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Unformatted text preview: Efficiency and Revenue in Certain Nash Equilibria of Keyword Auctions S ebastien Lahaie lahaies@yahoo-inc.com Yahoo Research New York, NY 10018 SISHOO 2007 p.1 Sponsored Search SISHOO 2007 p.2 Outline Model for keyword auctions. Efficiency in pure-strategy Nash equilibrium. Necessary conditions for equilibrium. Worst-case bound on efficiency. Revenue in symmetric equilibrium. General case. Restricted family of weights. Efficiency and relevance considerations. SISHOO 2007 p.3 Outline Model for keyword auctions. Efficiency in pure-strategy Nash equilibrium. Necessary conditions for equilibrium. Worst-case bound on efficiency. Revenue in symmetric equilibrium. General case. Restricted family of weights. Efficiency and relevance considerations. SISHOO 2007 p.4 Model K positions, N bidders. The click-through rate of bidder s in positions t is e s x t , i.e. separable into 1. advertiser effect (or relevance ) e s 2. position effect x t ( x 1 > x 2 > . . . > x K ) . Bidder s has per-click value of v s . If bidder s obtains slot t at price of p per click, utility is e s x t ( v s- p ) , i.e. quasi-linear. SISHOO 2007 p.5 Auction Rules The auctioneer assigns a weight w s to each bidder s [Aggarwal et al. 06]. Bidders submit bids (reported values) b s . Bidders are ranked in order of decreasing score w s b s . Bidder s pays per click the lowest bid necessary to maintain its position: w s b s w s +1 b s +1 b s w s +1 w s b s +1 Yahoo model: w s = 1 . Google model: w s = e s . SISHOO 2007 p.6 Efficient Ranking A bidders true score is r s = w s v s . An allocation of slots to bidders : K N maximizes the objective summationdisplay t x t w ( t ) v ( t ) if and only if bidders are ranked in decreasing order of true score. Follows easily from the fact that x 1 > x 2 . . . > x K . If w s = e s , the objective is the total value . SISHOO 2007 p.7 Outline Model for keyword auctions. Efficiency in pure-strategy Nash equilibrium. Necessary conditions for equilibrium....
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