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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