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See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/220066702 Impact of e-book technology: Ownership and market asymmetries in digital transformation Article in Electronic Commerce Research and Applications · September 2010 DOI: 10.1016/j.elerap.2010.06.003 · Source: DBLP CITATIONS 38 READS 508 2 authors: Some of the authors of this publication are also working on these related projects: Platform Complements View project 2D materials View project Yabing Jiang Florida Gulf Coast University 29 PUBLICATIONS 190 CITATIONS SEE PROFILE Evangelos Katsamakas Fordham University 49 PUBLICATIONS 872 CITATIONS SEE PROFILE All content following this page was uploaded by Yabing Jiang on 08 February 2018. 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Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright http://www.elsevier.com/copyright Author's personal copy Impact of e-book technology: Ownership and market asymmetries in digital transformation Yabing Jiang *, Evangelos Katsamakas Information Systems, Graduate School of Business Administration, Fordham University, 113 W. 60th Street, New York, NY 10023, United States a r t i c l e i n f o Article history: Available online 1 July 2010 Keywords: Product differentiation E-books Book industry Information goods Digital goods E-commerce Channel competition Economic analysis Ownership Transformation a b s t r a c t The book industry is undergoing a digital transformation enabled by the Internet and e-book technology, which offers a novel channel for delivering books to consumers who mostly purchase paper books from physical or online bookstores. With a game theory model that introduces the concepts of paper book mar- ket asymmetry and e-book market asymmetry, we examine how the entry of an e-book seller affects stra- tegic interaction in the book markets and impacts sellers and consumers. We show that market asymmetries, ownership of the e-book seller, and consumers’ preferences for e-books are important determinants of prices, market shares and total book readership. We find that prices in the book market may increase after the e-book entry. Total readership may decrease after e-book entry, if the e-book seller is owned by one of the paper book sellers. The lowest total readership occurs when the online paper book seller owns the e-book seller. � 2010 Elsevier B.V. All rights reserved. ‘‘Like many other parts of the media industry, publishing is being radically reshaped by the growth of the Internet. Online retailers are already among the biggest distributors of books. Now e-books threaten to undermine sales of the old-fashioned kind.” (The Economist 2010) 1. Introduction Publishing and book markets are undergoing a transformation due to the Internet and the emerging e-book technology. In November 2007, Amazon, the dominant online book seller, un- veiled Kindle, a lightweight e-book reader that many observers called the ‘‘iPod of books”, as it is likely to transform how people read books. The Kindle device is only one component of the e-book platform provided by Amazon. Other components include an e-book store that provides the e-books as well as the software that encodes and protects the books once they are downloaded into the device. Customers can browse books and download the purchased books through a 3G network. The original Kindle holds up to 1500 titles and features e-ink screen technology that makes reading as pleasant as reading paper.1 Using a Kindle software application, cus- tomers may also read their e-books on their iPhones or personal computers. In addition to Amazon’s Kindle, Sony offers Reader, an- other popular e-book device, and its own e-book store. Barnes and Noble announced its own e-book store and its Nook e-book reader in late 2009. In April 2010, Apple released its iPad tablet computer, which targets several media markets including e-books. E-book technologyoffers a new way for book delivery to read- ers, whereby a digital copy of a book (e-book) is delivered to a de- vice that a consumer uses. The American Association of Publishers estimates that e-book sales in the US reached $113 million in 2008. This is still a fraction of the $24.3 billion book market, but e-book sales grew 68.4% in 2008, while total book sales decreased 2.8% (AAP 2009). In addition to purchasing a paper book through a phys- ical bookstore or an online store, customers can now download an e-book from an e-book seller. According to Publishers Weekly, book- chains and online stores hold 32.5% and 30% shares of consumer physical book purchases in 2008 (Milliot 2008). Competition be- tween online and physical sellers of products has been analyzed in the literature on e-commerce and related channel-competition 1567-4223/$ - see front matter � 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.elerap.2010.06.003 * Corresponding author. Tel.: +1 212 636 6131; fax: +1 212 765 5573. E-mail addresses: yajiang@fordham.edu (Y. Jiang), katsamakas@fordham.edu (E. Katsamakas). 1 The popularity of the first Kindle motivated Amazon to introduce Kindle 2 (costs $259 as of January 2010) and Kindle DX, a larger screen device targeting the newspaper and textbook markets. Prices for Kindle e-books and newspaper subscriptions are typically cheaper than the paper versions. For instance, most best-sellers and new releases are $9.99, while the list price of the paper book is typically more than $20. Electronic Commerce Research and Applications 9 (2010) 386–399 Contents lists available at ScienceDirect Electronic Commerce Research and Applications journal homepage: www.elsevier .com/locate /ecra Author's personal copy (Balasubramaniam 1998, Viswanathan 2005, Cheng and Nault 2007), but this early literature has not considered competition be- tween digital and physical products across different channels. As shown in Fig. 1, this paper analyzes the novel phenomenon of the competition between the e-book seller who sells digital goods and pre-existing sellers of physical goods. The paper focuses on the strategic interaction between the selling of e-books and that of physical books in the book market. In the book market of Fig. 1, consumers must decide whether to buy a paper book from either seller A or B, or buy an e-book, or not buy any book. The e-book technology may enhance some users’ reading experience. For