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Abstract:
We extend Schmittlein et al.'s model (1987) of customer lifetime value to include satisfaction. Customer purchases are modeled as Poisson events and their rates of occurrence depend on the satisfaction of the most recent purchase encounter. Customers purchase at a higher rate when they are satisfied than when they are dissatisfied. A closed-form formula is derived for predicting total expected dollar spending from a customer base over a time period (0; T]. This formula reveals that approximating the mixture arrival processes by a single aggregate Poisson process can systematically under-estimate the total number of purchases and revenue.

Interestingly, the total revenue is increasing and convex in satisfaction. If the cost is sufficiently convex, our model reveals that the aggregate model leads to an over-investment in customer satisfaction. The model is further extended to include three other benefits of customer satisfaction: (1) satisfied customers are likely to spend more per trip on average than dissatisfied customers; (2) satisfied customers are less likely to leave the customer base than dissatisfied customers; and (3) previously satisfied customers can be more (or less) likely to be satisfied in the current visit than previously dissatisfied customers. We show that all the main results carry through to these general settings.

Customer Satisfaction, Customer Value Analysis, Hidden Markov Model, Non-stationarity, Stochastic Processes

Abstract:
We model how to measure consumer willingness to pay (WTP) from an English or ascending first-price auction based on two general bidding premises: no bidder bids more than her WTP, and no bidder allows a rival bidder to win at a price that she is willing to beat (Haile and Tamer 2003). In other words, we propose a "no regret" rule in bidding. Other than that, we do not impose restrictive assumptions on maximands or behavior of bidders in a competitive auction context. We postulate WTP as having two components: a pure product feature component and one based on the auction market environment. The latter includes bidder experience, seller reputation, and measures for competition among bidders and among items. The proposed model is general enough to include "buy it now" (BIN) (equivalent to a posted price) auction mechanism.

We use data of notebook auctions from one of the largest Internet auction sites in Korea. We find that most product characteristics matter in the expected ways. Our other primary findings are as follows: (1) WTP declines as more similar items are concurrently listed with the focal item; there is an additional effect if these similar items also belong to the same brand. Therefore, market thickness matters for consumer WTP. (2) More extensive site-surfing and bidding histories lead to lower WTP, implying that search costs and experience matter in bidding. As specific substantive benefits, we demonstrate how sellers can calculate changes in WTP, and hence the expected revenue, as the number of concurrently available similar items varies.

Abstract:
We develop a general parametric modeling framework for bidding behavior in Internet auctions. Toward this end, we incorporate and model simultaneously four key components of the bidding process under our integrated framework: Whether an auction will have a bid at all, (if so) who has bid, when they have bid, and how much they have bid over the entire sequence of bids in an auction.

This integrated framework is based on a single latent time-varying construct of consumer willingness to bid (WTB), which bidders have and update for a particular auction item over the course of the auction duration. Our modeling approach is also based on a simple yet very general bidding premise: The observed bidder's latent WTB at a specific bid is greater than the outstanding bid; yet, WTB is unconstrained for all other potential bidders. In this manner, we impose no structural assumption on bidder rationality or equilibrium behavior; instead, deriving our model using a probabilistic modeling paradigm. We describe in detail the advantages that our reducted-form approach allows us, and the limitations such an approach also entails.

Using a database of notebook auctions from one of the largest Internet auction sites in Korea, we demonstrate that this general (yet parsimonious) model captures the key behavioral aspects of bidding behavior. Furthermore, substantively, through a data-windowing procedure to assess the set of potential bidders for a given auctioned item, we provide a valuable tool for managers at auction sites to conduct their customer relationship management efforts which require them to evaluate the goodness (whether) of the listed auction items and the goodness (who, when, and how much to bid) of the potential bidders in their Internet auctions.

Bayesian inference, bidding behavior, probability model

Abstract:
A sequence of bids in Internet auctions can be viewed as record breaking events in which only those data points that break the current record are observed. We investigate stochastic versions of the classical record breaking problem for which we apply Bayesian estimation to predict observed bids and bid times in Internet auctions. Our approach to addressing this type of data is through data augmentation in which we assume that participants (bidders) have dynamically changing valuations for the auctioned item, but the latent number of bidders competing in those events is unseen.

