GSP with General Independent Click-Through-Rates

The popular generalized second price (GSP) auction for sponsored search is built upon a separable model of click-through-rates that decomposes the likelihood of a click into the product of a "slot effect" and an "advertiser effect" --- if the first slot is twice as good as the second for some bidder, then it is twice as good for everyone. Though appealing in its simplicity, this model is quite suspect in practice. A wide variety of factors including externalities and budgets have been studied that can and do cause it to be violated. In this paper we adopt a view of GSP as an iterated second price auction (see, e.g., Milgrom 2010) and study how the most basic violation of separability --- position dependent, arbitrary public click-through-rates that do not decompose --- affects results from the foundational analysis of GSP (Varian 2007, Edelman et al. 2007). For the two-slot setting we prove that for arbitrary click-through-rates, for arbitrary bidder values, an efficient pure-strategy equilibrium always exists; however, without separability there always exist values such that the VCG outcome and payments cannot be realized by any bids, in equilibrium or otherwise. The separability assumption is therefore necessary in the two-slot case to match the payments of VCG but not for efficiency. We moreover show that without separability, generic existence of efficient equilibria is sensitive to the choice of tie-breaking rule, and when there are more than two slots, no (bid-independent) tie-breaking rule yields the positive result. In light of this we suggest alternative mechanisms that trade the simplicity of GSP for better equilibrium properties when there are three or more slots

GSP with General Independent Click-Through-Rates *

Abstract The popular generalized second price (GSP) auction for sponsored search is built upon a separable model of click-through-rates that decomposes the likelihood of a click into the product of a "slot effect" and an "advertiser effect"-if the first slot is twice as good as the second for some bidder, then it is twice as good for everyone. Though appealing in its simplicity, this model is quite suspect in practice. A wide variety of factors including externalities and budgets have been studied that can and do cause it to be violated. In this paper we adopt a view of GSP as an iterated second price auction (see, e.g., Milgrom [2010]) and study how the most basic violation of separability-position dependent, arbitrary public click-throughrates that do not decompose-affects results from the foundational analysis of GS

Exploration via design and the cost of uncertainty in keyword auctions

We present a deterministic exploration mechanism for sponsored search auctions, which enables the auctioneer to learn the relevance scores of advertisers, and allows advertisers to estimate the true value of clicks generated at the auction site. This exploratory mechanism deviates only minimally from the mechanism being currently used by Google and Yahoo! in the sense that it retains the same pricing rule, similar ranking scheme, as well as, similar mathematical structure of payoffs. In particular, the estimations of the relevance scores and true-values are achieved by providing a chance to lower ranked advertisers to obtain better slots. This allows the search engine to potentially test a new pool of advertisers, and correspondingly, enables new advertisers to estimate the value of clicks/leads generated via the auction. Both these quantities are unknown a priori, and their knowledge is necessary for the auction to operate efficiently. We show that such an exploration policy can be incorporated without any significant loss in revenue for the auctioneer. We compare the revenue of the new mechanism to that of the standard mechanism at their corresponding symmetric Nash equilibria and compute the cost of uncertainty, which is defined as the relative loss in expected revenue per impression. We also bound the loss in efficiency, as well as, in user experience due to exploration, under the same solution concept (i.e. SNE). Thus the proposed exploration mechanism learns the relevance scores while incorporating the incentive constraints from the advertisers who are selfish and are trying to maximize their own profits, and therefore, the exploration is essentially achieved via mechanism design. We also discuss variations of the new mechanism such as truthful implementations.Comment: 19 pages, presentation improved, references added, title change

Click Efficiency: A Unified Optimal Ranking for Online Ads and Documents

Traditionally the probabilistic ranking principle is used to rank the search results while the ranking based on expected profits is used for paid placement of ads. These rankings try to maximize the expected utilities based on the user click models. Recent empirical analysis on search engine logs suggests a unified click models for both ranked ads and search results. The segregated view of document and ad rankings does not consider this commonality. Further, the used models consider parameters of (i) probability of the user abandoning browsing results (ii) perceived relevance of result snippets. But how to consider them for improved ranking is unknown currently. In this paper, we propose a generalized ranking function---namely "Click Efficiency (CE)"---for documents and ads based on empirically proven user click models. The ranking considers parameters (i) and (ii) above, optimal and has the same time complexity as sorting. To exploit its generality, we examine the reduced forms of CE ranking under different assumptions enumerating a hierarchy of ranking functions. Some of the rankings in the hierarchy are currently used ad and document ranking functions; while others suggest new rankings. While optimality of ranking is sufficient for document ranking, applying CE ranking to ad auctions requires an appropriate pricing mechanism. We incorporate a second price based pricing mechanism with the proposed ranking. Our analysis proves several desirable properties including revenue dominance over VCG for the same bid vector and existence of a Nash Equilibrium in pure strategies. The equilibrium is socially optimal, and revenue equivalent to the truthful VCG equilibrium. Further, we relax the independence assumption in CE ranking and analyze the diversity ranking problem. We show that optimal diversity ranking is NP-Hard in general, and that a constant time approximation is unlikely.Comment: Twenty Six Pages, Two Figures, Six Theorems. Initial Version Published in Workshop on Web and Databases 200