example, it provides value-added features such as automatic bookmark, dictionary, note taking, search capa- bility, and text-to-voice functions. The device can store multiple ti- tles so that users can easily carry around a personal library. However, there are also downsides to using the e-book device. The e-books are often protected by a DRM technology, which limits a book owner’s capability of sharing the titles they bought. In addi- tion, some customers may prefer the experience of holding and reading a paper book. E-book technology alleviates the need to produce, store, and distribute physical books. At the same time, it decreases the pro- duction costs of book publishing. However, publishers are con- cerned that e-books will cannibalize existing paper book sales and that consumers will get used to low e-book prices, which may put pressure on the prices of paper books (The Economist 2010). To examine this concern, this paper conveys three main observations. First, e-books compete with paper books, which may be sold by offline or online sellers. Consequently, one needs to consider carefully how costs and consumer preferences for e-books and paper books differ. Second, as e-books can be sold by an independent e-book seller or by sellers that already sell paper books (e.g. Amazon), it is important to consider whether ownership has a significant effect on prices and total readership. Third, the e-book market is currently small but growing as e-book technology advances, so it is helpful to understand how improve- ments in e-book technology can affect prices and the total reader- ship in the future. The research question is: how do the ownership of the e-book seller, the advances in e-book technology and the dif- ferences between selling paper books and e-books affect prices and the total readership in book markets? We answer this question by means of a game theory model based on the literature on product differentiation, channel compe- tition, and information goods. In particular, we extend Salop’s (1979) ‘‘unit circle” modeling idea2 to a new model that examines how the entry of an e-book seller affects strategic interactions in the book market. Introducing the concepts of book market asymmetry and e-book market asymmetry, our model shows that these market asymmetries affect not only the prices and total readership but also the incentives of online and offline sellers to own the e-book seller. Because e-book technology is new, we also examine whether the an- swer to our main research question is sensitive to alternative sequential pricing cases, where the e-book seller or the paper book sellers set prices first. Previous IS research on information and digital goods focused on issues of piracy and the value of digital rights management (DRM) technology (Chellappa and Shivendu 2005, Smith and Telang 2009, Sundararajan 2004) and pricing issues such as ver- sioning and bundling (Bakos and Brynjolfsson 2000). Multiple empirical studies used online book sales data and found that price dispersion does not disappear on the Internet (Brynjolfsson and Smith 2000, Clay et al. 2001, 2002); social welfare increases sub- stantially due to increased product variety offered by online sellers like Amazon (Brynjolfsson et al. 2003); price rigidity does not disappear and it differs across types of books and retailers (Bergen et al. 2005); and only 16% of used-book sales cannibalize new book sales at Amazon, leading to an increase of consumer and social welfare (Ghose et al. 2006). This literature has paid less attention to the theoretical analysis of the strategic interaction between digital and physical information goods. An exception is (Oestreicher-Singer and Sundararajan 2006) that analyzes the value of digital rights in the context of a monopolist selling a physical and a digital book, and finds that the monopolist should restrict certain digital rights in the presence of piracy. We find that in response to the entry of an e-book seller, firms may increase or decrease their prices on paper books, depending on market conditions. Similarly, as the e-book technology becomes acceptable to more customers, the price competition between the paper book sellers and the e-book seller is sometimes relaxed. This means that the prices for both the paper book and e-book can increase. Another counter-intuitive result is that the entry of an e-book seller does not always expand the total readership. We show that when a firm offers both the paper books and e-books and competes with a pure paper book seller, more customers are left un-served than when both firms only sell paper books. In addi- tion, we find that a paper book seller may prefer to compete with an integrated book seller that offers both paper books and e-books rather than compete with an independent e-book seller. Our analysis provides strategic insights for managers in the book and publishing industry, but it is also relevant, more generally, to managers of industries that undergo a digital transformation. Thus, we answer the call for more research on how digitization progres- sively transforms information-goods industries, as managers need to understand and manage this transformation (Agarwal and Lucas 2005). The article is structured as follows: Section 2 defines the model whereas Sections 3–5 analyze and discuss the results. In particular, Section 3 analyzes the physical book duopoly before the entry of the e-book seller. Section 4 discusses the entry of an e-book seller and its impact on the market when the market is symmetric. Sec- tion5 discusses the effects of market asymmetries. Section 6 pro- vides a few concluding remarks. Transformation of book market due to e-book technology Physical books e-books Physical books Consumers Book seller A Book seller B E-book seller E Book seller A Book seller B Consumers (a) Physical book market (a firm can be an online or offline seller) (b) E-book seller enters into the book market (strategic interaction of selling e-books and physical books) Fig. 1. Overview of research framework. 2 Building on Salop’s (1979) ‘‘circular” market is a well-established approach in IS economics, e.g. the analysis of search costs (Bakos 1997) and mass-customization strategies (Dewan et al. 2003). Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 387 Author's personal copy 2. The model We consider a book market in which consumers have a unit de- mand and a common reservation value V for a given book title that is independent of its electronic or physical format. Consumers are heterogeneous along two dimensions, which define consumers’ preferences for physical books and e-books. The first dimension conveys the consumer’s preferences for physical books in a circular spatial market, as in Salop (1979). Cus- tomers are distributed uniformly on a circle of unit circumference and their total mass is equal to 1. Two firms A and B, selling iden- tical paper books, are located on the circle symmetrically at equal distance apart from each other. Depending on their locations on the circle relative to firms A and B, customers who buy a paper book from B incur a disutility t per unit distance, whereas custom- ers who buy from A incur a disutility kt per unit distance, with k 6 1. We use the distance-related disutility term to capture the fact that customers have a different willingness to pay for books and different preferences for sellers. The source of this customer heter- ogeneity could be due to different transportation costs, opportu- nity costs, brand or service differentiation, convenience of shopping, loyalty to one firm rather than to another, or other transaction costs or sources of disutility (Ellison and Ellison 2005, Forman et al. 2009). Capturing the potential asymmetry of firms A and B, the parameter k constitutes a novel extension of Salop’s (1979) circular model. When k = 1, the circular component of our model is identical to Salop’s (1979) setup. But when k < 1, firm A is associated with a lower unit-distance disutility than firm B. As a result, the physical book market is asymmetric. While there can be many potential sources of such asymmetry, we will focus on the case that A is an online seller of physical books and B an offline seller of physical books. Now, some consumers of paper books may prefer buying online, while others may prefer buying offline. Online channels have shipping costs and delayed gratification. However, the unit-distance disutility of the online channel is lower than that of the offline channel, because the for- mer allows for greater personalization and flexibility (Viswanathan 2005). In addition, customers who buy offline do incur a physical transportation (travel) cost and a cost of traveling but not finding the book (Forman et al. 2009). Because of a limited selection of off- line sellers, online sellers face significant competition when they sell popular products, but little competition when it comes to niche products (Brynjolfsson et al. 2009). This suggests that, everything else being equal, the physical book market asymmetry may in- crease, the less popular the book is. The consumers’ preferences for e-books are defined by three assumptions: (a) consumers have a disutility te of buying the e-book that is either3 te1 or te2, (b) te1 < V < te2 and (c) for a consumer in the neighborhood of A, her disutility of e-books is te1 with proba- bility q, while for a consumer in the neighborhood of B, her disutility of e-books is te1 with probability mq, where 0 < m 6 1. Assumption (a) says that consumers have a different willing- ness to pay for e-books as they differ in their disutility te of buying the e-book. This disutility may be due to the need to purchase an e-book device, install e-book software, set up an e-book store account, and learn how to use the device. It may also be caused by the inconvenience of reading electronic texts or digital restric- tions regarding sharing the e-book with friends, or more generally the ‘‘quality” of e-book technology and other related costs. Assumption (b) means that customers of type te1 (low e-book disutility) will consider e-books in their purchase decision and they may buy the e-book if it offers them greater surplus than the physical book. Customers of type te2 (high e-book disutility) do not like e-books in general and they do not consider e-books in their purchase decisions. These consumers may not be techno- logically sophisticated (Oestreicher-Singer and Sundararajan 2006), they may not be early adopters, or they may not like e- books for some other reason (AAP 2009). Assumption (c) suggests that when compared to consumers close to B, consumers close to A may be differentially attracted to e-books. This assumption conveys the e-book market asymme- try. When parameter m = 1, there is no systematic difference be- tween physical book sellers A and B’s customers. However, when m < 1, more of firm A’s consumers are likely to consider e-books than firm B’s consumers. This asymmetry may happen when A is an online seller of paper books, whereas B is an offline seller of physical books, in which case consumers close to A are likely to be more technologically sophisticated or be more attracted to try- ing e-books. For instance, consumers close to A may feel more comfortable about using an e-book reader, and they may already have accounts at the online bookstore that can be accessed through the e-reader device. By introducing this e-book market asymmetry, we are able to further investigate the impact of e-book technology when it has a differential impact on physical book sellers’ customer bases. Another difference between paper books and e-books is the cost structure. Both the paper book sellers and the e-book seller have to pay the publisher/author for royalty. However, while the paper book sellers incur a marginal production and distribution cost c, the e-book seller has a near zero marginal production/distribution cost, which is typical in the literature on information goods (Bakos and Brynjolfsson 2000). Thus, we normalize the royalty cost for both the paper book sellers and the e-book seller, and assume that the former incurs a marginal cost c whereas the latter has a zero marginal cost. The closest paper to our model setup is Balasubramaniam (1998), which considers retailers located on a Salop (1979) circle competing with a direct marketer located in the middle of the cir- cle. But that paper focuses on the number of retailers and on the strategic role of information at equilibrium. It does not consider the two types of market asymmetry that we discuss above; it does not consider the issue of ownership of the direct seller; and also it does not consider sequential entry as we do. Another related model is (Viswanathan 2005), which considers online and offline channel competition in the presence of a ‘‘hybrid” firm that operates in both channels, but that paper has two touching Salop (1979) circles and the main focus is on channel network effects and on switching costs. We advance the line of research in Balasubramaniam (1998) and Viswanathan (2005) by considering the competition between digital and physical products across different channels. At the same time, we discuss the implications of our new results in the context of emerging book markets that are being transformed by the e-book technology and IT. Table 1 summarizes the modeling notations. 