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Unformatted text preview: Efficiency and Revenue in Certain Nash Equilibria of Keyword Auctions S ebastien Lahaie lahaies@yahooinc.com Yahoo Research New York, NY 10018 SISHOO 2007 p.1 Sponsored Search SISHOO 2007 p.2 Outline Model for keyword auctions. Efficiency in purestrategy Nash equilibrium. Necessary conditions for equilibrium. Worstcase 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 purestrategy Nash equilibrium. Necessary conditions for equilibrium. Worstcase 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 clickthrough 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 perclick 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. quasilinear. 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 purestrategy Nash equilibrium. Necessary conditions for equilibrium....
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 Fall '09

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