Combinatorial Problems in Online Advertising

Electronic commerce or eCommerce refers to the process of buying and selling of goods and services over the Internet. In fact, the Internet has completely transformed traditional media based advertising so much so that billions of dollars of advertising revenue is now flowing to search companies such as Microsoft, Yahoo! and Google. In addition, the new advertising landscape has opened up the advertising industry to all players, big and small. However, this transformation has led to a host of new problems faced by the search companies as they make decisions about how much to charge for advertisements, whose ads to display to users, and how to maximize their revenue. In this thesis we focus on an entire suite of problems motivated by the central question of "Which advertisement to display to which user?". Targeted advertisement happens when a user enters a relevant search query. The ads are usually displayed on the sides of the search result page. Internet advertising also takes place by displaying ads on the side of webpages with relevant content. While large advertisers (e.g. Coca Cola) pursue brand recognition by advertisement, small advertisers are happy with instant revenue as a result of a user following their ad and performing a desired action (e.g. making a purchase). Therefore, small advertisers are often happy to get any ad slot related to their ad while large advertisers prefer contracts that will guarantee that their ads will be delivered to enough number of desired users. We first focus on two problems that come up in the context of small advertisers. The first problem we consider deals with the allocation of ads to slots considering the fact that users enter search queries over a period of time, and as a result the slots become available gradually. We use a greedy method for allocation and show that the online ad allocation problem with a fixed distribution of queries over time can be modeled as maximizing a continuous non-decreasing submodular sequence function for which we can guarantee a solution with a factor of at least (1- 1/e) of the optimal. The second problem we consider is query rewriting problem in the context of keyword advertisement. This problem can be posed as a family of graph covering problems to maximize profit. We obtain constant-factor approximation algorithms for these covering problems under two sets of constraints and a realistic notion of ad benefit. We perform experiments on real data and show that our algorithms are capable of outperforming a competitive baseline algorithm in terms of the benefit due to rewrites. We next consider two problems related to premium customers, who need guaranteed delivery of a large number of ads for the purpose of brand recognition and would require signing a contract. In this context, we consider the allocation problem with the objective of maximizing either revenue or fairness. The problems considered in this thesis address just a few of the current challenges in e-Commerce and Internet Advertising. There are many interesting new problems arising in this field as the technology evolves and online-connectivity through interactive media and the internet become ubiquitous. We believe that this is one of the areas that will continue to receive greater attention by researchers in the near future

Network Security and Contagion

We develop a theoretical model of security investments in a network of interconnected agents. Network connections introduce the possibility of cascading failures due to an exogenous or endogenous attack depending on the profile of security investments by the agents. The general presumption in the literature, based on intuitive arguments or analysis of symmetric networks, is that because security investments create positive externalities on other agents, there will be underinvestment in security. We show that this reasoning is incomplete because of a first-order economic force: security investments are also strategic substitutes. In a general (non-symmetric) network, this implies that underinvestment by some agents will encourage overinvestment by others. We demonstrate by means of examples there can be overinvestment by some agents and also that aggregate probabilities of infection can be lower in equilibrium compared to the social optimum. We then provide sufficient conditions for underinvestment. This requires both sufficiently convex cost functions (convexity alone is not enough) and networks that are either symmetric or locally tree-like. We also characterize the impact of network structure on equilibrium and optimal investments. Finally, we show that when the attack location is endogenized (by assuming that the attacker chooses a probability distribution over the location of the attack in order to maximize damage), there is an additional incentive for overinvestment: greater investment by an agent shifts the attack to other parts of the network.We thank various numerous seminar and conference participants for useful suggestions. We gratefully acknowledge financial support from the Toulouse Network with Information Technology and Army Research Office

On random sampling auctions for digital goods

In the context of auctions for digital goods, an interesting Random Sampling Optimal Price auction (RSOP) has been proposed by Goldberg, Hartline and Wright; this leads to a truthful mechanism. Since random sampling is a popular approach for auctions that aims to maximize the seller’s revenue, this method has been analyzed further by Feige, Flaxman, Hartline and Kleinberg, who have shown that it is 15-competitive in the worst case – which is substantially better than the previously proved bounds but still far from the conjectured competitive ratio of 4. In this paper, we prove that RSOP is indeed 4-competitive for a large class of instances in which the number λ of bidders receiving the item at the optimal uniform price, is at least 6. We also show that it is 4.68 competitive for the small class of remaining instances thus leaving a negligible gap between the lower and upper bound. Furthermore, we develop a robust version of RSOP – one in which the seller’s revenue is, with high probability, not much below its mean – when the above parameter λ grows large. We employ a mix of probabilistic techniques and dynamic programming to compute these bounds