3. Duopoly market of physical book sellers Let us consider the book market in which only the physical book sellers A andB are active and e-books are not available. We use the superscript D to represent results of this duopoly market. Let PDA be the price charged by firm A and c be the common marginal cost. The net valuation of a customer located at distance x apart from firm A is given by V � PDA � ktx. Similarly, the net valuation of a customer lo- cated at distance x apart from firm B is given by V � PDB � tx. We focus on the market-uncovered case such that some customers are priced out of the market. We analyze the market- uncovered case here because we are interested in examining the 3 This discrete distribution significantly simplifies our model analysis versus even the simple uniform distribution case (Dewan et al. 2000), without loss of generality. 388 Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 Author's personal copy potential market-expansion effect of the e-book technology. If the physical books market was fully covered before the entry of e-book seller, then one would not be able to examine what factors may af- fect the potential expansion of book readership. Now, let yDA be the location of a customer who is indifferent be- tween purchasing the title from A and not participating in the mar- ket. Since V � PDA � kty D A ¼ 0, we deduce that yDA ¼ ðV � P D A Þ=kt. Firm A will choose the optimal price PDA to maximize its net profit, which is given by: PDA ¼ 2yDA P D A � c � � : ð1Þ The duopoly pricing equilibrium (Lemma 1) states that custom- ers located within (V – c)/(2kt) distance from firm A or (V – c)/(2t) from firm B will purchase the physical book, and customers located further away from the firms will not purchase any book. As ex- pected, prices increase in the marginal cost c, but shares and profits decrease in c. Shares and profits also decrease in the disutility parameter t, but prices are independent of t, because by our assumption of (V � c)(k + 1) < kt the market is uncovered and both sellers set prices like a local monopolist. We assume that this parameter condition holds for the rest of the analysis so that we can focus on the market-uncovered case. It is interesting to note that the ratio of shares and profits for the two firms is fixed: SDB=S D A ¼ k and P D B=P D A ¼ k. Because in general the market asymmetry parameter k 6 1, the equilibrium condition implies that A’s share and profit are in general greater than or equal to B’s share and profit, respectively. The total market cover- age (SDA þ S D B ) decreases in k, because A’s market share decreases in k. Both prices are independent of k. 4. The symmetric market with an e-book seller In this section, we analyze and discuss the entry of an e-book seller when the market is symmetric with k = m = 1. The symmetric market implies that there are no systematic differences between sellers A and B’s customers in terms of their physical book prefer- ences or their e-book preferences. This simplification allows for greater expositional clarity and a detailed examination of the im- pact of e-book entry. In particular, we study two types of ownership of the e-book seller: an independent e-book seller and an integrated e-book sell- er owned by one of the paper book sellers, in three cases of sequen- tial actions: Case 1: Entry of an independent e-book seller, who sets the price on e-books first, whereas physical book sellers set the prices second. Case 2: Entry of an independent e-book seller when physical book sellers set the prices first, and the e-book seller sets the price second; and, Case 3: Entry of an e-book seller, who is integrated with the physical book seller A, and A sets the prices first. We focus on sequential pricing action because e-book technol- ogy is new: the new e-book seller either responds to the paper book sellers’ prices or takes the lead in setting the price.4 Table 1 Table of modeling notation. Notation Definition Comments b, D, 1, 2, 3 Superscripts representing results of the simultaneous move benchmark, duopoly market, Case 1, Case 2, and Case 3, respectively c Paper book sellers’ marginal production and distribution cost i Subscript index i = A, B, representing paper book sellers A and B, respectively k k 6 1 is a parameter that captures the paper book market asymmetry concept (the market is symmetric when k = 1, and asymmetric when k < 1) Consumers who purchase from seller A incur kt disutility per unit distance, whereas consumers who purchase from seller B incur t disutility per unit distance on the circle m m 6 1 is a parameter that captures the e-book market asymmetry concept (the market is symmetric when m = 1, and asymmetric when m < 1) When the e-book seller enters, mq of seller B’s consumers will consider e-books whereas q of seller A’s consumers will consider e-books Pi Price charged by paper book seller i When PA = PB, we occasionally use PA/B to stand for the price charged by sellers A and B Pe Price charged by the e-book seller E Si The paper book seller i’s market shares When the paper book seller i also owns the e-book seller E, i’s total market shares are given by Si + Se Se Market shares of the e-book seller E t Consumers’ unit-distance disutility of purchasing a paper book te Consumers’ disutility of purchasing an e-book, and te is either te1 or te2 with te1 < V < te2 Type te2 consumers do not consider e-books in their purchasing decision, whereas type te1 consumers do consider e-books. TR Total readership Subscript IE, AE, and BE representing the total readership when E is independent, owned by A, owned by B, respectively V Consumers’ common reservation value for a book title x A customer’s distance from a paper book seller on the circle y The location on