91b75fb137f78170c3b7f56e91319fec.ppt
- Количество слайдов: 30
Introduction to Auctions David M. Pennock
Auctions: yesterday Going once, … going twice, . . .
Auctions: today Ebay: – 4 million auctions – 450 k new/day >800 others – auctionrover. com – biddersedge. com
Auctions: yesterday vs. today
What is an auction? Definition [Mc. Afee & Mc. Millan, 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:
B 2 B auctions and ecommerce Online B 2 B 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+1 st 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 Only pays $120 $150 $120 $90 $50
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 = 2 nd price; Dutch = 1 st price
Mth price auction English, Dutch, 1 st price, 2 nd 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 Buy offers (N=4) Sell offers (M=5) $300 $150 $120 $170 $130 $90 $110 $50 $80
Mth price auction Buy offers (N=4) Sell offers (M=5) $300 1 $170 2 3 $150 $130 4 5 $120 $110 $90 $80 $50 price = $120 Winning buyers/sellers
M+1 st price auction Buy offers (N=4) Sell offers (M=5) $300 1 $170 2 3 $150 $130 4 5 $120 $110 6 $90 $80 $50 price = $110 Winning buyers/sellers
Incentive compatibility M+1 st 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
k-double auction Buy offers (N=4) Sell offers (M=5) $300 1 $170 2 3 $150 $130 4 5 $120 $110 6 $90 $80 $50 price = $110 + $10*k Winning buyers/sellers
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
Combinatorial auctions E. g. : spectrum rights, computer system, … n goods bids allowed 2 n combinations Maximizing revenue: NP-hard (set packing) Enter computer scientists (hot topic). . .
Prediction auctions Iowa Electronic Markets http: //www. biz. uiowa. edu/iem $1 if Hillary Clinton wins $1 if Rick Lazio wins $1 if Rudy Giuliani wins
Prediction auction games Hollywood Stock Exchange http: //www. hsx. com/
Prediction auction games Foresight Exchange http: //www. ideosphere. com/ $1 iff Cancer cured by 2010 Machine Go champion by 2020 Canada breaks up by 2020 http: //www. us. newsfutures. com/ http: //www. 100 world. com/
Prediction markets