Amin Sayedi

We know who you followed last summer: inferring social link creation times in twitter

Understanding a networks temporal evolution appears to require multiple observations of the graph over time. These often expensive repeated crawls are only able to answer questions about what happened from observation to observation, and not what happened before or between network snapshots. Contrary to this picture, we propose a method for Twitters social network that takes a single static snapshot of network edges and user account creation times to accurately infer when these edges were formed. This method can be exact in theory, and we demonstrate empirically for a large subset of Twitter relationships that it is accurate to within a few hours in practice. We study users who have a very large number of edges or who are recommended by Twitter. We examine the graph formed by these nearly 1,800 Twitter celebrities and their 862 million edges in detail, showing that a single static snapshot can give novel insights about Twitters evolution. We conclude from this analysis that real-world events and changes to Twitters interface for recommending users strongly influence network growth.

Expressive auctions for externalities in online advertising

When online ads are shown together, they compete for user attention and conversions, imposing negative externalities on each other. While the competition for user attention in sponsored search can be captured via models of clickthrough rates, the post-click competition for conversions cannot: since the value-per-click of an advertiser is proportional to the conversion probability conditional on a click, which depends on the other ads displayed, the private value of an advertiser is no longer one-dimensional, and the GSP mechanism is not adequately expressive. We study the design of expressive GSP-like mechanisms for the simplest form that an advertisers private value can have in the presence of such externalities- an advertisers value depends on exclusivity, i.e., whether her ad is shown exclusively, or along with other ads. Our auctions take as input two-dimensional (per-click) bids for exclusive and nonexclusive display, and have two types of outcomes: either a single ad is displayed exclusively, or multiple ads are simultaneously shown. We design two expressive auctions that are both extensions of GSP- the first auction, GSP2D, is designed with the property that the allocation and pricing are identical to GSP when multiple ads are shown; the second auction, NP2D, is designed to be a next price auction. We show that both auctions have high efficiency and revenue in all reasonable equilibria; further, the NP2D auction is guaranteed to always have an equilibrium with revenue at least as much as the current GSP mechanism. However, we find that unlike with one-dimensional valuations, the GSP-like auctions for these richer valuations do not always preserve efficiency and revenue with respect to the VCG mechanism.

Competitive Poaching in Sponsored Search Advertising and Its Strategic Impact on Traditional Advertising

Traditional advertising, such as TV and print advertising, primarily builds awareness of a firms product among consumers, whereas sponsored search advertising on a search engine can target consumers closer to making a purchase because they reveal their interest by searching for a relevant keyword. Increased consumer targetability in sponsored search advertising induces a firm to “poach” a competing firms consumers by directly advertising on the competing firms keywords; in other words, the poaching firm tries to obtain more than its “fair share” of sales through sponsored search advertising by free riding on the market created by the firm being poached. Using a game theory model with firms of different advertising budgets, we study the phenomenon of poaching, its impact on how firms allocate their advertising budgets to traditional and sponsored search advertising, and the search engines policy on poaching. We find that, as budget asymmetry increases, the smaller-budget firm poaches more on the keywords of the larger-budget firm. This may induce the larger-budget firm to allocate more of its budget to traditional advertising, which, in turn, hurts the search engines advertising revenues. Therefore, paradoxically, even though poaching increases competition in sponsored search advertising, the search engine can benefit from limiting the extent of poaching. This explains why major search engines use “ad relevance” measures to handicap poaching on trademarked keywords.

A near Pareto optimal auction with budget constraints

In a setup where a divisible good is to be allocated to a set of bidders with budget constraints, we introduce a mechanism in the spirit of the Vickrey auction. In the mechanism we propose, understating budgets or values is weakly dominated. Since the revenue is increasing in budgets and values, all kinds of equilibrium deviations from true valuations turn out to be beneficial to the auctioneer. We also show that ex-post Nash equilibrium of our mechanism is near Pareto optimal in the sense that all full winnersʼ values are above all full losersʼ values.

Game-Theoretic Models of Information Overload in Social Networks

We study the effect of information overload on user engagement in an asymmetric social network like Twitter. We introduce simple game-theoretic models that capture rate competition between celebrities producing updates in such networks where users non-strategically choose a subset of celebrities to follow based on the utility derived from high quality updates as well as disutility derived from having to wade through too many updates. Our two variants model the two behaviors of users dropping some potential connections (followership model) or leaving the network altogether (engagement model). We show that under a simple formulation of celebrity rate competition, there is no pure strategy Nash equilibrium under the first model. We then identify special cases in both models when pure rate equilibria exist for the celebrities: For the followership model, we show existence of a pure rate equilibrium when there is a global ranking of the celebrities in terms of the quality of their updates to users. This result also generalizes to the case when there is a partial order consistent with all the linear orders of the celebrities based on their qualities to the users. Furthermore, these equilibria can be computed in polynomial time. For the engagement model, pure rate equilibria exist when all users are interested in the same number of celebrities, or when they are interested in at most two. Finally, we also give a finite though inefficient procedure to determine if pure equilibria exist in the general case of the followership model.