the circle of the customer who is indifferent between purchasing the paper book from a paper book seller and not participating in the market yDA represents the location of a customer who is indifferent between purchasing the title from A and not participating in the duopoly market yp The location on the circle of the customer who is indifferent between purchasing the paper book and the e-book Gi Paper book seller i’s profit When the paper book seller i also owns the e-book seller E, i’s total profits are given by Gi + Ge Ge The e-book seller’s profit q The mass of paper book seller A’s consumers who have a low disutility te1 on e-books The mass of paper book seller B’s consumers who have a low disutility te1 on e-books is mq 4 As a benchmark, we also derived the pricing equilibrium when the paper book sellers and the e-book seller set prices simultaneously (Appendix Lemma 2). We use the superscript b to represent results of this simultaneous price move scenario. Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 389 Author's personal copy 4.1. Entry of an independent e-book seller Let us consider the same firms A and B selling physical books whereas a new independent entrant E obtains the right to sell the same titles as e-books through an e-book platform that may consist of a specialized reading device, a digital rights management (DRM) technology, and e-book software. A customer’s net valua- tion for the e-book depends on the price of the e-book Pe and the customer’s disutility te, and it is independent of the customer’s location on the circle. Due to the symmetry of the model, we illustrate the half-circle market on A’s side and omit the subscript A for the moment in or- der to simplify the notation. As shown in Fig. 2, let seller A be lo- cated at point 0; thus, A’s potential customers are located [0, 1=4] away from its location on both sides, before the entry of the e-book seller. This half-circle market has two segments: y and 1=4 � y where y = (V � P)/t, representing the location of the marginal cus- tomer for seller A. First, consider the 1=4 � y segment after the entry of the e-book seller. Customers in this segment will not purchase the paper book. However, customers with a low disutility te1 in this segmentmay purchase the e-book. Since a customer’s transaction cost te is independent of her location, the demand for e-book in the 1=4 � y segment is given by 2q(1=4 � y). Next, consider the y segment. We only focus on the case with Pe + te1 > P, which means that firm A always has some loyal customers who prefer paper books even though they have a low disutility of e-books. The marginal cus- tomer who prefers the paper book over the e-book is located at yp = (Pe + te1 � P)/t since V� P� typ = V� Pe� te1. Thus, the demand for the e-book in this segment is given by 2q(y � yp). The profit functions for the paper book sellers and the indepen- dent e-book seller can be simplified as: PA ¼ PB ¼ 2ðP � cÞ½ðV � PÞ=t � qðV � Pe � te1Þ=t� ð2Þ Pe ¼ 4qPe½1=4� ðPe þ te1 � PÞ=t�: ð3Þ Paper book sellers and the e-book seller will set the optimal prices to maximize their profits. We consider two cases of the Stac- kelberg game depending on whether the e-book seller moves first (Case 1), or the physical book sellers move first (Case 2). 4.1.1. Case 1: the independent e-book seller anticipates the move of physical book sellers In the first case, the e-book seller sets the price first, anticipat- ing the move of paper book sellers. This case applies when the pa- per book sellers do not foresee the entry of the new comer E, who secretly developed the electronic device and worked through deals with content providers. It also applies when the paper book sellers cannot observe which titles will be available on firm E’s electronic device. We use the superscript 1 to represent results of Case 1. The pricing equilibrium of this Stackelberg game is presented in Appendix Lemma 3. Comparing Pbe , the e-book price when all players move simulta- neously, with P1e , the e-book price when the independent E moves first, we find that P1e > P b e . That is, when E moves first, anticipating paper book sellers’ price response, it will set a higher price than when they move simultaneously. As a result, E captures a smaller market share (S1e < S b e). However, the profit comparison shows that P1e > P b e . Hence, compared with the simultaneous move scenario, the e-book seller E gains a higher profit level since E can determine its price taking into account the paper book sellers’ pricing response. In response to E’s price, the paper book sellers as the followers will also raise their prices from the simultaneous-move level (P1A=B > P b A=B). Because the price increase on the e-book is higher than that on the paper book, the market shares of the paper book sellers are actually higher than the simultaneous-move levels (S1A=B > S b A=B). Thus, the paper book sellers also benefit when the e-book seller acts first rather than when they move simultaneously. Compared with the physical book duopoly case, here the paper book sellers charge a lower price in response to the entry of the independent e-book seller, P1A=B < P D A=B. However, the market shares of the paper book sellers are reduced (S1A=B < S D A=B), even with re- duced prices. Thus, the paper book sellers’ profits are lower as well (P1A=B < P D A=B). We illustrate the impact of the entry of an independent e-book seller on the book market in a numerical example. Fig. 3 represents the one-quarter circular market in Case 1with firm A located at zero. Parameter values for this example are: V = 26, c = 10, t = 35, te1 = 20, and q = 0.2. Customers are uniformly distributed in the x–y space, with the x-axis representing the customer location on the circle and the y-axis representing the customer preference for the e-book. For example, customers below the line of q = 0.2 have a low disutility te1 on e-books and will consider e-books in their purchase decision. The vertical dotted line represents the customers who are indif- ferent between purchasing the paper book and not buying in the physical book duopoly case before E’s entry. The solid vertical line y represents the new marginal customers when an independent e-book seller enters. In this case, the price of the paper book is Firm A y ¼ - y y ¼ - y Fig. 2. Illustration of the half-circle market on firm A’s side. Case 1 0 1 0 0.25 Circular location D is tr ib ut io n of d is ut ili ty on e -b oo ks A y ρ =0.2 te2 te1 yp A E Fig. 3. An illustration of market shares for the 1=4 circular market in Case 1. 