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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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PraxisPraxis

Cassady on executing the (English) Cassady on executing the (English) bidbid

Book bids, anticipating eBayBook bids, anticipating eBay Mail-bid salesMail-bid sales Buy-or-Bid sales (cf Buy-It-Now on Buy-or-Bid sales (cf Buy-It-Now on

eBay)eBay) Ticks (= increments)Ticks (= increments)

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Theory: the four basic Theory: the four basic auctionsauctions

English English weakly equivalent toweakly equivalent to

VickreyVickrey

Dutch Dutch strategically equivalent tostrategically equivalent to FP FP

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Theory: truthful biddingTheory: truthful bidding

Truthful bidding is Truthful bidding is weakly dominantweakly dominant in Vickrey auctionsin Vickrey auctions

Truthful bidding is also Truthful bidding is also weakly weakly dominantdominant

in (Japanese button) English in (Japanese button) English auctions, but auctions, but notnot in ascending-price in ascending-price or outcry English auctionsor outcry English auctions

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Theory: probabilityTheory: probability

pdf pdf cdf cdf

Expectation Expectation

xdyyfxwprobxF )(}{)(

)()()()(][ xdFxdxxfxE

f

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Theory:Theory: probabilityprobability

Almost universal assumption: range Almost universal assumption: range normalized to normalized to [0,1][0,1]

Common assumption for examples, Common assumption for examples, etc., etc., v v ’s “’s “uniformly distributed onuniformly distributed on [0,1][0,1]” , which means ” , which means

f f ((x x ) = 1) = 1 , , F F ((x x ) = ) = xx

and and iidiid = “independently and = “independently and identically distributed”identically distributed”

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PraxisPraxis Disincentives to truthful biddingDisincentives to truthful bidding

Evolution of eBay from mail-bid sales Evolution of eBay from mail-bid sales (conceptually anyway)(conceptually anyway)

The "California auction" as an abstractionThe "California auction" as an abstraction

Other online closing rules, Amazon & Other online closing rules, Amazon & Yahoo Yahoo

Taobao, the Chinese online auction site? Taobao, the Chinese online auction site?

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Theory: simplest RETheory: simplest RE Back to Back to n=2 n=2 bidders, uniform iid bidders, uniform iid v v ’s’s E[pay] in SP, when bidders bid truthfully, E[pay] in SP, when bidders bid truthfully,

is average second-priceis average second-price

= 1/3 (to be proved shortly)= 1/3 (to be proved shortly) E[pay] in FP at equilibrium isE[pay] in FP at equilibrium is

E[pay] in FP is average of this over E[pay] in FP is average of this over vv11 == 1/6 times 2 bidders = 1/3 … same as SP1/6 times 2 bidders = 1/3 … same as SP

21210

)2/1()2/1(1

vdvvv