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Abstract:
Despite the growing research interest in Internet auctions, particularly those on eBay, little is known about quantifiable consumer surplus levels in such mechanisms. Using an ongoing novel field experiment that involves real bidders participating in real auctions, and voting with real dollars, we collect and examine a unique dataset to estimate consumer surplus in eBay auctions. The estimation procedure relies mainly on knowing the highest bid, which is not disclosed by eBay, but is available to us from our experiment. At the outset we assume a private value second-price sealed-bid auction setting, as well as a lack of alternative buying options within or outside eBay. Our analysis, based on a sample of 4514 eBay auctions, indicates that consumers extract a median surplus of at least $4 per eBay auction. This estimate is unbiased under the above assumptions, and otherwise it is a lower bound. The distribution of surplus is highly skewed given the diverse nature of the data. We find that eBay's auctions generate at least $7.05 billion in total consumer surplus in the year 2003 and may generate up to $7.68 billion if the private value sealed-bid assumption does not hold. We check for the validity of our assumptions and the robustness of our estimates using an additional dataset from 2005 and a randomly sampled validation dataset from eBay.

eBay, sniping, highest bid, consumer surplus

Abstract:
Despite the growing research interest in Internet auctions, particularly those on eBay, little is known about quantifiable consumer surplus levels in such mechanisms. Using an ongoing novel field experiment that involves real bidders participating in real auctions, and voting with real dollars, we collect and examine a unique dataset to empirically quantify and understand determinants of consumer surplus in eBay auctions. The estimation procedure for private value auctions relies mainly on knowing the highest bid, which is not disclosed by eBay, but is available to us from our experiment. For common value auctions, where bidders bid strategically to avoid winner's curse, we develop an estimation procedure that infers the bidders' signals from their bids, and subsequently infers the item's common value and resulting surplus, from the signals. Our analysis, based on a sample of 4514 eBay auctions, indicates that the average surplus level per eBay auction is $15.59, which roughly translates to $6.5 billion in accrued consumer surplus for the year 2003 alone. We find that consumer surplus is significantly different across currencies and item categories, negatively influenced by seller experience, auction duration and competition, and positively influenced by bidder experience, bidder aggressiveness and item price.

eBay, sniping, highest bid, Weibull distribution

Abstract:
Sales by small volume sellers are systematically undercounted in public and private surveys of ecommerce. The twin results are that the contribution of small sellers to the ecommerce marketplace is considerably larger than generally assumed and the overall market is larger by this difference.

As the costs of selling things online have fallen with cheaper equipment and communications fees, and with the availability of retail platform services provided by eBay, Amazon.com, Google, and many other firms, Internet retailing has grown to include many small businesses and individual occasional sellers, particularly in the United States. But how much do these "small sellers" sell each year?

U.S. Government statistics give some insight into the type and sales volume of online sellers, but the Government's current methods of data collection and analysis are better suited to tracking larger, traditionally organized businesses, rather than "small sellers," whether operating as small businesses or as individuals. Traditionally, small sellers simply were ignored. In traditional retail markets, the number of businesses with low annual revenues may not be significant because the contribution of such small sellers to the overall size of the market is relatively small. However, in Internet retailing, there are millions of small sellers that, in the aggregate, make a large contribution to the overall market. Yet these small sellers are systematically overlooked in government and private data collection and analysis.

In this paper, we estimate the size of Internet retailing in 2004 to have been over 20% above U.S. Government estimates - and the difference is explained by a more accurate accounting of sales by small sellers. We do this through a variety of methods and the development of confidence intervals in our data. We hope that the techniques outlined in this paper will give greater insight into the magnitude of Internet retailing, particularly in the "long tail" of the ecommerce market occupied by small volume sellers.

Internet Retailing, Long Tail, Electronic Commerce

Abstract:
Online auctions, consumer surplus, eBay, sniping.

