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Introduction to Auctions

Introduction to Auctions. David M. Pennock. Going once, … going twice,. Auctions: yesterday. Ebay: 4 million auctions 450k new/day >800 others auctionrover.com biddersedge.com. Auctions: today. Auctions: yesterday vs. today. What is an auction?.

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Introduction to Auctions

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  1. Introduction to Auctions David M. Pennock

  2. Going once, … going twice, ... Auctions: yesterday

  3. Ebay: 4 million auctions 450k new/day >800 others auctionrover.com biddersedge.com Auctions: today

  4. Auctions: yesterday vs. today

  5. 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:

  6. 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

  7. Why auctions? • For object of unknown value • Flexible • Dynamic • Mechanized • reduces complexity of negotiations • ideal for computer implementation • Economically efficient!

  8. Taxonomy of common auctions • Open auctions • English • Dutch • Sealed-bid auctions • first price • second price (Vickrey) • Mth price, M+1st price • continuous double auction

  9. 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 English auction

  10. 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

  11. 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

  12. 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 Only pays $120  $150 $120 $90 $50

  13. 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

  14. 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.

  15. 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

  16. 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

  17. Buy offers (N=4) Sell offers (M=5) Mth price auction $300 $150 $170 $120 $130 $90 $110 $50 $80

  18. Sell offers (M=5) Buy offers (N=4) Mth price auction 1 $300 $170 2 $150 3  $130 4 price = $120 $120 5  $110  $90 $80  $50 • Winning buyers/sellers

  19. Sell offers (M=5) Buy offers (N=4) M+1st price auction 1 $300 $170 2 $150 3  $130 4 $120 5  price = $110 $110  6 $90 $80  $50 • Winning buyers/sellers

  20. 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

  21. 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

  22. Sell offers (M=5) Buy offers (N=4) k-double auction 1 $300 $170 2 $150 3  $130 4 price = $110 + $10*k $120 5  $110  6 $90 $80  $50 • Winning buyers/sellers

  23. 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

  24. Continuous double auction

  25. Winner’s curse • Common, unknown value for item (e.g., potential oil drilling site) • Most overly optimistic bidder wins; true value is probably less

  26. 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/

  30. Prediction markets

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