Fellowship. Portions of this work were completed while the author was a postdoctoral

Internet search companies sell advertisement slots based on users ’ search queries via an auction. Advertisers have to determine how to place bids on the keywords of their interest in order to maximize their return for a given budget: this is the budget optimization problem. The solution depends on the distribution of future queries. In this paper, we formulate stochastic versions of the budget optimization problem based on natural probabilistic models of distribution over future queries, and address two questions that arise. Evaluation Given a solution, can we evaluate the expected value of the objective function? Optimization Can we find a solution that maximizes the objective function in expectation? Our main results are approximation and complexity results for these two problems in our three stochastic models. In particular, our algorithmic results show that simple prefix strategies that bid on all cheap keywords up to some level are either optimal or good approximations for many cases; we show other cases to be NP-hard. 1

We initiate the study of online pricing problems in markets with “buyback, ” i.e., markets in which prior allocation decisions can be revoked, but at a cost. In our model, a seller receives requests online and chooses which requests to accept, subject to constraints on the subsets of requests which may be accepted simultaneously. A request, once accepted, can be canceled at a cost which is a fixed fraction of the request value. This scenario models a market for web advertising, in which the buyback cost represents the cost of canceling an existing contract. We analyze a simple constant-competitive algorithm for a single-item auction in this model, and we prove that its competitive ratio is optimal among deterministic algorithms. Moreover, we prove that an extension of this algorithm achieves the same competitive ratio in any matroid domain, i.e., when the sets of requests which may be simultaneously satisfied constitute the independent sets of a matroid. This broad class of domains includes, for example, advertising markets in which each request is for a unit of supply coming from a specified subset of the available impressions. We also present algorithms and lower bounds for knapsack domains, i.e., when advertisers request varying quantities of a homogeneous but limited supply of impressions. 1.

We model budget-constrained keyword bidding in sponsored search auctions as a stochastic multiple-choice knapsack problem (S-MCKP) and design an algorithm to solve S-MCKP and the corresponding bidding optimization problem. Our algorithm selects items online based on a threshold function which can be built/updated using historical data. Our algorithm achieved about 99 % performance compared to the offline optimum when applied to a real bidding dataset. With synthetic dataset and iid item-sets, its performance ratio against the offline optimum converges to one empirically with increasing number of periods.

We study online pricing problems in markets with cancellations, i.e., markets in which prior allocation decisions can be revoked, but at a cost. In our model, a seller receives requests online and chooses which requests to accept, subject to constraints on the subsets of requests which may be accepted simultaneously. A request, once accepted, can be canceled at a cost which is a fixed fraction of the request value. This scenario models a market for web advertising campaigns, in which the buyback cost represents the cost of canceling an existing contract. We analyze a simple constant-competitive algorithm for a single-item auction in this model, and we prove that its competitive ratio is optimal among deterministic algorithms, but that the competitive ratio can be improved using a randomized algorithm. We then model ad campaigns using knapsack domains, in which the requests differ in size as well as in value. We give a deterministic online algorithm that achieves a bi-criterion approximation in which both approximation factors approach 1 as the buyback factor and the size of the maximum request approach 0. We show that the bi-criterion approximation is unavoidable for deterministic algorithms, but that a randomized algorithm is capable of achieving a constant competitive ratio. Finally, we discuss an extension of our randomized algorithm to matroid domains (in which the sets of simultaneously satisfiable requests constitute the independent sets of a matroid) as well as present results for domains in which the buyback factor of different requests varies.

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.

We empirically investigate whether advertisers are maximizing their return on investment (ROI) across multiple keywords in sponsored search auctions. Because testing for ROI maximization relies on knowledge of advertisers ’ private true values per click, we instead use necessary (although not sufficient) conditions for ROI maximizing behavior that rely only on advertisers ’ bids. We classify advertisers based on the extent to which they satisfy the test conditions. Our results indicate that a large fraction of advertisers in the Yahoo Webscope first price data set may be following ROIbased strategies.

Sponsored search auctions provide a marketplace where advertisers can bid for millions of advertising opportunities to promote their products. The main difficulty facing the advertisers in this market is the complexity of picking and evaluating keywords and phrases to bid on. This is due to the sheer number of possible keywords that the advertisers can bid on, and leads to inefficiencies in the market such as lack of coverage for “rare ” keywords. Approaches such as broad matching have been proposed to alleviate this problem. However, as we will observe in this paper, broad matching has undesirable economic properties (such as the non-existence of equilibria) that can make it hard for an advertiser to determine how much to bid for a broad-matched keyword. The main contribution of this paper is to introduce a bidding language for sponsored search auctions based on broad-matching keywords to non-overlapping clusters that greatly simplifies the bidding problem for the advertisers. We investigate the algorithmic problem of computing the optimal clustering given a set of estimated values and give an approximation algorithm for this problem. Furthermore, we present experimental results using real advertisers ’ data that show that it is possible to extract close to the optimal social welfare with a number of clusters considerably smaller than the number of keywords. This demonstrates the applicability of the clustering scheme and our algorithm in practice. 1

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We provide an overview of recent research that has been conducted on the design of sponsored search auctions. We mainly focus on game theoretic and mechanism design aspects of these auctions, and we analyze the issues associated with each of the three participating entities, i.e. the search engine, the advertisers, and the users of the search engine, as well as their resulting behavior. Regarding the search engine, we overview the various mechanisms that have been proposed including the currently used GSP mechanism. The issues that are addressed include analysis of Nash equilibria and their performance, design of alternative mechanisms and aspects of competition among search engines. We then move on to the advertisers and discuss the problem of choosing a bidding strategy, given the mechanism of the search engine. Following this, we consider the end users and we examine how user behavior may create externalities and influence the performance of the advertisers. Finally, we also overview statistical methods for estimating modeling parameters that are of interest to the three entities. In each section, we point out interesting open problems and directions for future research. 1