Cos 444 internet auctions theory and practice
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COS 444 Internet Auctions: Theory and Practice. Spring 2008 Ken Steiglitz ken@cs.princeton.edu. Mechanics. COS 444 home page Classes: - experiments - discussion of papers (empirical, theory): you and me - theory (blackboard) Grading:

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COS 444 Internet Auctions: Theory and Practice

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COS 444 Internet Auctions:Theory and Practice

Spring 2008

Ken Steiglitz

ken@cs.princeton.edu


Mechanics

  • 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


Background

  • Freshman calculus, integration by parts

  • Basic probability, order statistics

  • Statistics, significance tests

  • Game theory, Nash equilibrium

  • Java or UNIX tools or equivalent


Why study auctions?

  • 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


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; …


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.


Auctions: Methods of Study

  • Theory (1961--)

  • Empirical observation (recent on internet)

  • Field experiments (recent on internet)

  • Laboratory experiments (1980--)

  • Simulation (not much)

  • fMRI (?)


History


History


History


History


History


History


History

Route 6: Long John Nebel pitching hard


Standard theoretical setup

  • 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


English auctions: variations

  • Outcry ( jump bidding allowed )

  • Ascending price

  • Japanese button

Truthful bidding is dominant in Japanese button auctions


Vickrey Auction: sealed-bid second-price

William Vickrey, 1961

Vickrey wins Nobel Prize, 1996


Truthful bidding is dominant in Vickrey auctions

Japanese button and Vickrey auctions are (weakly) strategically equivalent


Dutch descending-price

Aalsmeer flower market, Aalsmeer, Holland, 1960’s


Sealed-Bid First-Price

  • Highest bid wins

  • Winner pays her bid

    How to bid? How to choose bidding function

    Notice: bidding truthfully is now pointless


Enter John Nash

  • Equilibrium translates question of human behavior to math

  • Howmuch to shade?

Nash wins Nobel Prize, 1994


Equilibrium

  • 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.


Simple example: first-price

  • n=2bidders

  • v1 and v2uniformlydistributed 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[ ]”


Verifying a guess

  • 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] =

    Bidders 1’s best choice of bid is b =v1 / 2 … QED.


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