Sponsored Search Auction

def. Sponsored Search Auction. This is a different game layout. Imagine a search engine selling advertisement slots.

• There are $k$ ad slots, with click-thru rate, largest to smallest: ${\alpha }_1,\dots ,{\alpha }_k$
• There are $n$ bidders, for whom the value-per-click is $v_1,\dots ,v_n$. Each bids $b_i$ to get any slot.
• Then, if bidder $i$ is assigned slot $l$ and charged $p_i(\vec{b})$
  • Allocation matrix is $\mathbf{x}$ and ${\mathbf{x}}_{il}=1$
  • price matrix is $\mathbf{p}$ and ${\mathbf{p}}_{il}$ is the price charged

def. Generalized Second Price Auction.