User Satisfaction in Competitive Sponsored Search

We present a model of competition between web search algorithms, and study the impact of such competition on user welfare. In our model, search providers compete for customers by strategically selecting which search results to display in response to user queries. Customers, in turn, have private preferences over search results and will tend to use search engines that are more likely to display pages satisfying their demands. Our main question is whether competition between search engines increases the overall welfare of the users (i.e., the likelihood that a user finds a page of interest). When search engines derive utility only from customers to whom they show relevant results, we show that they differentiate their results, and every equilibrium of the resulting game achieves at least half of the welfare that could be obtained by a social planner. This bound also applies whenever the likelihood of selecting a given engine is a convex function of the probability that a user's demand will be satisfied, which includes natural Markovian models of user behavior. On the other hand, when search engines derive utility from all customers (independent of search result relevance) and the customer demand functions are not convex, there are instances in which the (unique) equilibrium involves no differentiation between engines and a high degree of randomness in search results. This can degrade social welfare by a factor of the square root of N relative to the social optimum, where N is the number of webpages. These bad equilibria persist even when search engines can extract only small (but non-zero) expected revenue from dissatisfied users, and much higher revenue from satisfied ones

Agent Behavior Prediction and Its Generalization Analysis

Machine learning algorithms have been applied to predict agent behaviors in real-world dynamic systems, such as advertiser behaviors in sponsored search and worker behaviors in crowdsourcing. The behavior data in these systems are generated by live agents: once the systems change due to the adoption of the prediction models learnt from the behavior data, agents will observe and respond to these changes by changing their own behaviors accordingly. As a result, the behavior data will evolve and will not be identically and independently distributed, posing great challenges to the theoretical analysis on the machine learning algorithms for behavior prediction. To tackle this challenge, in this paper, we propose to use Markov Chain in Random Environments (MCRE) to describe the behavior data, and perform generalization analysis of the machine learning algorithms on its basis. Since the one-step transition probability matrix of MCRE depends on both previous states and the random environment, conventional techniques for generalization analysis cannot be directly applied. To address this issue, we propose a novel technique that transforms the original MCRE into a higher-dimensional time-homogeneous Markov chain. The new Markov chain involves more variables but is more regular, and thus easier to deal with. We prove the convergence of the new Markov chain when time approaches infinity. Then we prove a generalization bound for the machine learning algorithms on the behavior data generated by the new Markov chain, which depends on both the Markovian parameters and the covering number of the function class compounded by the loss function for behavior prediction and the behavior prediction model. To the best of our knowledge, this is the first work that performs the generalization analysis on data generated by complex processes in real-world dynamic systems

Pricing average price advertising options when underlying spot market prices are discontinuous

Advertising options have been recently studied as a special type of guaranteed contracts in online advertising, which are an alternative sales mechanism to real-time auctions. An advertising option is a contract which gives its buyer a right but not obligation to enter into transactions to purchase page views or link clicks at one or multiple pre-specified prices in a specific future period. Different from typical guaranteed contracts, the option buyer pays a lower upfront fee but can have greater flexibility and more control of advertising. Many studies on advertising options so far have been restricted to the situations where the option payoff is determined by the underlying spot market price at a specific time point and the price evolution over time is assumed to be continuous. The former leads to a biased calculation of option payoff and the latter is invalid empirically for many online advertising slots. This paper addresses these two limitations by proposing a new advertising option pricing framework. First, the option payoff is calculated based on an average price over a specific future period. Therefore, the option becomes path-dependent. The average price is measured by the power mean, which contains several existing option payoff functions as its special cases. Second, jump-diffusion stochastic models are used to describe the movement of the underlying spot market price, which incorporate several important statistical properties including jumps and spikes, non-normality, and absence of autocorrelations. A general option pricing algorithm is obtained based on Monte Carlo simulation. In addition, an explicit pricing formula is derived for the case when the option payoff is based on the geometric mean. This pricing formula is also a generalized version of several other option pricing models discussed in related studies.Comment: IEEE Transactions on Knowledge and Data Engineering, 201

Ad auctions and cascade model: GSP inefficiency and algorithms

The design of the best economic mechanism for Sponsored Search Auctions (SSAs) is a central task in computational mechanism design/game theory. Two open questions concern the adoption of user models more accurate than that one currently used and the choice between Generalized Second Price auction (GSP) and Vickrey-Clark-Groves mechanism (VCG). In this paper, we provide some contributions to answer these questions. We study Price of Anarchy (PoA) and Price of Stability (PoS) over social welfare and auctioneer's revenue of GSP w.r.t. the VCG when the users follow the famous cascade model. Furthermore, we provide exact, randomized, and approximate algorithms, showing that in real-world settings (Yahoo! Webscope A3 dataset, 10 available slots) optimal allocations can be found in less than 1s with up to 1000 ads, and can be approximated in less than 20ms even with more than 1000 ads with an average accuracy greater than 99%.Comment: AAAI16, to appea

Truthful Learning Mechanisms for Multi-Slot Sponsored Search Auctions with Externalities

Sponsored search auctions constitute one of the most successful applications of microeconomic mechanisms. In mechanism design, auctions are usually designed to incentivize advertisers to bid their truthful valuations and to assure both the advertisers and the auctioneer a non-negative utility. Nonetheless, in sponsored search auctions, the click-through-rates (CTRs) of the advertisers are often unknown to the auctioneer and thus standard truthful mechanisms cannot be directly applied and must be paired with an effective learning algorithm for the estimation of the CTRs. This introduces the critical problem of designing a learning mechanism able to estimate the CTRs at the same time as implementing a truthful mechanism with a revenue loss as small as possible compared to an optimal mechanism designed with the true CTRs. Previous work showed that, when dominant-strategy truthfulness is adopted, in single-slot auctions the problem can be solved using suitable exploration-exploitation mechanisms able to achieve a per-step regret (over the auctioneer's revenue) of order $O(T^{-1/3})$ (where T is the number of times the auction is repeated). It is also known that, when truthfulness in expectation is adopted, a per-step regret (over the social welfare) of order $O(T^{-1/2})$ can be obtained. In this paper we extend the results known in the literature to the case of multi-slot auctions. In this case, a model of the user is needed to characterize how the advertisers' valuations change over the slots. We adopt the cascade model that is the most famous model in the literature for sponsored search auctions. We prove a number of novel upper bounds and lower bounds both on the auctioneer's revenue loss and social welfare w.r.t. to the VCG auction and we report numerical simulations investigating the accuracy of the bounds in predicting the dependency of the regret on the auction parameters