1. SIMS Nash equilibrium of Google auction Hal Varian

2. SIMS Simplified model Advertiser in slot s pays price p s (In Google auction this is bid of the advertiser below but we don’t need that here.) Equilibrium: Each advertiser prefers to be in slot it is in than any other slot. In particular each advertiser doesn’t want to move up or down 1 position. Each advertiser cares about expected profit.

3. SIMS Equilibrium Notation Equilibrium

4. SIMS Pricing recursion and value bounds So prices must satisfy Allows us to solve for equilibrium prices Rearranging –Bid until incremental cost per click exceeds value

5. SIMS “Debt consolidation”

6. SIMS “Chewable vitamins”