1. week 1 1 COS 444 Internet Auctions: Theory and Practice Spring 2008 Ken Steiglitz ken@cs.princeton.edu

2. week 12 Mechanics COS 444 home page COS 444 home page COS 444 home page COS 444 home page Classes: Classes: - experiments - experiments - discussion of papers (empirical, theory): - discussion of papers (empirical, theory): you and me you and me - theory (blackboard) - theory (blackboard)  Grading: - problem set assignments, programming - problem set assignments, programming assignments assignments - class work - class work - term paper - term paper

3. week 13 Background Freshman calculus, integration by parts Freshman calculus, integration by parts Basic probability, order statistics Basic probability, order statistics Statistics, significance tests Statistics, significance tests Game theory, Nash equilibrium Game theory, Nash equilibrium Java or UNIX tools or equivalent Java or UNIX tools or equivalent

4. week 14 Why study auctions? Auctions are trade; trade makes civilization possible Auctions are trade; trade makes civilization possible Auctions are for selling things with uncertain value Auctions are for selling things with uncertain value Auctions are a microcosm of economics Auctions are a microcosm of economics Auctions are algorithms run on the internet Auctions are algorithms run on the internet Auctions are a social entertainment Auctions are a social entertainment

5. week 15 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)

6. week 16 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. week 17 Auctions: Methods of Study Theory (1961--) Theory (1961--) Empirical observation (recent on internet) Empirical observation (recent on 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 (?)

8. week 18History

9. 9 History

10. 10History

11. week 111 History

12. week 112History

13. week 113History

14. week 114History Route 6: Long John Nebel pitching hard

15. week 115 Standard theoretical setup One item, one seller One item, one seller n bidders n bidders Each has value v i Each has value v i Each wants to maximize her Each wants to maximize her surplus i = v i – payment i surplus i = v i – payment i  Values usually randomly assigned  Values may be interdependent

16. week 116 English auctions: variations Outcry ( jump bidding allowed ) Outcry ( jump bidding allowed ) Ascending price Ascending price Japanese button Japanese button Truthful bidding is dominant in Japanese button auctions

17. week 117 Vickrey Auction: sealed-bid second-price Vickrey wins Nobel Prize, 1996 William Vickrey, 1961

18. week 118 Truthful bidding is dominant in Vickrey auctions Japanese button and Vickrey auctions are (weakly) strategically equivalent

19. week 119 Dutch descending-price Aalsmeer flower market, Aalsmeer, Holland, 1960’s

20. week 120 Sealed-Bid First-Price Highest bid wins Highest bid wins Winner pays her bid Winner pays her bid How to bid? How to choose bidding function Notice: bidding truthfully is now pointless

21. week 121 Enter John Nash Equilibrium translates question of human behavior to math Equilibrium translates question of human behavior to math How much to shade? How much to shade? Nash wins Nobel Prize, 1994

22. week 122 Equilibrium A strategy (bidding function) is a (symmetric) equilibrium if it is a best response to itself. 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. That is, if all others adopt the strategy, you can do no better than to adopt it also.

23. week 123 Simple example: first-price n=2 bidders n=2 bidders v 1 and v 2 on [0,1] v 1 and v 2 uniformly distributed on [0,1] Find b (v 1 ) for bidder 1 that is best response to b (v 2 ) for bidder 2 in the sense that Find b (v 1 ) for bidder 1 that is best response to b (v 2 ) for bidder 2 in the sense that E [surplus ] = max E [surplus ] = max  We need “uniformly distributed” and “E[ ]”

24. week 124 Verifying a guess Assume for now that v/ 2 is an equilibrium strategy Assume for now that v/ 2 is an equilibrium strategy Bidder 2 bids v 2 / 2 ; Fix v 1. What is bidder 1’s best response b (v 1 ) ? Bidder 2 bids v 2 / 2 ; Fix v 1. What is bidder 1’s best response b (v 1 ) ? E[surplus] = Bidders 1’s best choice of bid is b = v 1 / 2 … QED.