Introduction to Auctions

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Introduction to Auctions

• David M. Pennock

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Auctions yesterday
3
Auctions today

• Ebay
• 4 million auctions
• 450k new/day
• 800 others
• auctionrover.com
• biddersedge.com

4
Auctions yesterday vs. today
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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

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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

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Why auctions?

• For object of unknown value
• Flexible
• Dynamic
• Mechanized
• reduces complexity of negotiations
• ideal for computer implementation
• Economically efficient!

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Taxonomy of common auctions

• Open auctions
• English
• Dutch
• Sealed-bid auctions
• first price
• second price (Vickrey)
• Mth price, M1st price
• continuous double auction

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English auction

• Open
• One item for sale
• Auctioneer begins low typically with sellers
  reserve price
• Buyers call out bids to beat the current price
• Last buyer remaining winspays the price that
  (s)he bid

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Dutch auction

• Open
• One item for sale
• Auctioneer begins highabove the maximum
  foreseeable bid
• Auctioneer lowers price in increments
• First buyer willing to accept price winspays
  last announced price
• less information

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Sealed-bid first price auction

• All buyers submit their bids privately
• buyer with the highest bid winspays the price
  (s)he bid

?
150
120
90
50
12
Sealed-bid second price auction (Vickrey)

• All buyers submit their bids privately
• buyer with the highest bid winspays the price
  of the second highest bid

Only pays 120
?
150
120
90
50
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Incentive compatibility

• Telling the truth is optimal in second-price
  auction
• Suppose your value for the item is 100if 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

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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.

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Revenue equivalence

• Which auction is best for the seller?
• In second-price auction, buyer pays
• 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

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Mth price auction

• English, Dutch, 1st price, 2nd priceN 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
• let x min(n,m)
• the x highest buy offers and x lowest sell offers
  win

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Mth price auction

• Buy offers (N4)

• Sell offers (M5)

300
150
170
120
130
90
110
50
80
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Mth price auction

• Buy offers (N4)

• Sell offers (M5)

1
300
170
2
150
3
?
130
4
price 120
120
5
?
110
?
90
80
?
50

• Winning buyers/sellers

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M1st price auction

• Buy offers (N4)

• Sell offers (M5)

1
300
170
2
150
3
?
130
4
120
5
?
price 110
110
?
6
90
80
?
50

• Winning buyers/sellers

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Incentive compatibility

• M1st price auction is incentive compatible for
  buyers
• buyers dominant strategy is to bid truthfully
• M1 is Vickrey second-price auction
• Mth price auction is incentive compatible for
  sellers
• sellers dominate strategy is to make offers
  truthfully

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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

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k-double auction

• Buy offers (N4)

• Sell offers (M5)

1
300
170
2
150
3
?
130
4
price 110 10k
120
5
?
110
?
6
90
80
?
50

• Winning buyers/sellers

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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

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Continuous double auction
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Winners 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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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)...

27
Prediction auctionsIowa Electronic Markets
http//www.biz.uiowa.edu/iem
1 if Hillary Clinton wins
1 if Rick Lazio wins
1 if Rudy Giuliani wins
28
Prediction auction gamesHollywood Stock Exchange
http//www.hsx.com/
29
Prediction auction gamesForesight Exchange
http//www.ideosphere.com/
1 iff Cancer curedby 2010
Canada breaks upby 2020
Machine Go championby 2020
http//www.us.newsfutures.com/
http//www.100world.com/
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Prediction markets