Abstract. One of the most important yet insufficiently studied issues in online advertising is the externality effect among ads: the value of an ad impression on a page is affected not just by the location that the ad is placed in, but also by the set of other ads displayed on the page. For instance, a high quality competing ad can detract users from another ad, while a low quality ad could cause the viewer to abandon the page altogether. In this paper, we propose and analyze a model for externalities in sponsored search ads. Our model is based on the assumption that users will visually scan the list of ads from the top to the bottom. After each ad, they make independent random decisions with ad-specific probabilities on whether to continue scanning. We then generalize the model in two ways: allowing for multiple separate blocks of ads, and allowing click probabilities to explicitly depend on ad positions as well. For the most basic model, we present a polynomial-time incentive-compatible auction mechanism for allocating and pricing ad slots. For the generalizations, we give approximation algorithms for the allocation of ads. 1

It is widely believed that the value of acquiring a slot in a sponsored search list (that comes along with the organic links in a search engine’s result page) highly depends on who else is shown in the other sponsored positions. To capture such externality effects, we consider a model of keyword advertising where bidders participate in a Generalized Second Price (GSP) auction and users perform ordered search (they browse from the top to the bottom of the sponsored list and make their clicking decisions slot by slot). Our contribution is twofold: first, we use impression and click data from Microsoft Live to estimate the ordered search model. With these estimates in hand, we are able to assess how the click-through rate of an ad is affected by the user’s click history and by the other competing links. Further, we compare the clicking predictions of our ordered search model to those of the most widely used model of user behavior: the separable click-through rate model. Second, we study complete information Nash equilibria of the GSP under different scoring rules. First, we characterize the efficient and revenue-maximizing complete information Nash equilibrium (under any scoring rule) and show that such an equilibrium can be implemented with any set of advertisers if and only if a particular weighting rule that combines click-through rates and continuation probabilities is used. Interestingly, this is the same ranking rule derived in [11] for solving the efficient allocation problem. On the negative side, we show that there is no scoring rule that implements an efficient equilibrium with VCG payments (VCG equilibrium) for all profiles of valuations and search parameters. This result extends [8], who argue that the rank-by-revenue GSP does not possess a VCG equilibrium. 1.

When online ads are shown together, they compete for user attention and conversions, imposing negative externalities on each other. We study the simplest form that an advertiser’s valuation can have in the presence of such externalities – an advertiser’s value depends on whether her ad is shown exclusively, or along with other ads. A mechanism such as the GSP auction, which always displays a full slate of ads, can be arbitrarily inefficient given such two-dimensional valuations; further, expanding the outcome space need not be enough– when the advertiser pays for an impression or a click, but derives value from a conversion, the private value of the advertiser is affected by the externality as well, leading to the need for a more expressive bidding language. In this paper, we study the design of expressive mechanisms which are extensions of the GSP auction currently used in practice. Our mechanisms show either a single ad exclusively, or multiple ads simultaneously, with the property that the allocation and pricing are identical to GSP when multiple ads are shown. We investigate the equilibria of these mechanisms, and show that the revenue when multiple ads are shown dominates the VCG revenue. In equilibria where a single ad is shown, the revenue can actually be lower than that of VCG; however, this loss is bounded within a factor of two. The increased efficiency from using the more expressive mechanism can come, unfortunately, with a loss in revenue with respect to the existing GSP mechanism in some cases. We design a mechanism which has a one-dimensional bidding language, while still allowing two types of outcomes, for situations where the private values are approximately one-dimensional. We show that this mechanism, while retaining the revenue and efficiency properties of the previous mechanisms, also revenue dominates the existing GSP mechanism. Part of this work was done while Amin Sayedi was visiting

Position auctions were widely used by search engines to sell keyword advertising before being well understood (and, indeed, studied) theoretically. To date, theorists have made significant progress, for example showing that a given auction is efficient or revenue-dominates a benchmark auction such as VCG. This paper augments that line of work, relying on computational equilibrium analysis. By computing Nash equilibria and calculating their expected revenue and social welfare, we can quantitatively answer questions that theoretical methods have not. Broadly, the questions we answer are: (1) How often do the theoretically predicted “good” (i.e., efficient, high-revenue) equilibria of GSP occur? (2) In models where GSP is known to be inefficient, how much welfare does it waste? We also use our data to examine the larger question of whether GSP is a good choice, compared with the alternatives.

