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Algorithmic methods for sponsored search advertising
 II. Mathematical Programming Study
, 1978
"... Abstract Modern commercial Internet search engines display advertisements along side the search results in response to user queries. Such sponsored search relies on market mechanisms to elicit prices for these advertisements, making use of an auction among advertisers who bid in order to have their ..."
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Abstract Modern commercial Internet search engines display advertisements along side the search results in response to user queries. Such sponsored search relies on market mechanisms to elicit prices for these advertisements, making use of an auction among advertisers who bid in order to have their ads shown for specific keywords. We present an overview of the current systems for such auctions and also describe the underlying gametheoretic aspects. The game involves three parties— advertisers, the search engine, and search users—and we present example research directions that emphasize the role of each. The algorithms for bidding and pricing in these games use techniques from three mathematical areas: mechanism design, optimization, and statistical estimation. Finally, we present some challenges in sponsored search advertising. 1
Weighted proportional allocation
 In Proceedings of ACM Sigmetrics
, 2011
"... We consider a weighted proportional allocation of resources that allows providers to discriminate usage of resources by users. This framework is a generalization of wellknown proportional allocation by accommodating allocation of resources proportional toweightedbidsor proportional tosubmitted bids ..."
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We consider a weighted proportional allocation of resources that allows providers to discriminate usage of resources by users. This framework is a generalization of wellknown proportional allocation by accommodating allocation of resources proportional toweightedbidsor proportional tosubmitted bids but with weighted payments. We study a competition game where everyone is selfish: providers choose user discrimination weights aiming at maximizing their individual revenues while users choose their bids aiming at maximizing their individual payoffs. We analyze revenue and social welfare of this game. We find that the revenue is lower bounded by k/(k+1) times the revenue under standard price discrimination scheme, where a set of k users is excluded. For users with linear utility functions, we find that the social welfare is at least 1/(1+2 / √ 3) of the maximum social welfare (approx. 46%) and that this bound is tight. We extend this efficiency result to a broad class of utility functions and multiple competing providers. We also describe an algorithm for adjusting discrimination weights by providers without a prior knowledge of user utility functions and establish convergence to equilibrium points of the competition game. Our results show that, in many cases, weighted proportional sharing achieves competitive revenue and social welfare, despite the fact that everyone is selfish.
Revenue Maximization via Nash Implementation
"... Abstract: We consider the problem of maximizing revenue in priorfree auctions for general single parameter settings. The setting is modeled by an arbitrary downwardclosed set system, which captures many special cases such as single item, digital goods and singleminded combinatorial auctions. We r ..."
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Abstract: We consider the problem of maximizing revenue in priorfree auctions for general single parameter settings. The setting is modeled by an arbitrary downwardclosed set system, which captures many special cases such as single item, digital goods and singleminded combinatorial auctions. We relax the truthfulness requirement by the solution concept of Nash equilibria. Implementation by Nash equilibria is a natural and relevant framework in many applications of computer science, where auctions are run repeatedly and bidders can observe others ’ strategies, but the auctioneer needs to design a mechanism in advance and cannot use any information on the bidders ’ private valuations. We introduce a worstcase revenue benchmark which generalizes the second price of single item auction and the F2 benchmark, introduced by Goldberg et al., for digital goods. We design a mechanism whose Nash equilibria obtains at least a constant factor of this benchmark and prove that no truthful mechanisms can achieve a constant approximation.
The weighted proportional allocation mechanism
, 2010
"... AbstractWe consider a weighted proportional allocation of resources that allows providers to discriminate usage of resources by users. This framework is a generalization of wellknown proportional allocation accommodating allocation of resources proportional to weighted bids or proportional to sub ..."
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AbstractWe consider a weighted proportional allocation of resources that allows providers to discriminate usage of resources by users. This framework is a generalization of wellknown proportional allocation accommodating allocation of resources proportional to weighted bids or proportional to submitted bids but with weighted payments. We study a competition game where everyone is selfish: providers choose discrimination weights aiming at maximizing their individual revenues while users choose their bids aiming at maximizing their individual payoffs. We analyze revenue and social welfare of this game. We find that the revenue is lower bounded by k/(k + 1) times the revenue under standard price discrimination scheme, where a set of k users is excluded. For users with linear utility functions, we find that the social welfare is at least 1/(1 + 2/ √ 3) of the maximum social welfare (approx. 46%) and that this bound is tight. We extend the efficiency result to a broad class of utility functions and to multiple competing providers. We also describe an algorithm used by the provider to adjust the user discrimination weights without a prior knowledge of user utility functions and establish convergence to equilibrium points of our game. Our results show that, in many cases, weighted proportional sharing achieves competitive revenue and social welfare, despite the fact that everyone is selfish. The mechanism allows for resource constraints described by general polyhedrons, thus accommodating a variety of resources, including bandwidth of communication networks, systems of computing resources, and sponsored search ad slots.
Offline Ad Slot Scheduling
, 2010
"... We consider the Offline Ad Slot Scheduling problem, where advertisers must be scheduled to sponsored search slots during a given period of time. Advertisers specify a budget constraint, as well as a maximum cost per click, and may not be assigned to more than one slot for a particular search. We giv ..."
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We consider the Offline Ad Slot Scheduling problem, where advertisers must be scheduled to sponsored search slots during a given period of time. Advertisers specify a budget constraint, as well as a maximum cost per click, and may not be assigned to more than one slot for a particular search. We give a truthful mechanism under the utility model where bidders try to maximize their clicks, subject to their personal constraints. In addition, we show that the revenuemaximizing mechanism is not truthful, but has a Nash equilibrium whose outcome is identical to our mechanism. As far as we can tell, this is the first treatment of sponsored search that directly incorporates both multiple slots and budget constraints into an analysis of incentives. Our mechanism employs a descendingprice auction that maintains a solution to a certain machine scheduling problem whose job lengths depend on the price, and hence is variable over the auction. The price stops when the set of bidders that can afford that price pack exactly into a block of ad slots, at which point the mechanism allocates that block and continues on the remaining slots. To prove our result on the equilibrium of the revenuemaximizing mechanism, we first show that a
Near Optimal Nontruthful Auctions
"... In several ecommerce applications, nontruthful auctions have been preferred over truthful weakly dominant strategy ones partly because of their simplicity and scalability. Although nontruthful auctions can have weaker incentive constraints than truthful ones, the question of how much more revenue ..."
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In several ecommerce applications, nontruthful auctions have been preferred over truthful weakly dominant strategy ones partly because of their simplicity and scalability. Although nontruthful auctions can have weaker incentive constraints than truthful ones, the question of how much more revenue they can generate than truthful auctions is not well understood. We study this question for natural and broad classes of nontruthful mechanisms, including quasiproportional sharing and weakly monotonic auctions. Quasiproportional sharing mechanisms allocate to each bidder i an amount of resource proportional to a monotonic and concave function f(bi) where bi is the bid of bidder i and ask for a payment of bi. Weakly monotonic auctions refer to a more general class of auctions which satisfy some natural continuity and monotonicity conditions. We prove that although weakly monotonic auctions are much broader and require weaker incentive constraints than dominant strategy auctions, they are not more powerful with respect to the revenue in the setting of selling a single item. Furthermore, we show that quasiproportional sharing with multiple bidders cannot guarantee a revenue that is larger than the second highest valuation, asymptotically as the number of bidders grows large. However, in a more general singleparameter