We use data from notebook auctions provided by one of the largest Internet auction sites in Korea. We find significant variation in the number of latent bidders across auctions. Our other primary findings are as follows: (1) The latent bidders are significant in number relative to observed bidders; (2) The latent number of remaining bidders is considerably smaller than that of new entrants to the auction, after a given bid; and (3) Larger bid and time increments significantly influence the bidding participation behavior of the remaining bidders. As part of our substantive contribution, we highlight the model's ability to understand brand equity in an Internet auction context through a brand's ability to simultaneously bring in bidders, higher bid amounts and faster bidding.

Latent bidders, Bidding dynamics, Record breaking events, Bayesian inference, Data augmentation

Abstract:
In this paper, we study the bidding strategies of vertically differentiated firms that bid for sponsored search advertisement positions for a keyword at a search engine. We study two popular auction mechanisms: pay-per-impression and pay-per-click. Our model yields several interesting insights and one main counter-intuitive result we focus on is the “position paradox.” The paradox is that a superior firm may bid lower than an inferior firm and obtain a position below it, but still obtain more clicks than the inferior firm. Our results are in contrast to the extant literature on position auctions in sponsored search advertising which has shown, or often simply assumed, that higher positions obtain more clicks and firms will bid so as to order themselves in decreasing order of quality.

Under a pay-per-impression mechanism, the inferior firm wants to be at the top where more consumers click on its link, even though it has to pay a higher advertising fee. At the same time, the superior firm is better off by displaying its link at a lower position as it pays less but some consumers will still reach it in the search of a higher-quality firm. We also find that, surprisingly, as the quality premium for the superior firm increases, the incentive for the inferior firm to be at the top may increase. Furthermore, under the pay-per-click mechanism, we find that the inferior firm has a stronger incentive to be at the top since now it only has to pay for the consumers who do not know the firms' reputations and, therefore, click on its link. We also and that if more consumers know the identity of the superior firm, the incentive for the inferior firm to be at the top may increase. We test our basic results empirically using a unique dataset from a major search engine firm in Korea and find strong empirical support for the position paradox.

sponsored search advertising, search cost, vertical differentiation, bidding strategy, pay-per-impression, pay-per-click

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

Abstract:
We develop a model of consumer learning and choice behavior in response to uncertain serviceat the marketplace. Learning could be asymmetric, i.e., consumers may associate differentweights with positive and negative experiences. Under this consumer model, we characterize thesteady-state distribution of demand for retailers given that each retailer holds constant in-stockservice level. We then consider a non-cooperative game at the steady-state between two retailerscompeting on the basis of their service levels. Our model yields a unique pure strategy Nashequilibrium. We show that asymmetry in consumer learning has a significant impact on theoptimal service levels, market shares and profits of the retailers. When retailers have differentcosts, it also determines the extent of competitive advantage enjoyed by the lower cost retailer.

Asymmetric Consumer Learning, Customer Satisfaction, Inventory Competition, Retail Operations

Abstract:
We develop a model of consumer learning and choice behavior in response to uncertain service in the marketplace. Learning could be asymmetric, i.e., consumers may associate different weights with positive and negative experiences. Under this consumer model, we characterize the steady-state distribution of demand for retailers given that each retailer holds constant in-stock service level. We then consider a non-cooperative game in steady-state between two retailers competing on the basis of their service levels. The demand distributions of retailers in this game are modeled using a multiplicative aggregate market-share model in which, the mean demands are obtained from the steady-state results for individual purchases, but the model is simplified in other respects for tractability. Our model yields a unique pure strategy Nash equilibrium. We show that asymmetry in consumer learning has a significant impact on the optimal service levels, market shares and profits of the retailers. When retailers have different costs, it also determines the extent of competitive advantage enjoyed by the lower cost retailer.

Asymmetric Consumer Learning, Customer Satisfaction, Inventory Competition, Retail Operations