Keyword Management Costs and “Broad Match” in Sponsored Search Advertising

In sponsored search advertising, advertisers bid to be displayed in response to a keyword search. The operational activities associated with participating in an auction, i.e., submitting the bid and the ad copy, customizing bids and ad copies based on various factors (such as the geographical region from which the query originated, the time of day and the season, the characteristics of the searcher), and continuously measuring outcomes, involve considerable effort. We call the costs that arise from such activities keyword management costs . To reduce these costs and increase advertisers’ participation in keyword auctions, search engines offer an opt-in tool called broad match with automatic and flexible bidding , wherein the search engine automatically places bids on behalf of the advertisers and takes over the above activities as well. The bids are based on the search engine’s estimates of the advertisers’ valuations and, therefore, may be less accurate than the bids the advertisers would have turned in themselves. Using a game-theoretic model, we examine the strategic role of keyword management costs, and of broad match, in sponsored search advertising. We show that because these costs inhibit participation by advertisers in keyword auctions, the search engine has to reduce the reserve price, which reduces the search engine’s profits. This motivates the search engine to offer broad match as a tool to reduce keyword management costs. If the accuracy of broad match bids is sufficiently high, advertisers adopt broad match and benefit from the cost reduction, whereas if the accuracy is very low, advertisers do not use it. Interestingly, at moderate levels of bid accuracy, advertisers individually find it attractive to reduce costs by using broad match, but competing advertisers also adopt broad match and the increased competition hurts all advertisers’ profits, thus creating a “prisoner’s dilemma.” When advertisers adopt broad match, search engine profits increase. It therefore seems natural to expect that the search engine will be motivated to improve broad match accuracy. Our analysis shows that the search engine will increase broad match accuracy up to the point where advertisers choose broad match, but that increasing the accuracy any further reduces the search engine’s profits.

Expertise in Online Markets

We examine the effect of the presence of knowledgeable buyers (experts) in online markets where auctions with a hard close and posted prices are widely used. We model buyer expertise as the ability to accurately predict the quality, or condition, of an item. In auctions with a hard close, sniping – submitting bids in the last minute – emerges as an equilibrium strategy for experts. We show that non-experts bid more aggressively as the proportion of experts increases. As a consequence, we establish that the auction platform may obtain a higher revenue by (i) enforcing a hard close and allowing sniping, and (ii) withholding information regarding the quality of the item. Moreover, in online markets where both auctions and posted prices are available, we show that the presence of experts allows the sellers of high quality items to signal their quality by choosing to sell via auctions.

Multi-Unit Auctions with Budget Constraints

Motivated by sponsored search auctions, we study multi-unit auctions with budget constraints. In the mechanism we propose, Sort-Cut, understating budgets or values is weakly dominated. Since Sort-Cuts revenue is increasing in budgets and values, all kinds of equilibrium deviations from true valuations turn out to be beneficial to the auctioneer. We show that the revenue of Sort-Cut can be an order of magnitude greater than that of the natural Market Clearing Price mechanism, and we discuss the efficiency properties of its ex-post Nash equilibrium.

Mechanism Design for Complexity-Constrained Bidders

A well-known result due to Vickery gives a mechanism for selling a number of goods to interested buyers in a way that achieves the maximum social welfare. In practice, a problem with this mechanism is that it requires the buyers to specify a large number of values. In this paper we study the problem of designing optimal mechanisms subject to constraints on the complexity of the bidding language in a setting where buyers have additive valuations for a large set of goods. This setting is motivated by sponsored search auctions, where the valuations of the advertisers are more or less additive, and the number of keywords that are up for sale is huge. We give a complete solution for this problem when the valuations of the buyers are drawn from simple classes of prior distributions. For a more realistic class of priors, we show that a mechanism akin to the broad match mechanism currently in use provides a reasonable bicriteria approximation.

Exclusive Placement in Online Advertising

A recent development in online advertising has been the ability of advertisers to have their ads displayed exclusively on (a part of) a web page. We study this phenomenon in the context of both spo...