390 Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 Author's personal copy lower than that in the duopoly case, so some customers who were previously priced out of the market are able to purchase the paper book when the independent e-book seller enters. The solid vertical line yp represents the marginal customers who are indifferent between the paper book and e-book. For firm A, customers located in [yp, y] and with type te1 will now purchase the e-book instead of the paper book. Thus, when the independent e-book seller enters and acts as the leader in the Stackelberg game, the paper book sellers gain some new customers by lowering their prices, but they also lose some customers to the e-book seller. The entry of the e-book seller further expands the total book consumption because some type te1 customers (located between the dotted line and 0.25), who did not participate before E’s entry, now purchase an e-book. In summary, the total book market expands with some new customers purchas- ing physical books, and some other new customers purchasing the e-book. Thus, in Case 1 consumer surplus and social welfare increase with the entry of an independent e-book seller. 4.1.2. Case 2: the physical book sellers anticipate the entry of the independent e-book seller In the second case, the paper book sellers move first. This spe- cial case enables the study of e-book entry under adverse market conditions for the entrant firm. We use the superscript 2 to repre- sent results of case 2. The pricing equilibrium of this Stackelberg game is presented in Appendix Lemma 4. This case is similar to Case 1 in that not only the paper book sellers benefit by acting as the leaders in the price game, but the e-book seller also gains a higher profit level than when they move simultaneously. That is, P2A=B > P b A=B and P 2 e > P b e . However, when the paper book sellers are leaders in the Stackelberg game, the price of the paper book can be lower or high- er than the price in the duopoly case depending on the parameter conditions. It is a little surprise to see that the entry of an indepen- dent e-book seller can sometimes lead to a price increase for the paper books. This happens when consumers’ disutility is high rel- ative to their reservation value (V < te1 + t/4). In this case, the entry of e-book seller forces paper book sellers to focus more on loyal customers near the sellers’ locations only. However, when consum- ers’ disutility is low relative to their reservation value (V > te1 + t/4), the price of paper book is lower than the price in the duopoly case. Whether the price of paper book is lower or higher than that in the duopoly case, paper book sellers’ market shares are lower than those in the duopoly case, and so are their profits. Proposition 1 (Conditions for prices to increase and readership to decrease after e-book entry in Case 2). When the physical book sellers anticipate the entry of an independent e-book seller, the price of physical book may increase and the paper book readership may decrease from the physical book duopoly case. The condition for that to happen is V < te1 + t/4, i.e., the disutility is relatively large. We illustrate the scenario described in Proposition 1 with Fig. 4, which only shows one-quarter of the circular market with firm A located at zero. Comparing Fig. 4 with Fig. 3, we see that the entry of the e-book seller actually leads to an increase of the price of the paper book—the new marginal paper book customers represented by the solid line y are located to the left of the dotted line, which represents themarginal customers before the entry of seller E. Thus, the entry of an independent e-book seller can lead to the exit of some potential readers from the book market. 4.2. Entry of an e-book seller owned by one of the two physical book sellers Let us consider the case in which A and E are an integrated com- pany. In other words, firm A, while competing with B in the paper book market, also starts selling e-books. By developing an e-book technology, including a specialized electronic device and possible DRM technology, firm A is able to obtain the right to sell some book titles in an electronic format. Customers who acquire the electronic device from firm A can then purchase and consume e-books offered by A. 4.2.1. Case 3: the integrated firm A sets its prices (PA and Pe) anticipating the move of firm B Clearly, e-books compete directly with A’s paper book, raising cannibalization concerns. However, firm A may gain by taking market share from firm B and serving previously un-served customers. The analysis of the e-book and paper book sellers’ markets discussed in Section 4.1 still applies here, except that now A also owns the e-book seller E, and A and B may charge different prices for the paper book. Firm B’s profit function (5) is the same as (2) while firm A’s (4) includes a term of profit from e-books as well, and firm A will decide both Pe and PA: PA ¼ 2ðPA � cÞ½ðV � PAÞ=t � qðV � Pe � te1Þ=t� þ 2qPeDe; ð4Þ PB ¼ 2ðPB � cÞ½ðV � PBÞ=t � qðV � Pe � te1Þ=t�; ð5Þ where De = ½ � (pe + te1 � PA)/t � (Pe + te1 � PB)/t. We focus on the Stackelberg game with firm A as the leader. Firm A maximizes its profit by determining the optimal prices of the paper book and e-book and by anticipating the price response of firm B. We use the superscript 3 to represent results of Case 3. The pricing equilib- rium of this Stackelberg game is presented in Appendix Lemma 5. In this case, the two paper book sellers may charge different prices for the paper book. 0 1 0 0.25 Circular location D is tr ib ut io n of d is ut ili ty o n e- bo ok s A te2 te1 y A yp ρ =0.2 E Fig. 4. An illustration of market shares for the 1=4 circular market in Case 2. Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 391 Author's personal copy When firm A also offers e-books and acts as the leader in the Stackelberg game, it will charge a higher price than that in the duopoly case, but in response, firm B will charge a lower price than before, P3A > P D A=B > P 3 B. This suggests that the introduction of e- books by an integrated firm such as Amazon creates a price pres- sure on a pure paper book seller such as Barnes and Noble, and that explains the interest of Barnes and Noble to move into the e-book market segment. 