Introduction to Auctions David M. Pennock

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

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

Auctions: yesterday vs. today

What is an auction? 4 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. 4 Examples:

B2B auctions and ecommerce 4 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? 4 For object of unknown value 4 Flexible 4 Dynamic 4 Mechanized –reduces complexity of negotiations –ideal for computer implementation 4 Economically efficient!

Taxonomy of common auctions 4 Open auctions –English –Dutch 4 Sealed-bid auctions –first price –second price (Vickrey) –Mth price, M+1st price –continuous double auction

English auction 4 Open 4 One item for sale 4 Auctioneer begins low; typically with seller’s reserve price 4 Buyers call out bids to beat the current price 4 Last buyer remaining wins; pays the price that (s)he bid

Dutch auction 4 Open 4 One item for sale 4 Auctioneer begins high; above the maximum foreseeable bid 4 Auctioneer lowers price in increments 4 First buyer willing to accept price wins; pays last announced price 4 less information

Sealed-bid first price auction 4 All buyers submit their bids privately 4 buyer with the highest bid wins; pays the price (s)he bid $150 $120 $90 $50 

Sealed-bid second price auction (Vickrey) 4 All buyers submit their bids privately 4 buyer with the highest bid wins; pays the price of the second highest bid $150 $120 $90 $50  Only pays $120

Incentive compatibility 4 Telling the truth is optimal in second-price auction 4 Suppose your value for the item is $100; if you win, your net gain (loss) is $100 - price 4 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 4 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 4 Dominant optimal strategy: bid $100 –Key: the price you pay is out of your control

Collusion 4 Notice that, if some bidders collude, they might do better by lying (e.g., by forming a ring) 4 In general, essentially all auctions are subject to some sort of manipulation by collusion among buyers, sellers, and/or auctioneer.

Revenue equivalence 4 Which auction is best for the seller? 4 In second-price auction, buyer pays < bid 4 In first-price auction, buyers “shade” bids 4 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 4 English, Dutch, 1st price, 2nd price: N buyers and 1 seller 4 Generalize to N buyers and M sellers 4 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 4 Buy offers (N=4) 4 Sell offers (M=5) $80

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

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

Incentive compatibility 4 M+1st price auction is incentive compatible for buyers –buyers’ dominant strategy is to bid truthfully –M=1 is Vickrey second-price auction 4 Mth price auction is incentive compatible for sellers –sellers’ dominate strategy is to make offers truthfully

Impossibility 4 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 4 Buy offers (N=4) 4 Sell offers (M=5)     4Winning buyers/sellers 6 price = $110 + $10*k

Continuous double auction 4 k-double auction repeated continuously over time 4 buyers and sellers continually place offers 4 as soon as a buy offer > a sell offer, a transaction occurs 4 At any given time, there is no overlap btw highest buy offer & lowest sell offer

Continuous double auction

Winner’s curse 4 Common, unknown value for item (e.g., potential oil drilling site) 4 Most overly optimistic bidder wins; true value is probably less

Combinatorial auctions 4 E.g.: spectrum rights, computer system, … 4 n goods  bids allowed  2 n combinations Maximizing revenue: NP-hard (set packing) 4 Enter computer scientists (hot topic)...

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