Online auctions, consumer surplus, eBay, sniping

Abstract:
In this paper, we develop a model for estimating flight departure delay distributions required by air traffic congestion prediction models. We identify and study major factors influencing flight departure delays, and develop a strategic departure delay prediction model. This model employs nonparametric methods for daily and seasonal trends. In addition, the model uses a mixture distribution to estimate the residual errors. In order to overcome problems with local optima in the mixture distribution, we develop a global optimization version of the Expectation Maximization algorithm, borrowing ideas from Genetic Algorithms. The model demonstrates reasonable goodness of fit, robustness to the choice of the model parameters, and good predictive capabilities. We use flight data from United Airlines and Denver International Airport from the years 2000/01 to train and validate our model.

Smoothing spline, mixture model, Expectation Maximization (EM), Genetic Algorithm (GA), airline delay, airspace congestion, delay distribution

Abstract:
This research uses functional data modelling to study the price formation process of online auctions. It conceptualizes the price curve and its first and second derivatives(velocity and acceleration respectively) as the primary objects of interest. Together these three functional objects permit us to talk about the energy of an auction, and how the influence of its determinants vary as a function of auction time. For instance, we find that the incremental impact of an additional bidder's arrival on the rate of price increase is smaller towards the end of the auction. Our analysis suggests that "stakes" do matter and that the rate of price increase is faster for more expensive items, especially at the start and the end of an auction. It is observed that higher seller ratings (which correlate with experience) positively influence the price dynamics, but the effect is weaker in auctions with longer durations. Interestingly, we find that the price level is negatively related to auction duration when the seller has low rating whereas in auctions with high-rated sellers longer auctions achieve higher price levels throughout the auction, and especially at the start and end. Our methodological contributions include the introduction of functional data analysis as a viable toolkit for exploring the structural characteristics of electronic markets.

Functional regression analysis, data smoothing, eBay, online auction, auction dynamics, electronic commerce

Abstract:
Electronic commerce, and in particular online auctions, have received an extreme surge of popularity in recent years. While auction theory has been studied for a long time from a game-theory perspective, the electronic implementation of the auction mechanism poses new and challenging research questions. In this work, we focus on the price formation process and its dynamics. We present a new source of rich auction data and introduce an innovative way of modelling and analyzing price dynamics. We represent auctions as functional objects by accommodating the special structure of bidding data. We then use functional data analysis to characterize different types of auctions. Our findings suggest that there are several types of dynamics even for auctions of comparable items. By profiling these differences with respect to features associated with the auction format, the seller and the winner we find new relationships between dynamics and auction settings, and we tie these findings to the existing literature on online auctions.

functional data analysis, clustering, differential equations, electronic commerce, online auction, eBay, price dynamics, auction types

Abstract:
Empirical research of online auctions has dramatically grown in recent years. Studies using publicly available bid data from websites such as eBay.com have found many divergences of bidding behavior and auction outcomes compared to ordinary offline auctions and auction theory. Among the main differences between online and offline auctions is their longer duration (typically a few days). Along with the anonymity of bidders and sellers and the low barriers of entry, the longer online auctions tend to exhibit variable dynamics both in the bid arrivals and in the price process. In this paper we propose a family of differential equations models that captures the dynamics in online auctions. We show that a second-order differential equation well-approximates the three-phase dynamics that take place during an eBay auction. We then propose a novel multiple-comparisons test to compare dynamic models of auction sub-populations, where the population grouping is based on characteristics of the auction, the item, the seller, and the bidders. We accomplish the modeling task within the framework of principal differential analysis and functional data models.

