COS 444 Internet Auctions: Theory and Practice

1. COS 444 Internet Auctions:Theory and Practice Spring 2009 Ken Steiglitz ken@cs.princeton.edu

2. 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

3. Background • Freshman calculus, integration by parts • Basic probability, order statistics • Statistics, significance tests • Game theory, Nash equilibrium • Java or UNIX tools or equivalent

4. 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

5. 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; …

6. 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.

7. Auctions: Methods of Study • Theory (1961--) • Empirical observation (recent on internet) • Field experiments (recent on internet) • Laboratory experiments (1980--) • Simulation (not much) • fMRI (?)

8. History

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14. History Route 6: Long John Nebel pitching hard

15. 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

16. English auctions: variations • Outcry ( jump bidding allowed ) • Ascending price • Japanese button Truthful bidding is dominant in Japanese button auctions Is it dominant in outcry? Ascending price?

17. Vickrey Auction: sealed-bid second-price William Vickrey, 1961 Vickrey wins Nobel Prize, 1996

18. Truthful bidding is dominant in Vickrey auctions Japanese button and Vickrey auctions are (weakly) strategically equivalent

19. Dutch descending-price Aalsmeer flower market, Aalsmeer, Holland, 1960’s

21. 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!

22. Dutch and First-Price auctions are (strongly) strategically equivalent So we have two pairs, comprising the four most common auction forms

23. Enter John Nash • Equilibrium translates question of human behavior to math • Howmuch to shade? Nash wins Nobel Prize, 1994

24. 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”

25. Simple example: first-price • n=2bidders • v1 and v2uniformly 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[ ]”

26. 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.

27. and Hurwicz + Myerson + Maskin win Nobel prize in 2007 for theory of mechanism design

28. New directions: Simulation Agent-Based Simulation of Dynamic Online Auctions,“ H. Mizuta and K. Steiglitz, Winter . Simulation Conference, Orlando, FL, Dec. 10-13, 2000

29. New directions: Sociology M. Shohat and J. Musch “Online auctions as a research tool: A field experiment on ethnic discrimination” Swiss Journal of Psychology62 (2), 2003, 139-145

30. New directions: Category clustering Courtesy 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