COS 444 Internet Auctions Theory and Practice Spring

COS 444 Internet Auctions: Theory and Practice Spring 2009 Ken Steiglitz ken@cs. princeton. edu week 2 1

Evolution of e. Bay • Cassady on executing the (English) bid - signals • Book bids (anticipating e. Bay) - ticks or increments - reserves - the integrity of the auctioneer… and e. Bay as a trusted third party • Mail-bid sales, disincentives to value revelation - bid-taker cheating; future use Buy-or-Bid sales (cf Buy-It-Now on e. Bay) week 2 2

Terms of sale • • • Estimates often given Prices realized often available Reserves often 60% Mail-bid: increment policies often vague English: Buyer’s fee often 10% week 2 3

What to post in a second-price online auction? Suppose you post highest bid so far, and winner pays second price: bidder 1 bids $1 bidder 2 bids $100 There is no further incentive to bid above $1, and bidder 2 steals the item at $1 week 2 4

Evolution of e. Bay (Summary) English book bids mail-bid sales pay second price online pay and post second price + deadline week 2 5

Online variations • Auctions with extendable closing rules: Amazon, Yahoo (auctions now gone), others? • Taobao, the Chinese online auction site (“California auction” is an abstraction of e. Bay) week 2 6

Expected revenue Vickrey auction: what price does the seller expect? (values uniform, iid on [0, 1]) E[revenue] = E[2 nd highest of 2 draws] = week 2 7

Expected revenue Vickrey auction: what price does the seller expect? (values uniform, iid on [0, 1]) E[revenue] = E[2 nd highest of 2 draws] = 1/3 (to be proven soon) week 2 8

Continuing theory: E[revenue] First-price auction: what price does the seller expect? (values uniform, iid on [0, 1]) In equilibrium (nota bene): E[revenue from 1] = Average over all v 1 , multiply by 2 1/3 week 2 SAME AS VICKREY! 9

Probability setting • pdf • cdf “atomless” • Expectation week 2 10

Probability setting • Almost universal assumption: range normalized to [0, 1] • Common assumption for examples, etc. , v ’s “uniformly distributed on [0, 1]” , which means f (x ) = 1 , F (x ) = x and iid = “independently and identically distributed” week 2 11