COS 444 Internet Auctions: Theory and Practice

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 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.

COS 444 Internet Auctions: Theory and Practice