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COS 444 COS 444 Internet Auctions:Internet Auctions:Theory and PracticeTheory and Practice

Spring 2008

Ken Steiglitz ken@cs.princeton.edu

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MechanicsMechanics COS 444 home pageCOS 444 home page

Classes:Classes: - experiments- experiments - discussion of papers (empirical, theory): - discussion of papers (empirical, theory): you and meyou and me - theory (blackboard)- theory (blackboard) Grading:Grading: - problem set assignments, programming- problem set assignments, programming assignments assignments - class work - class work - term paper - term paper

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BackgroundBackground

Freshman calculus, integration by Freshman calculus, integration by partsparts

Basic probability, order statisticsBasic probability, order statistics Statistics, significance testsStatistics, significance tests Game theory, Nash equilibriumGame theory, Nash equilibrium Java or UNIX tools or equivalentJava or UNIX tools or equivalent

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Why study auctions?Why study auctions?

Auctions are trade; trade makes Auctions are trade; trade makes civilization possiblecivilization possible

Auctions are for selling things with Auctions are for selling things with uncertain valueuncertain value

Auctions are a microcosm of Auctions are a microcosm of economicseconomics

Auctions are algorithms run on the Auctions are algorithms run on the internetinternet

Auctions are a social entertainmentAuctions are a social entertainment

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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)

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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 Auctions: Methods of StudyStudy

Theory (1961--)Theory (1961--) Empirical observation (recent on Empirical observation (recent on

internet)internet) Field experiments (recent on internet)Field experiments (recent on internet) Laboratory experiments (1980--)Laboratory experiments (1980--) Simulation (not much)Simulation (not much) fMRI (?)fMRI (?)

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HistoryHistory

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HistoryHistory

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HistoryHistory

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HistoryHistory

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HistoryHistory

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HistoryHistory

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HistoryHistory

Route 6: Long John Nebel pitching hard

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Standard theoretical Standard theoretical setupsetup One item, one sellerOne item, one seller nn bidders bidders Each has value Each has value vvii

Each wants to maximize herEach wants to maximize her

surplussurplusii = v = vii – payment – paymentii

Values usually randomly Values usually randomly assignedassigned

Values may be interdependentValues may be interdependent

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English auctions: English auctions: variationsvariations Outcry ( Outcry ( jump biddingjump bidding allowed ) allowed ) Ascending priceAscending price Japanese buttonJapanese button

Truthful bidding is dominant in Japanese button auctions

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Vickrey Auction: sealed-Vickrey Auction: sealed-bid bid second-pricesecond-price

Vickrey wins Nobel Prize, 1996

William Vickrey, 1961

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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-Dutch descending-priceprice

Aalsmeer flower market, Aalsmeer, Holland, 1960’s

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Sealed-Bid First-PriceSealed-Bid First-Price

Highest bid winsHighest bid wins Winner pays her bidWinner pays her bid

How to bid? How to choose bidding How to bid? How to choose bidding function function

Notice: bidding truthfully is now pointlessNotice: bidding truthfully is now pointless

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Enter John NashEnter John Nash

EquilibriumEquilibrium translates question translates question of human of human behaviorbehavior to to mathmath

HowHow much to much to shadeshade??

Nash wins Nobel Prize, 1994

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EquilibriumEquilibrium

A strategy (bidding function) is a A strategy (bidding function) is a (symmetric) equilibrium if it is a (symmetric) equilibrium if it is a best response to itself. best response to itself.

That is, if all others adopt the That is, if all others adopt the strategy, you can do strategy, you can do no no betterbetter than to adopt it also. than to adopt it also.

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Simple example: first-Simple example: first-priceprice n=2n=2 biddersbidders vv11 and and vv22 uniformly distributed on on [0,1][0,1]

Find Find b b ((vv1 1 )) for bidder 1 that is best response for bidder 1 that is best response to to b b ((vv2 2 )) for bidder 2 in the sense that for bidder 2 in the sense that

EE [[surplus surplus ]] = max = max

We need “uniformly distributed” and “E[ ]” We need “uniformly distributed” and “E[ ]”

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Verifying a guessVerifying a guess

Assume for now that Assume for now that v/ 2v/ 2 is an equilibrium is an equilibrium strategystrategy

Bidder 2 bids Bidder 2 bids vv2 2 / 2/ 2 ; Fix ; Fix vv1 1 . What is bidder 1’s . What is bidder 1’s best response best response b b ((vv11 )) ??

E[surplus] = E[surplus] =

Bidders 1’s best choice of bid is Bidders 1’s best choice of bid is b =b = vv11 / 2 / 2 … QED.… QED.

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