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COS 444 Internet Auctions:

Theory and Practice

Spring 2010

Ken Steiglitz ken@cs.princeton.edu

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Mechanics• COS 444 home page

• Classes: - assigned reading: come ready to discuss - theory (ppt + chalk) - practice/discussion/news - experiments

• Grading: - problem sets, programming assignments - class participation - term paper

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Background

• 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?

• 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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Goals

• The central theory, classic papers

• A bigger picture

• Even bigger picture

• Experimental and empirical technique

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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 Study

• 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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Google Ad Auctions – Hal Varian

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Standard theoretical setup• One item, one seller• n bidders

• Each knows her value vi (private value)

• Each wants to maximize her

surplusi = vi – paymenti

• Values usually randomly assigned• Values may be interdependent

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English auctions: variations

• Outcry ( jump bidding allowed )

• Ascending price

• Japanese button

Truthful bidding is dominant in Japanese button auctionsIs it dominant in outcry? Ascending price?

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Vickrey Auction: sealed-bid second-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-price

Aalsmeer flower market, Aalsmeer, Holland, 1960’s

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Sealed-Bid First-Price

• Highest bid wins• Winner pays her bid

How to bid? That is, how to choose bidding function

Notice: bidding truthfully is now pointless!

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Dutch and First-Price auctions are (strongly) strategically equivalent

DUTCHFP

ENGLISHSP

So we have two pairs, comprising the four most common auction forms

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Enter John Nash

• Equilibrium translates question of human behavior to math

• How much to shade?

Nash wins Nobel Prize, 1994

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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.

Note: Cannot call this “optimal”

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Simple example: first-price

• 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 Note: We need some probability theory for

“uniformly distributed” and “E[ ]”

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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] =

… the average is over the values of v2 when 1 wins

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

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2

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and Hurwicz + Myerson + Maskin

win Nobel prize in 2007 for theory of mechanism design

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New directions: SimulationAgent-Based Simulation of Dynamic Online

Auctions,“ H. Mizuta and K. Steiglitz, Winter .

Simulation Conference, Orlando, FL, Dec. 10-13, 2000

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New directions: Sociology

M. Shohat and J. Musch “Online auctions as a research tool: A field experiment on ethnic discrimination” Swiss Journal of Psychology 62 (2), 2003, 139-145

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New directions: Category clusteringCourtesy of Matt Sanders ’09• Categories connected by mutual bidders• Darker lines mean higher probability that

two categories will share bidders• Categories with higher totals near center• Color random• Only top 25% lines by weight are shown• Based on 278,593 recorded auctions from bid histories of 18,000 users