week 21 COS 444 Internet Auctions: Theory and Practice Spring 2009 Ken Steiglitz

week 22 Evolution of eBay Cassady on executing the (English) bid - signals Book bids (anticipating eBay) - ticks or increments - reserves - the integrity of the auctioneer… and eBay 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 eBay)

week 23 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 24 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 25 Evolution of eBay (Summary) English  book bids  mail-bid sales pay second price  online pay and post second price + deadline

week 26 Auctions with extendable closing rules: Amazon, Yahoo (auctions now gone), others? Amazon Taobao, the Chinese online auction siteTaobao (“California auction” is an abstraction of eBay) Online variations

week 27 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 28 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 29 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 SAME AS VICKREY!

week 210 Probability setting pdf cdf Expectation “atomless”

week 211 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”