4.3. The impact of e-book technology on symmetric book market We now discuss the comparative statics5 of Cases 1–3. We begin with a discussion of how factors such as consumers’ e-book prefer- ences, cost and disutility terms of paper and e-books may affect the competition in the book market. We then compare the prices, market shares, and profits with and without e-book entry in a numerical example. 4.3.1. Distribution of consumers’ e-book preferences It is interesting to note that the change in q, the fraction of cus- tomers with type te1, has a different impact on prices depending on parameter values or who leads the Stackelberg game. An increase in q means more customers have a low disutility (te1) on e-books, and this is in favor of the e-book seller. When the independent e-book seller E is the leader (Case 1), E’s price and market share both increase in q, which means that the e- book seller has more market power as more customers accept the e-book technology. However, when the paper book sellers are the leaders (Case 2), the price of the e-book can increase or decrease in q depending on parameter values. In particular, when the reser- vation value of consumers is low relative to disutility, i.e., V < te1 + t/4, the prices of both paper and e-book increase in q, but the former increases more (@P2i =@q > @P 2 e=@q > 0 (i = A, B)). While more customers having a lower disutility of e-books should intensify the competition between paper and e-book sellers, the price competition is actually relaxed with both the paper book sell- ers and the e-book seller increasing their prices. But when V > te1 + t/4, as more customers have a lower disutility of e-books, the price competition is in fact intensified. As paper book sellers aggressively reduce their prices, in response the e-book seller also reduces its price, but the paper book sellers reduce their prices at a higher rate (@P2i =@q < @P 2 e=@q < 0 (i = A, B)). Proposition 2 (Effect of q on prices in Case 2). When physical book sellers anticipate the entry of an independent e-book seller, all sellers’ prices increase in q if V < te1 + t/4, and all prices decrease in q if V > te1 + t/4. Research and industry data (AAP 2009, Greco 2005, Oestreicher- Singer and Sundararajan 2006) suggest that the book industry is in its early stages of transformation due to IT and e-book technology. This implies that there is a small but increasing fraction of consum- ers that consider e-books in their purchase decisions (q is low and increasing). We can also conjecture that the ‘‘quality” of e-book technology is low, but it is improving, so te1 is high and decreasing. Given these conditions, Proposition 2 suggests that as more con- sumers consider e-books in their purchase decisions, prices in the book market increase above a te1 threshold and decrease below the same threshold. In Case 3, when the fraction of customers considering e-books increases, we have @P3A=@q > 0, @P 3 e=@q > 0, @S 3 A=@q < 0, and @S3e=@q > 0. That is, when q increases, the integrated firm A will fo- cus more on the loyal customers (customers close to A’s location) in the paper book market and increase its price on e-books. Again, in this case even though the e-book’s price increases in q, the mar- ket share of the e-book also increases in q. As a result, the total market shares of A increase (@ðS3e þ S 3 AÞ=@q > 0) and are higher than the duopoly case (S3e þ S 3 A > S D A ). This means that the market-expan- sion effect of e-books for A offsets the cannibalization effect. The effect of q on B’s physical book-price and market-share could be positive or negative depending on parameter condition. 4.3.2. Costs and differentiation The three scenarios with an independent e-book seller and an integrated e-book seller have some common properties. The paper book sellers will increase prices when the marginal cost of paper book increases. Consequently, the e-book seller will also increase the price of e-books (@Pnj =@c > 0; j = A, B, e and n = 1, 2, 3). When consumers’ unit-distance disutility of paper book t increases, paper books become less attractive to consumers. However, because paper book sellers are insulated from direct competition, the price of paper book actually increases (@Pni =@t > 0; i = A, B and n = 1, 2, 3). In response, the e-book seller will also increase the price of e-books (@Pne=@t > 0; n = 1, 2, 3). As a result, the market shares of both paper books and e-books de- crease in t, (@Snj =@t < 0; j = A, B, e and n = 1, 2, 3). As consumers’ disutility of e-book te1 decreases over time be- cause of technology improvement, e-books become more attrac- tive to consumers, and the e-book seller is able to increase its price on e-books. To compete with the e-book seller, paper book sellers will, however, reduce their prices on paper books as te1 de- creases. Interestingly, even though the e-book seller increases its price on e-books and the paper book sellers reduce their prices on paper books, the market share of e-book increases and the mar- ket share of paper book decreases (@Pni =@te1 P 0; @P n e=@te1 < 0; and @Sni =@te1 > 0, @S n e=@te1 < 0, i = A, B and n = 1, 2, 3). When seller A owns the e-book seller, A’s priceon paper book is independent of the disutility parameter te1 (@P 3 A=@te1 ¼ 0). Again in the context of Amazon, this means that the per- ceived ‘‘quality” (inverse of disutility) of Amazon’s Kindle in the eyes of customers considering e-books (type te1) does not affect Amazon’s physical book prices. The market share of paper books decreases and the share of e-books increases as te1 de- creases over time, as in the case of the independent e-book sell- er. However, the total market shares of the integrated book- seller A increase (@ðS3e þ S 3 AÞ=@te1 < 0). This happens because, as te1 decreases, the increased shares in e-books offset the decreased shares in paper books. As e-book technology improves, the market- expansion effect of e-books offsets the cannibalization effect, benefiting an integrated company like Amazon that introduces the e-book platform. Proposition 3 (Effects of q and te1 in Case 3). When firm A owns the e-book seller, its total market share decreases in te1, but it increases in q. Firm B’s share and price can increase or decrease in q and A’s prices (physical and e-book) increase in q. This analysis suggests that investment in an e-book technology that allows a paper book seller like Amazon to sell e-books to cus- tomers is an important strategic factor in the competitive interac- tion in the book market. 