COS 444 Internet Auctions: Theory and Practice

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COS 444 Internet AuctionsTheory and Practice
Spring 2009 Ken Steiglitz
ken_at_cs.princeton.edu
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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)

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Terms of sale

• Estimates often given
• Prices realized often available
• Reserves often 60
• Mail-bid increment policies often vague
• English Buyers fee often 10

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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

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Evolution of eBay (Summary)

• English ?
• book bids ?
• mail-bid sales pay second price ?
• online pay and post second price deadline

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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
  eBay)

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Expected revenue

• Vickrey auction what price does the seller
  expect? (values uniform, iid on 0,1)
• Erevenue E2nd highest of 2 draws

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Expected revenue

• Vickrey auction what price does the seller
  expect? (values uniform, iid on 0,1)
• Erevenue E2nd highest of 2 draws
• 1/3 (to be proven soon)

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Continuing theory Erevenue

• First-price auction what price does the seller
  expect? (values uniform, iid on 0,1)
• In equilibrium (nota bene)
• Erevenue from 1
• Average over all v1 , multiply by 2 ? 1/3
• SAME AS VICKREY!

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Probability setting

• pdf
• cdf
• Expectation

atomless
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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