1. week 7 1 COS 444 Internet Auctions: Theory and Practice Spring 2008 Ken Steiglitz ken@cs.princeton.edu

2. week 72 Theory Conditional expectation Conditional expectation Interpretation of first-price equilibrium Interpretation of first-price equilibrium Stronger revenue equivalence Stronger revenue equivalence Graphical interpretation Graphical interpretation Check RE for all-pay auction Check RE for all-pay auction

3. week 73 Theory : Revenue equivalence III If P(v) = E[pay] as a function of v,

5. week 75 Theory: Preference revelation Theorem: A symmetric equilibrium bidding function in an IPV auction is monotonically nondecreasing. Proof: Follows directly from definition of equilibrium! (… if it exists)

6. week 76 Theory: Entry Value Define: Entry Value = v * = value at which it becomes advantageous to enter an auction. Example: FP, no reserve: v * = 0 Example: FP, reserve = 0.5: v * = 0.5

7. week 77 Field experiment “A Test of the Revenue Equivalence Theorem using Field Experiments on eBay” T. Hossain, J. Morgan, 2004 Theory predicts revenue equivalence for a wide class of auctions with the same entry value. This paper uses eBay to field-test this prediction.

8. week 78 Hypothesis testing  We often need to test the statistical significance of observations (as in Hossein- Morgan 04)  This is a huge subject  Many common tests use normal distributions and their derivatives  The one-tailed binomial test is the simplest  Such tests can easily be abused