Introduction to Auctions

David M. Pennock

Auctions: yesterday

Going once, …going twice, ...

Auctions: today

Ebay:– 4 million auctions

– 450k new/day

>800 others– auctionrover.com

– biddersedge.com

Auctions: yesterday vs. today

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Market Capitalization (billions)

Sotheby's (1744)Ebay (1995)

What is an auction?

Definition [McAfee & McMillan, JEL 1987]: – a market institution with an

– explicit set of rules

– determining resource allocation and prices

– on the basis of bids from the market participants.

Examples:

B2B auctions and ecommerce

Online B2B marketplaces have been established recently for more than a dozen major industries, including the automotive; pharmaceuticals; scientific supplies; asset management; building and construction; plastics and chemicals; steel and metals; computer; credit and financing; energy; news and information; and livestock sectors.

– Reuters March 29, 2000

Why auctions?

For object of unknown value Flexible Dynamic Mechanized

– reduces complexity of negotiations– ideal for computer implementation

Economically efficient!

Taxonomy of common auctions

Open auctions– English– Dutch

Sealed-bid auctions– first price– second price (Vickrey)– Mth price, M+1st price– continuous double auction

English auction

Open One item for sale Auctioneer begins low;

typically with seller’s reserve price Buyers call out bids to beat the current price Last buyer remaining wins;

pays the price that (s)he bid

Dutch auction

Open One item for sale Auctioneer begins high;

above the maximum foreseeable bid Auctioneer lowers price in increments First buyer willing to accept price wins;

pays last announced price less information

Sealed-bid first price auction

All buyers submit their bids privately buyer with the highest bid wins;

pays the price (s)he bid

$150$120

$90

$50

Sealed-bid second price auction (Vickrey) All buyers submit their bids privately buyer with the highest bid wins;

pays the price of the second highest bid

$150$120

$90

$50

Only pays $120

Incentive compatibility Telling the truth is optimal in second-price auction Suppose your value for the item is $100;

if you win, your net gain (loss) is $100 - price If you bid more than $100:

– you increase your chances of winning at price >$100

– you do not improve your chance of winning for < $100

If you bid less than $100:– you reduce your chances of winning at price < $100

– there is no effect on the price you pay if you do win

Dominant optimal strategy: bid $100– Key: the price you pay is out of your control

Collusion

Notice that, if some bidders collude, they might do better by lying (e.g., by forming a ring)

In general, essentially all auctions are subject to some sort of manipulation by collusion among buyers, sellers, and/or auctioneer.

Revenue equivalence

Which auction is best for the seller? In second-price auction, buyer pays < bid In first-price auction, buyers “shade” bids Theorem:

– expected revenue for seller is the same!– requires technical assumptions on buyers,

including “independent private values”– English = 2nd price; Dutch = 1st price

Mth price auction

English, Dutch, 1st price, 2nd price:N buyers and 1 seller

Generalize to N buyers and M sellers Mth price auction:

– sort all bids from buyers and sellers

– price = the Mth highest bid

– let n = # of buy offers >= price

– let m = # of sell offers <= price

– let x = min(n,m)

– the x highest buy offers and x lowest sell offers win

Mth price auction

$150

$120

$90

$50

$300

$170

$130

$110

Buy offers (N=4) Sell offers (M=5)

$80

$50$80

$90$110

$120$130

Mth price auction

$150$170$300

Buy offers (N=4) Sell offers (M=5)

12345

Winning buyers/sellers

price = $120

$50$80

$90$110

$120$130

M+1st price auction

$150$170$300

Buy offers (N=4) Sell offers (M=5)

12345

Winning buyers/sellers

6 price = $110

Incentive compatibility

M+1st price auction is incentive compatible for buyers– buyers’ dominant strategy is to bid truthfully– M=1 is Vickrey second-price auction

Mth price auction is incentive compatible for sellers– sellers’ dominate strategy is to make offers

truthfully

Impossibility

Essentially no auction whatsoever can be simultaneously incentive compatible for both buyers and sellers!– if buyers are induce to reveal their true values,

then sellers have incentive to lie, and vice versa– the only way to get both to tell the truth is to

have some outside party subsidize the auction

$50$80

$90$110

$120$130

k-double auction

$150$170$300

Buy offers (N=4) Sell offers (M=5)

12345

Winning buyers/sellers

6

price = $110 + $10*k

Continuous double auction

k-double auction repeated continuously over time

buyers and sellers continually place offers as soon as a buy offer > a sell offer, a

transaction occurs At any given time, there is no overlap btw

highest buy offer & lowest sell offer

Continuous double auction

Winner’s curse

Common, unknown value for item (e.g., potential oil drilling site)

Most overly optimistic bidder wins; true value is probably less

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$ valuation of item

pro

ba

bil

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Combinatorial auctions

E.g.: spectrum rights, computer system, … n goods bids allowed 2n combinations

Maximizing revenue: NP-hard (set packing) Enter computer scientists (hot topic)...

http://www.biz.uiowa.edu/iem

Prediction auctionsIowa Electronic Markets

$1 if Rudy Giuliani wins

$1 if Hillary Clinton wins

$1 if Rick Lazio wins

Prediction auction gamesHollywood Stock Exchange

http://www.hsx.com/

Prediction auction gamesForesight Exchange

$1 iff Cancer curedby 2010

Machine Go championby 2020

Canada breaks upby 2020

http://www.ideosphere.com/

http://www.us.newsfutures.com/http://www.100world.com/

Prediction markets