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COS 444 Internet Auctions: Theory and Practice

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COS 444 Internet Auctions:Theory and Practice

Spring 2008

Ken Steiglitz

ken@cs.princeton.edu

- 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

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

- 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; …

... 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.

- Theory (1961--)
- Empirical observation (recent on internet)
- Field experiments (recent on internet)
- Laboratory experiments (1980--)
- Simulation (not much)
- fMRI (?)

Route 6: Long John Nebel pitching hard

- 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

- Outcry ( jump bidding allowed )
- Ascending price
- Japanese button

Truthful bidding is dominant in Japanese button auctions

William Vickrey, 1961

Vickrey wins Nobel Prize, 1996

Truthful bidding is dominant in Vickrey auctions

Japanese button and Vickrey auctions are (weakly) strategically equivalent

Aalsmeer flower market, Aalsmeer, Holland, 1960’s

- Highest bid wins
- Winner pays her bid
How to bid? How to choose bidding function

Notice: bidding truthfully is now pointless

- Equilibrium translates question of human behavior to math
- Howmuch to shade?

Nash wins Nobel Prize, 1994

- 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.

- 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[ ]”

- 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.