economics

for fundamental contributions to the economic theory of incentives under asymmetric information.

April 22, 2006

13

Teck-Hua Ho

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

April 22, 2006

14

Teck-Hua Ho

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

April 22, 2006

15

Teck-Hua Ho

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)( )(

April 22, 2006

16

Teck-Hua Ho

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( )(

April 22, 2006

17

Teck-Hua Ho

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

April 22, 2006

18

Teck-Hua Ho

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

April 22, 2006

19

Teck-Hua Ho

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?

April 22, 2006

20

Teck-Hua Ho

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

April 22, 2006

21

Teck-Hua Ho

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

April 22, 2006

22

Teck-Hua Ho

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?

April 22, 2006

23

Teck-Hua Ho

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

April 22, 2006

24

Teck-Hua Ho

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

April 22, 2006

25

Teck-Hua Ho

Name:__________________________

Estimate: __________________________

Bid: __________________________

Your Response on Index CardYour Response on Index Card

April 22, 2006

26

Teck-Hua Ho

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

April 22, 2006

27

Teck-Hua Ho

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!