Auction dynamics, functional data analysis, differential equation, price curve, multiple comparisons

Abstract:
Research literature to date shows few attempts to formalize a successful method for bidding in online auctions. We have collected and analyzed data from approximately 5,000 eBay auctions of laptop computers, in order to develop a system that could guide an auction participant to winning without overpaying. As the foundation for our work, we construct three different models of final auction prices, one of which uses solely mean normalized price levels to make predictions. Next, we describe a strategy for using any one of our models in a live auction setting. The strategy is based on plausible assumptions about the general behavior and motivations of online auction participants. In the context of this strategy, we examine the performance of each of our models on test data. For the subset of test auctions that each model wins, we also examine the performance of the two alternative models, in order to quantify a user's incentive to switch from one model to another. Results for the model of mean normalized price levels are very promising, and our paper concludes with some discussion of this finding.

online auctions, statistical models, price prediction, strategic bidding

Abstract:
Summary.We introduce a new family of non-homogeneous Poisson processes (NHPP) that are useful for modeling pure and contaminated self-similar processes which describe arrivals within a finite time period. Our motivation comes from the bid arrival process in online auctions.

Modeling bid arrivals in online auctions is challenging since bidding dynamics change over the course of the auction. While the start of the auction typically sees an unusual amount of early bidding which is followed by a period of little activity, the auction end typically experiences an enormous amount of last minute bidding, also known as sniping. This observed heterogeneity in bidding dynamics commands a very flexible class of models. We address these modeling challenges by proposing a class of 3-stage non-homogenous Poisson processes. We investigate the probabilistic and statistical properties of these models and illustrate their usefulness for fitting and interpreting real data from eBay.com.

Non-homogenous Poisson process,online auction,bid data, self-similarity, bidding dynamics

Abstract:
In this paper we propose a sampling-based implementation of the EM algorithm for modelbased clustering. By sampling-based we mean that the algorithm uses only a small sample from the entire database in every iteration. Using only a small sample allows for significant computational improvements. In contrast to previous sampling-based versions, we suggest to select the sample randomly since a random selection allows for statistical evaluation of the algorithm's progress. By appealing to EM's famous likelihood ascent property, the algorithm chooses samples as small as possible, thus ensuring computational efficiency, at the same time the samples are large enough to advance the progress of the method. The algorithm is stochastic in nature and has the potential of overcoming local traps and suboptimal solutions. We apply the algorithm to the problem of clustering infinite-dimensional curves and illustrate it on a large database of online auctions.

stochastic optimization, monte carlo, em algorithm, clustering, functional data, electronic commerce, online auction, eBay

Abstract:
Semi-continuous data arise in many applications where naturally-continuous data become contaminated by the data generating mechanism. The resulting data contain several values that are too frequent, and in that sense are a hybrid between discrete and continuous data. The main problem is that standard statistical methods, which are geared towards continuous or discrete data,cannot be applied adequately to semi-continuous data. We propose a new set of two transformations for semi-continuous data that iron-out the too-frequent values thereby transforming the data to completely continuous. We show that the transformed data maintain the properties of the original data, but are suitable for standard analysis. The transformations and their performance are illustrated using simulated data and real auction data from the online auction site eBay.

data tranformation, too-frequent values, jittering, local-regeneration, max-bin histogram, online auction, eBay

Abstract:
We introduce a semiparametric approach for modeling the effect of concurrent events on an outcome of interest. Concurrency manifests itself as temporal and spatial dependencies. By temporal dependency we mean the effect of an event in the past. Modeling this effect is challenging since events arrive at irregularly spaced time intervals and thus the standard definition of time-lags does not apply. Our concurrency model also takes spatial effects into account. We interpret the meaning of "space" in a slightly non-traditional way in order to conceptualize the more abstract notion of space among a set of item-features. We motivate our model in the context of eBay's online auctions. In particular, we model the effect of concurrent auctions on an auction's price. Our concurrency model consists of three components: a transaction-related component that accounts for auction-design and bidding-competition, a spatial component that takes into account similarity among item-features, and a temporal component that accounts for events in the past. To construct each of these model components, we borrow ideas from spatial modeling and from the mixed model methodology. We also develop a new time-lag metric to handle unevenly-spaced time series by interpreting a time-lag as the information distributed over a certain time-window in the past and by incorporating this information via inclusion of appropriate summary measures. We illustrate the power of this model by applying it to a large and diverse set of laptop auctions crawled off 1 eBay.com. We show that our model results in superior predictive performance compared to a set of competitor models. Our model also allows for new insight into the factors that drive price in eBay's online auctions and their relationship to bidding-competition, auction-design, product-variety and temporal learning effects.