Mechanism Design for Value Maximizers

In many settings, money is a tool of exchange with minimal inherent utility --- agents will spend it in a way that maximizes the value of goods received subject to reasonable constraints, giving only second-order consideration to the trade-off between value and price. While this perspective is commonly captured in consumer choice theory, market equilibrium theory, and other fields, it is markedly absent from the mechanism design literature --- agents strategizing in a mechanism with money are almost always assumed to incorporate money as an objective through quasilinear valuations. We study a simple model of value maximizers that captures online advertisers and other agents who may view money solely as a constraint, and study general questions of mechanism design for such agents. We show that the feasible and optimal points faced by a mechanism designer change dramatically from the quasilinear realm and lay a foundation for a broader study of value maximization in mechanism design. Along the way, we offer new insight into the generalized second price (GSP) auction commonly used in Internet advertising. Through the lens of value maximization, GSP metamorphosizes into a truthful auction, sound in its principles and elegant in its simplicity

Position Auctions with Externalities and Brand Effects

This paper presents models for predicted click-through rates in position auctions that take into account two possibilities that are not normally considered---that the identities of ads shown in other positions may affect the probability that an ad in a particular position receives a click (externalities) and that some ads may be less adversely affected by being shown in a lower position than others (brand effects). We present a general axiomatic methodology for how click probabilities are affected by the qualities of the ads in the other positions, and illustrate that using these axioms will increase revenue as long as higher quality ads tend to be ranked ahead of lower quality ads. We also present appropriate algorithms for selecting the optimal allocation of ads when predicted click-through rates are governed by either the models of externalities or brand effects that we consider. Finally, we analyze the performance of a greedy algorithm of ranking the ads by their expected cost-per-1000-impressions bids when the true click-through rates are governed by our model of predicted click-through rates with brand effects and illustrate that such an algorithm will potentially cost as much as half of the total possible social welfare.Comment: 19 pages. A shorter version of this paper will appear in WINE 201

Sponsored Search Auctions with Markovian Users

Sponsored search involves running an auction among advertisers who bid in order to have their ad shown next to search results for specific keywords. Currently, the most popular auction for sponsored search is the "Generalized Second Price" (GSP) auction in which advertisers are assigned to slots in the decreasing order of their "score," which is defined as the product of their bid and click-through rate. In the past few years, there has been significant research on the game-theoretic issues that arise in an advertiser's interaction with the mechanism as well as possible redesigns of the mechanism, but this ranking order has remained standard. From a search engine's perspective, the fundamental question is: what is the best assignment of advertisers to slots? Here "best" could mean "maximizing user satisfaction," "most efficient," "revenue-maximizing," "simplest to interact with," or a combination of these. To answer this question we need to understand the behavior of a search engine user when she sees the displayed ads, since that defines the commodity the advertisers are bidding on, and its value. Most prior work has assumed that the probability of a user clicking on an ad is independent of the other ads shown on the page. We propose a simple Markovian user model that does not make this assumption. We then present an algorithm to determine the most efficient assignment under this model, which turns out to be different than that of GSP. A truthful auction then follows from an application of the Vickrey-Clarke-Groves (VCG) mechanism. Further, we show that our assignment has many of the desirable properties of GSP that makes bidding intuitive. At the technical core of our result are a number of insights about the structure of the optimal assignment

A "Quantal Regret" Method for Structural Econometrics in Repeated Games

We suggest a general method for inferring players' values from their actions in repeated games. The method extends and improves upon the recent suggestion of (Nekipelov et al., EC 2015) and is based on the assumption that players are more likely to exhibit sequences of actions that have lower regret. We evaluate this "quantal regret" method on two different datasets from experiments of repeated games with controlled player values: those of (Selten and Chmura, AER 2008) on a variety of two-player 2x2 games and our own experiment on ad-auctions (Noti et al., WWW 2014). We find that the quantal regret method is consistently and significantly more precise than either "classic" econometric methods that are based on Nash equilibria, or the "min-regret" method of (Nekipelov et al., EC 2015)

The value of location in keyword auctions

Sponsored links on search engines are an emerging advertising tool, whereby a number of slots are put on sale through keyword auctions. This is also known as contextual advertising. Slot assignment and pricing in keyword auctions are then essential for the search engine\u2019s management since provide the main stream of revenues, and are typically accomplished by the Generalized Second Price (GSP) mechanism. In GSP the price of slots is a monotone function of the slot location, being larger for the highest slots. Though a higher location is associated with larger revenues, the lower costs associated with the lowest slots may make them more attractive for the advertiser. The contribution of this research is to show, by analytical and simulation results based on the theory of order statistics, that advertisers may not get the optimal slot they aim at (the slot maximizing their expected profit) and that the GSP mechanism may be unfair to all the winning bidders but the one who submitted the lowest bid