1. week 4 1 COS 444 Internet Auctions: Theory and Practice Spring 2008 Ken Steiglitz ken@cs.princeton.edu

2. week 42 Theory First-Price equilibrium: Intuition First-Price equilibrium: Intuition Third-Price equilibrium: Intuition Third-Price equilibrium: Intuition Why study third-price auctions? Why study third-price auctions? (Kagel-Levin 93, more later) (Kagel-Levin 93, more later)

3. week 43 Theory Equilibrium on First-Price auctions Baseline IPV model, values iid as F (v) E[surplus of 1] = pr[1 wins][ v 1 – b ( v 1 ) ] pr[1 wins][ v 1 – b ( v 1 ) ] Bidder 2 bids  (v)

4. week 44 Theory The equilbrium condition is that

5. week 45 Theory This leads to a linear, first-order differential equation for b(v) :

6. week 46 Theory Solution: …optimal shade …optimal shade

9. week 49 eBay observed Assignment 2 provides a tool for visualizing behavior… Assignment 2 provides a tool for visualizing behavior… Some examples: Some examples:

10. week 410 Early bidding vs. Sniping But early bidding affects behavior But early bidding affects behavior WAR

12. week 412 Dangers of early bidding, con’t As bait

14. week 414 Dangers of early bidding, con’t Curiosity

16. week 416 A (likely) shill Bidder 3 bids $94 when the reserve is $95 and the high bid is below that. She has feedback of 1. A likely shill. Bidder 3 bids $94 when the reserve is $95 and the high bid is below that. She has feedback of 1. A likely shill. Reserve = $95 ______