Nonparametric model, distance measure, dissimilarity, spatial model, timelag, mixed model, online auction, E-Bay

Abstract:
Creating a loyal customer base is one of the most important, and at the same time, most difficult tasks a company faces. Creating loyalty online (e-loyalty) is especially difficult since customers can "switch" to a competitor with the click of a mouse. In this paper we investigate e-loyalty in online auctions. Using a unique data set of over 30,000 auctions from one of the main consumer-to-consumer online auction houses, we propose a novel measure of e-loyalty via the associated network of transactions between bidders and sellers. Using a bipartite network of bidder and seller nodes, two nodes are linked when a bidder purchases from a seller and the number of repeat-purchases determines the strength of that link. We employ ideas from functional principal component analysis to derive, from this network, the loyalty distribution which measures the perceived loyalty of every individual seller, and associated loyalty scores which summarize this distribution in a parsimonious way. We then investigate the effect of loyalty on the outcome of an auction. In doing so, we are confronted with several statistical challenges in that standard statistical models lead to a mis-representation of the data and a violation of the model assumptions. The reason is that loyalty networks result in an extreme clustering of the data, with few high-volume sellers accounting for most of the individual transactions. We investigate several remedies to the clustering problem and conclude that loyalty networks consist of very distinct segments that can best be understood individually.

Online auction, electronic commerce, functional data, principal component analysis, model assumptions, random effects model, weighted least squares, clustering

Abstract:
Pre-release demand forecasting is crucial for allocating limited marketing resources and is one of the most challenging tasks facing decision makers. In this study, we present a powerful pre-release forecasting method via functional shape analysis (FSA) of the trading price histories of an online virtual stock market (VSM). Specifically, we use FSA to extract the key characteristics that capture the similarities and differences in the shapes across various trading histories and then use these key characteristics to produce forecasts.

We analyze one of the best-known online VSMs, the Hollywood Stock Exchange, in forecasting release week box office revenues of motion pictures. While several conventional forecasting methods result in forecasting errors as high as 60%, our method has a forecasting error of only 8.31%. As compared to the VSM literature that has largely focused on the most recent trading prices alone, our approach of analyzing the trading histories reduces the forecasting errors by up to 50%. Moreover, applying our method to the early, partial trading histories yields early and dynamic forecasts that are highly valuable to decision makers and are not readily available from using conventional methods. Our approach represents a novel contribution to both the VSM and marketing literature. We further provide conceptual interpretations of the shapes of the trading histories that help decision makers identify the key indicators (e.g. a last-moment price spurt) of a potentially successful new product or service.

Forecasting, Innovation, Marketing Research, Entertainment Marketing, Motion Picture, Online Virtual Stock Market, Prediction Market, Trading Dynamics, Nonparametric Statistical Method, Functional Shape Analysis, Functional Data Analysis, Smoothing, Functional Principal Component Analysis

Abstract:
Initial applications of prediction markets (PMs) indicate they provide good forecasting instruments in many settings, such as elections, the box office, or product sales. One particular characteristic of these “first-generation” (G1) PMs is that they link the payoff value of a stock’s share to the outcome of an event. Recently, “second-generation” (G2) PMs have introduced alternative mechanisms to determine payoff values which allow them to be used as preference markets for determining preferences for product concepts or as idea markets for generating and evaluating new product ideas. Three different G2 payoff mechanisms appear in existing literature, but they have never been compared. This study conceptually and empirically compares the forecasting accuracy of the three G2 payoff mechanisms and investigates their influence on participants’ trading behavior. We find that G2 payoff mechanisms perform almost as well as their G1 counterpart, and trading behavior is very similar in both markets (i.e., trading prices and trading volume), except during the very last trading hours of the market. These results indicate that G2 PMs are valid instruments and support their applicability shown in previous studies for developing new product ideas or evaluating new product concepts.

