COS 444 Internet Auctions: Theory and Practice

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COS 444 Internet AuctionsTheory and Practice
Spring 2008 Ken Steiglitz
ken_at_cs.princeton.edu
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Theory Riley Samuelson 81

• Landmark paper constructs the benchmark theory
  for optimal IPV auctions with reserves
• Elegant and deceptively simple-looking in
  retrospect
• Paradoxically, gets more powerful results more
  easily by generalizing

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Theory Riley Samuelson 81

• The Class of auctions
• One seller, one indivisible object
• Reserve b0 (open reserve)
• N bidders, with valuations vi i1,,n
• Values iid according to cdf F, which is
• strictly increasing, differentiable, with
  support 0,1
• There is a symmetric equilibrium bidding function
  b(v) (which we know must be increasing )
• Highest acceptable bid wins
• Rules are anonymous

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Theory Riley Samuelson 81

• bid as if value z
• Revenue v1 F(z) n-1 - P(z)
• General for the entire class of auctions.
• Then, differentiate wrt z, set to zero at zv,
  impose boundary coundition at v

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Theory Riley Samuelson 81

• leads to revenue at equilibrium
• marginal revenue virtual valuation

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Theory Riley Samuelson 81

• Result All auctions in Riley Samuelsons class
  are revenue equivalent.
• Furthermore, expected revenue depends only on the
  entry value v , which determines the set of
  active bidders

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Reserves Test of benchmark theory

• Field Experiments on the Effects of Reserve
  Prices in Auctions More Magic on the Internet
  Lucking-Reiley, 2000
• Pre-eBay, first-price sealed-bid auctions
• with control over open reserve

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Reserves Test of benchmark theory

• Theory (more to come) predicts that higher
  reserves
• reduces of bidders OK
• decreases prob. of sale OK
• increases price conditional on sale OK
• increases total revenue NO!
• Bidders respond strategically to increased
  reserve OK

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Theory Riley Samuelson 81
quick equilibrium
which gives us immediately
Example