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Mohammad Mahdian


Publications by Mohammad Mahdian (bibliography)

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Ghosh, Arpita and Mahdian, Mohammad (2008): Externalities in online advertising. In: Proceedings of the 2008 International Conference on the World Wide Web 2008. pp. 161-168. Available online

Most models for online advertising assume that an advertiser's value from winning an ad auction, which depends on the clickthrough rate or conversion rate of the advertisement, is independent of other advertisements served alongside it in the same session. This ignores an important 'externality effect': as the advertising audience has a limited attention span, a high-quality ad on a page can detract attention from other ads on the same page. That is, the utility to a winner in such an auction also depends on the set of other winners. In this paper, we introduce the problem of modeling externalities in online advertising, and study the winner determination problem in these models. Our models are based on choice models on the audience side. We show that in the most general case, the winner determination problem is hard even to approximate. However, we give an approximation algorithm for this problem with an approximation factor that is logarithmic in the ratio of the maximum to the minimum bid. Furthermore, we show that there are some interesting special cases, such as the case where the audience preferences are single peaked, where the problem can be solved exactly in polynomial time. For all these algorithms, we prove that the winner determination algorithm can be combined with VCG-style payments to yield truthful mechanisms.

© All rights reserved Ghosh and Mahdian and/or ACM Press

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Borgs, Christian, Chayes, Jennifer, Immorlica, Nicole, Jain, Kamal, Etesami, Omid and Mahdian, Mohammad (2007): Dynamics of bid optimization in online advertisement auctions. In: Proceedings of the 2007 International Conference on the World Wide Web 2007. pp. 531-540. Available online

We consider the problem of online keyword advertising auctions among multiple bidders with limited budgets, and study a natural bidding heuristic in which advertisers attempt to optimize their utility by equalizing their return-on-investment across all keywords. We show that existing auction mechanisms combined with this heuristic can experience cycling (as has been observed in many current systems), and therefore propose a modified class of mechanisms with small random perturbations. This perturbation is reminiscent of the small time-dependent perturbations employed in the dynamical systems literature to convert many types of chaos into attracting motions. We show that the perturbed mechanism provably converges in the case of first-price auctions and experimentally converges in the case of second-price auctions. Moreover, the point of convergence has a natural economic interpretation as the unique market equilibrium in the case of first-price mechanisms. In the case of second-price auctions, we conjecture that it converges to the "supply-aware" market equilibrium. Thus, our results can be alternatively described as a tatonnement process for convergence to market equilibrium in which prices are adjusted on the side of the buyers rather than the sellers. We also observe that perturbation in mechanism design is useful in a broader context: In general, it can allow bidders to "share" a particular item, leading to stable allocations and pricing for the bidders, and improved revenue for the auctioneer.

© All rights reserved Borgs et al. and/or International World Wide Web Conference Committee

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Mahdian, Mohammad and Tomak, Kerem (2007): Towards a pay-per-action model in sponsored search. In: Gini, Maria L., Kauffman, Robert J., Sarppo, Donna, Dellarocas, Chrysanthos and Dignum, Frank (eds.) Proceedings of the 9th International Conference on Electronic Commerce - ICEC 2007 August 19-22, 2007, Minneapolis, MN, USA. pp. 87-88. Available online

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