prediction markets, preference markets, idea markets, forecasting, decision making, new product development

Abstract:
Forecasting the price in online auctions is important for buyers and sellers. With good forecasts, bidders can make informed bidding decisions and sellers can select the right time and place to list their products. While information from other auctions can help forecast an ongoing auction, it should be weighted by its relevance to the auction of interest. We propose a novel functional K-nearest neighbor (fKNN) forecaster for real-time forecasting of online auctions. The forecaster uses information from other auctions and weighs their contribution by their relevance in terms of auction, seller and product features, and by similarity of the price paths. We capture an auction's price path borrowing ideas from functional data analysis. We propose a novel Beta growth model, and then measure distances between two price paths via the Kullback-Leibler distance. Our resulting fKNN forecaster incorporates a mixture of functional and non-functional distances. We apply the forecaster to several large datasets of eBay auctions, showing improved predictive performance over several competing models. We also investigate performance across various levels of data heterogeneity, finding that fKNN is particularly effective for forecasting heterogeneous auction populations.

eBay, functional forecasting, functional data, Kullback-Leibler distance, Beta distribution, dynamics

Abstract:
The flexibility of time and location as well as the availability of an abundance of both old and new products makes online auctions an important part of people's daily shopping experience. While many bidders rely on variants of the well-documented early or last-minutes bidding strategies, neither strategy takes into account the aspect of auction competition: at any point in time, there are hundreds, even thousands of same or similar items up for sale, competing for the same bidder. In this paper, we propose a novel automated and data-driven bidding strategy. Our strategy consists of two main components. First, we develop a dynamic, forward-looking model for price in competing auctions. By incorporating dynamic features of the auction process and its competitive environment, our model is capable of accurately predicting an auction's price, outperforming model-alternatives such as GAM, CART or Neural Networks. Then, using the idea of maximizing consumer surplus, we build a bidding framework around this model that determines the best auction to bid on and the best bid-amount. The best auction to bid on yields the highest predicted surplus and the best bid-amount is the predicted auction price. In simulations, we compare our automated strategy with early and last-minute bidding and find that our approach extracts 97% and 15% more expected surplus, respectively.

functional data, dynamics, online auction, bidding, forecasting, competition, eBay, electronic commerce, consumer surplus

Abstract:
The Expectation-Maximization (EM) algorithm is a very popular optimization tool for mixture problems and in particular for model-based clustering problems. However, while the algorithm is convenient to implement and numerically very stable, it only produces local solutions. Thus, it may not achieve the globally optimal solution in problems that have a large number of local optima. This paper introduces several new algorithms designed to produce global solutions in model-based clustering. The building blocks for these algorithms are methods from the operations research literature, namely the Cross-Entropy (CE) method and Model Reference Adaptive Search (MRAS). One problem with applying these methods directly is the efficient simulation of positive definite covariance matrices. We propose several new solutions to this problem. One solution is to apply the principles of Expectation-Maximization updating, which leads to two new algorithms, CE-EM and MRAS-EM. We also propose two additional algorithms, CE-CD and MRAS-CD, which rely on the Cholesky decomposition. We conduct numerical experiments of varying complexity to evaluate the effectiveness of the proposed algorithms in comparison to classical EM. We find that although a single run of the new algorithms is slower than a single run of EM, all have the potential for producing significantly better solutions. We also find that although repeat application of EM may achieve similar results, our algorithms provide automated, data-driven decision rules which may significantly reduce the burden of searching for the global optimum.

EM algorihm, global optimum, mixture model

Abstract:
Even though auctions are capturing an increasing share of commerce, they are typically treated in the theoretical economics literature as isolated. That is, an auction is typically treated as a single seller facing multiple buyers or as a single buyer facing multiple sellers. In this paper, we review the state of the art of competition between auctions. We consider three different types of competition: competition between auctions, competition between formats, and competition between auctioneers vying for auction traffic. We highlight the newest experimental, statistical and analytical methods in the analysis of competition between auctions.

auctions, bidding, competition, auction formats, auction houses