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Nash equilibrium of Google auction

Hal Varian. Nash equilibrium of Google auction. 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.)

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Nash equilibrium of Google auction

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  1. Hal Varian Nash equilibrium of Google auction

  2. Simplified model • Advertiser in slot s pays price ps • (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. Equilibrium • Notation • Equilibrium

  4. 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. “Debt consolidation”

  6. “Chewable vitamins”

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