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Revenue analysis of a family of ranking rules for keyword auctions

Revenue analysis of a family of ranking rules for keyword auctions,10.1145/1250910.1250918,Sébastien Lahaie,David M. Pennock

Revenue analysis of a family of ranking rules for keyword auctions   (Citations: 32)
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Keyword auctions lie at the core of the business models of today's leading search engines. Advertisers bid for place- ment alongside search results, and are charged for clicks on their ads. Advertisers are typically ranked according to a score that takes into account their bids and potential click- through rates. We consider a family of ranking rules that contains those typically used to model Yahoo! and Google's auction designs as special cases. We find that in general neither of these is necessarily revenue-optimal in equilib- rium, and that the choice of ranking rule can be guided by considering the correlation between bidders' values and click-through rates. We propose a simple approach to deter- mine a revenue-optimal ranking rule within our family, tak- ing into account effects on advertiser satisfaction and user experience. We illustrate the approach using Monte-Carlo simulations based on distributions fitted to Yahoo! bid and click-through rate data for a high-volume keyword.
Conference: ACM Conference on Electronic Commerce - EC , pp. 50-56, 2007
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    • ...Previous work by Lahaie [1] modeled and analyzed a family of ranking rules of the form ������×������ ∝ . This family of rules includes the old Yahoo value per click, the current value per impression model used by most search engines, as well as combinations of the two.,In this paper, we reproduce the simulations and results of [1] and then extend the model they used to include what we call the pollution effect, the impact of repeatedly showing searchers irrelevant advertisements that do not attract clicks.,Our new model that includes a pollution effect is a simple and reasonable extension of the model used in [1].,Our work can be seen as building on the work of [1], using a similar model, comparable Monte-Carlo simulations, and their probability distributions derived from Yahoo data.,Lahaie [5] describes a theoretical framework on which his later work [1] was based.,Alpha values in the range [0,1] yield models that are combinations of the old and new Yahoo ranking functions, and so weight bids more heavily than is common.,Since we reproduce the results of previous work [1] as well as extending it, we explore negative alpha values in the range [-2, 0] as the earlier work did, but we should note that those ranking functions are usually considered impractical given that they have an undesirable effect of strongly favoring advertisements that get few clicks.,As in [1] and as supported by [3], we assume that bidders are playing the smallest symmetric equilibrium, which causes bidders to be ranked in decreasing order of ����×������������ , where ����= (��������) ∝ and ������������ is the unknown true value of a click to the bidder.,For further discussion of symmetric equilibrium (which is sometimes referred to as “locally envy-free equilibrium”) and truth telling in advertising auctions, we refer the reader to [1], [2], [3], [4], and [12].,Please see [1] for further discussion of symmetric equilibrium and the derivation of revenue as a function of advertiser value.,[1]) assumed that the relevance distribution of the ads is independent of the setting of alpha.,In the Monte-Carlo simulation, for additional realism, we used the marginal distributions from [1] that the authors derived from empirical Yahoo bid and clickthrough data for a high volume keyword.,The empirical data from [1] showed a positive Spearman correlation of 0.4 between the value of an advertisement to an advertiser and the CTR of the ad. We used a Gaussian copula – a method from finance of creating a joint distribution from two marginal distributions – to allow the Monte-Carlo simulation to represent this dependence.,We modeled position bias using the positional effects observed in Yahoo empirical data from [1].,Before we attempted to analyze the impact of the pollution effect, we ran our simulations using these parameters, which we sought to make identical to the parameters used in [1].,Specifically, we set the beta parameter of the relevance beta distribution at 25.43, as derived in [1] for empirical data when alpha was 1, but then we change the beta parameter over the range [18.43,46.43] as alpha changes in the range [-2, 2]. This smoothly shifts the CTR distribution to the left as alpha drops to 0 and below, representing the decreasing likelihood that searchers will view and click on ads after continually being shown ...,The results from the first group of simulations establishes that the optimal setting of alpha to maximize revenue is 0 when ranking advertisements by ������×������ ∝ . This confirms the results of previous work [1] where their simulations also found an optimal setting of alpha at 0. Figure 4 below shows total revenue normalized to the range [0,1] for alpha in the range [-2,2] using Yahoo‟s empirically observed correlation of 0.4 ...,The results from the first group of simulations establishes that the optimal setting of alpha to maximize revenue is 0 when ranking advertisements by ������×������ ∝ . This confirms the results of previous work [1] where their simulations also found an optimal setting of alpha at 0. Figure 4 below shows total revenue normalized to the range [0,1] for alpha in the range [-2,2] using Yahoo‟s empirically observed correlation of 0.4 ...,In the other direction, we found that if the shift in the CTR distributions are 20% higher, then the revenue curve in Figure 7 changes to slope upward beyond an alpha of 1, suggesting that alpha in the range [1,2] is optimal...

    Greg Lindenet al. The Pollution Effect: Optimizing Keyword Auctions by Favoring Relevant...

    • ...Setting this weight equal to the advertiser’s relevance recovers the standard rank-by-revenue model; setting it equal to 1 recovers rank-by-bid [11]...

    John Langfordet al. Maintaining Equilibria During Exploration in Sponsored Search Auctions

    • ...From the static models, extensions have considered dynamic variations, often evaluated through simulation [12,30,39]...
    • ...Lahaie and Pennock [30] introduce a family of ranking algorithms that can interpolate between rank-by-bid and rank-by-revenue...
    • ...The ranking method in TAC/AA uses the Lahaie and Pennock [30] parameterization...

    Patrick R. Jordanet al. Designing an Ad Auctions Game for the Trading Agent Competition

    • ...We can nd also AGG representations of Lahaie and Pennock’s family of ranking rules [25] by adjusting the values of appropriately...

    David Robert Martin Thompsonet al. Computational analysis of perfect-information position auctions

    • ...In the context of the separable model, [2, 12] and [13] compared various bid weighing procedures regarding their revenue properties...

    Renato Gomeset al. Externalities in Keyword Auctions: An Empirical and Theoretical Assess...

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