Abstract. On the Internet, there are advertisements (ads) of different kinds: image, text, video and other specially marked objects that are distinct from the underlying content of the page. There is an industry behind the management of such ads, and they face a number of algorithmic challenges. This note will present a small selection of such problems, some insights and open research directions. 1

We consider the problem of designing auctions in social networks for goods that exhibit single-parameter submodular network externalities in which a bidder’s value for an outcome is a fixed private type times a known submodular function of the allocation of his friends. Externalities pose many issues that are hard to address with traditional techniques; our work shows how to resolve these issues in a specific setting of particular interest. We operate in a Bayesian environment and so assume private values are drawn according to known distributions. We prove that the optimal auction is APX-hard. Thus we instead design auctions whose revenue approximates that of the optimal auction. Our main result considers step-function externalities in which a bidder’s value for an outcome is either zero, or equal to his private type if at least one friend has the good. For these e e+1 settings, we provide a-approximation. We also give a 0.25-approximation auction for general single-parameter submodular network externalities, and discuss optimizing over a class of simple pricing strategies.

Externalities are recognized to exist in the sponsored search market, where two co-located ads compete for user attention. Existing work focuses on the effect of another ad on the quantity of clicks received. We focus instead on the negative effect of another ad on the value per click, and propose a general model of externalities, in which a bidder has no value for a slot under a set of certain conditions, each on one other bidder’s allocated slot. We provide a generic greedy algorithm for the winner determination problem (WDP) in this model together with a pricing scheme that closely follow the Generalized Second Price (GSP) auction used in practice. For value externalities that satisfy a property of downward-monotonicity, these mechanisms provide no new opportunities for manipulation beyond the ones already available via untruthful claims about bid value in GSP under the standard slot auction model. Our main instantiation of downward-monotonic constraints is an identity-specific language, in which a bidder can require that it precedes some subset of other bidders. For this language’s WDP, we establish worst-case complexity and inapproximability results. This motivates the choice of approximations, e.g. via the greedy algorithm. As another way of circumventing the hardness results, we present fixed-parameter algorithms for the WDPs of two sub-languages of the identityspecific model. 1.

When a decision must be made based on the preferences of multiple agents, and the space of possible outcomes is combinatorial in nature, it becomes necessary to think about how preferences should be represented, and how this affects the complexity of finding an optimal (or at least a good) outcome. We study settings with externalities, where each agent controls one or more variables, and how these variables are set affects not only the agent herself, but also potentially the other agents. For example, one agent may decide to reduce her pollution, which will come at a cost to herself, but will result in a benefit for all other agents. We formalize how to represent such domains and show that in a number of key special cases, it is NPcomplete to determine whether there exists a nontrivial feasible solution (and therefore the maximum social welfare is completely inapproximable). However, for one important special case, we give an algorithm that converges to the solution with the maximal concession by each agent (in a linear number of rounds for utility functions that additively decompose into piecewise constant functions). Maximizing social welfare, however, remains NP-hard even in this setting. We also demonstrate a special case that can be solved in polynomial time using linear programming.

Which ads should we display in sponsored search in order to maximize our revenue? How should we dynamically rank information sources to maximize the value of the ranking? These applications exhibit strong diminishing returns: Redundancy decreases the marginal utility of each ad or information source. We show that these and other problems can be formalized as repeatedly selecting an assignment of items to positions to maximize a sequence of monotone submodular functions that arrive one by one. We present an efficient algorithm for this general problem and analyze it in the no-regret model. Our algorithm possesses strong theoretical guarantees, such as a performance ratio that converges to the optimal constant of 1 − 1/e. We empirically evaluate our algorithm on two real-world online optimization problems on the web: ad allocation with submodular utilities, and dynamically ranking blogs to detect information cascades. 1

We introduce the TAC Ad Auctions game (TAC/AA), a new game for the Trading Agent Competition. The Ad Auctions game investigates complex strategic issues found in real sponsored search auctions that are not captured in current analytical models. We provide an overview of TAC/AA, introducing its key features and design rationale. TAC/AA will debut in summer 2009, with the final tournament commencing in conjunction with the TADA-09 workshop.