Transcript COS 444 Internet Auctions: Theory and Practice

COS 444
Internet Auctions:
Theory and Practice
Spring 2008
Ken Steiglitz
[email protected]
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Mechanics
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COS 444 home page
Classes:
- experiments
- discussion of papers (empirical, theory):
you and me
- theory (blackboard)
Grading:
- problem set assignments, programming
assignments
- class work
- term paper
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Background
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Freshman calculus, integration by parts
Basic probability, order statistics
Statistics, significance tests
Game theory, Nash equilibrium
Java or UNIX tools or equivalent
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Why study auctions?
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Auctions are trade; trade makes
civilization possible
Auctions are for selling things with
uncertain value
Auctions are a microcosm of economics
Auctions are algorithms run on the
internet
Auctions are a social entertainment
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Cassady on the romance of auctions (1967)
Who could forget, for example, riding up the Bosporus
toward the Black Sea in a fishing vessel to inspect a fishing
laboratory; visiting a Chinese cooperative and being the
guest of honor at tea in the New Territories of the British
crown colony of Hong Kong; watching the frenzied but
quasi-organized bidding of would-be buyers in an
Australian wool auction; observing the "upside-down"
auctioning of fish in Tel Aviv and Haifa; watching the
purchasing activities of several hundred screaming female
fishmongers at the Lisbon auction market; viewing the
fascinating "string selling" in the auctioning of furs in
Leningrad; eating fish from the Seas of Galilee while seated
on the shore of that historic body of water; …
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Cassady on the romance of auctions (1967)
... observing "whispered“ bidding in such far-flung places
as Singapore and Venice; watching a "handshake" auction
in a Pakistanian go-down in the midst of a herd of dozing
camels; being present at the auctioning of an early Van
Gogh in Amsterdam; observing the sale of flowers by
electronic clock in Aalsmeer, Holland; listening to the chant
of the auctioneer in a North Carolina tobacco auction;
watching the landing of fish at 4 A.M. in the market on the
north beach of Manila Bay by the use of amphibious
landing boats; observing the bidding of Turkish merchants
competing for fish in a market located on the Golden Horn;
and answering questions about auctioning posed by a
group of eager Japanese students at the University of
Tokyo.
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Auctions: Methods of Study
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Theory (1961--)
Empirical observation (recent on internet)
Field experiments (recent on internet)
Laboratory experiments (1980--)
Simulation (not much)
fMRI (?)
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History
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History
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History
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History
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History
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History
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History
Route 6:
Long John
Nebel
pitching
hard
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Standard theoretical setup
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One item, one seller
n bidders
Each has value vi
Each wants to maximize her
surplusi = vi – paymenti
 Values usually randomly assigned
 Values may be interdependent
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English auctions: variations
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Outcry ( jump bidding allowed )
Ascending price
Japanese button
Truthful bidding is dominant
in Japanese button auctions
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Vickrey Auction: sealed-bid
second-price
William Vickrey, 1961
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Vickrey wins Nobel Prize, 1996
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Truthful bidding is dominant in
Vickrey auctions
Japanese button and Vickrey
auctions are (weakly)
strategically equivalent
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Dutch descending-price
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Aalsmeer flower market, Aalsmeer,
Holland, 1960’s
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Sealed-Bid First-Price
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Highest bid wins
Winner pays her bid
How to bid? How to choose bidding function
b(v)
Notice: bidding truthfully is now pointless
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Enter John Nash
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Equilibrium translates
question of human
behavior to math
How much to shade?
Nash wins Nobel Prize, 1994
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Equilibrium
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A strategy (bidding function) is a
(symmetric) equilibrium if it is a best
response to itself.
That is, if all others adopt the strategy,
you can do no better than to adopt it
also.
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Simple example: first-price
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n=2 bidders
v1 and v2 uniformly distributed on [0,1]
Find b (v1 ) for bidder 1 that is best response
to b (v2 ) for bidder 2 in the sense that
E [surplus ] = max
 We need “uniformly distributed” and “E[ ]”
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Verifying a guess
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Assume for now that v/ 2 is an equilibrium strategy
Bidder 2 bids v2 / 2 ; Fix v1 . What is bidder 1’s best
response b (v1 ) ?
E[surplus] =

2b
0
(v1  b)dv2  2b(v1  b)
Bidders 1’s best choice of bid is b = v1 / 2 … QED.
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