4.3.3. Prices, market shares, and profit comparison with and without e- book entry With the same numerical example used in Sections 4.1 and 4.2, we summarize the prices, market shares, profits of each player in the duopoly, simultaneous move with an independent e-book sell- er, and three sequential move cases in Table 2. This numerical example illustrates some interesting results. First, in Case 3 the integrated firm A’s total profit is given by 3.781—the sum of profits5 A summary of the comparative statics formulas is provided in Appendix Table A1. 392 Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 Author's personal copy from paper books and e-books. Thus, a paper book seller (A) prefers to be an integrated book seller who offers both paper and elec- tronic books than be just a paper book seller competing with an independent e-book seller. The reason is that the integrated book seller can internalize the competition between paper and elec- tronic books. However, comparing Case 3 with Cases 1 and 2, we see that the paper book seller B also prefers to compete with an integrated book seller rather than with an independent e-book seller. This happens because the integrated book seller tends to charge a high- er price on e-books. Thus, the paper book seller B loses less market share to e-books. Also, comparing Case 1 with Case 2, we see that the independent e-book seller can gain a higher profit level, if it acts as the follower rather than the leader in the price competition game. Similarly, the paper book sellers prefer to be the followers when competing with an independent e-book seller. This validates the result of the second-mover advantage in a price-setting Stackelberg game (Gal-Or 1985), as prices are strategic complements.6 Next, we compare the total market served in each case, which includes both the paper book and e-book. Comparing with the duopoly case without the entry of e-books, the entry of an independent e-book seller increases the total readership in the simultaneous-move case and Cases 1 and 2. The simultaneous- move case leads to the highest readership. This happens because in price-setting Stackelberg games, firms tend to increase their prices compared to the simultaneous-move case. However, Case 3 actually reduces the readership. That is, an integrated book seller may reduce the total readership when introducing e-books through an e-book platform. This insight is generalized in Section 5.3. 5. Effects of market asymmetries Section 4 provided a detailed discussion of the effects of e-book technology on a symmetric book market with k = m = 1. In this Sec- tion, we offer an in-depth discussion of the effects of market asym- metries when the e-book technology enters the book market. As defined in Section 2, our model allows for two types of market asymmetry: the physical book market asymmetry, captured by parameter k, and the e-book market asymmetry, represented by parameter m. The implications of these asymmetries are best explained when we assume that A is an online physical book seller (e.g., Amazon) and B an offline physical book seller (e.g., a bookstore chain). The physical book market asymmetry suggests that, everything else being equal, customers that buy from A incur a lower disutility per unit-distance than do customers that buy from B. This gives the on- line seller an advantage in the physical book market, because the online seller can capture a larger market share and be more profit- able than the offline seller. This assumption reflects the greater on- line seller’s ‘‘reach”, which is now a textbook concept (Laudon and Laudon 2010). The e-book market asymmetry suggests that there are more cus- tomers that consider e-books in seller A’s customer base than in B’s. Seller A’s customers are more likely to be technologically sophisticated (Oestreicher-Singer and Sundararajan 2006) or early adopters. These consumers may already be familiar with purchas- ing and paying online, and they are likely to have accounts at on- line bookstores that can be leveraged for e-books. For instance, Amazon’s Kindle e-book store is an extension of the traditional Amazon online physical book store. Kindle users benefit from using the same payment and shipping information, as they maintain a wish-list, read reviews posted by the Amazon community of book readers, and receive personalized recommendations that leverage their historical book preferences and purchase behavior at Ama- zon. Consumers close to A may also feel more comfortable buying and using an e-reader device or reading e-books via e-book soft- ware. Amazon’s Kindle hardware is aggressively promoted at Ama- zon’s website, and Kindle software can be easily downloaded. A collection of thousands of public domain e-books is available for consumers who are interested in trying the e-book experience for free. It is thus plausible that the digital channel of selling e- books is ‘‘closer” to the online than the offline channel of selling physical books. The concept of e-book market asymmetry reflects also the grad- ual transformation of the book industry whereby both the distribu- tion channel and the product are becoming digital: from selling physical products through offline channels to selling physical prod- ucts through online channels, and finally to selling e-books through digital e-book distribution technologies like Kindle. This gradual transformation can be represented in a pair (type of chan- nel, type of product) that gradually shifts from (physical, physical) to (digital, physical) to (digital, digital). Seen as a continuum, consum- ers who are in the (digital, physical) state are more likely to switch to the (digital, digital) state than consumers in the (physical, physi- cal) state. Now we discuss in detail how the interaction of market asym- metries and ownership type is affecting market outcomes in the following cases: � An independent third party like Apple selling e-books (the equi- librium is formally defined in Appendix Lemma 3 and was dis- cussed for the symmetric market in Section 4). � An established online seller like Amazon selling e-books (the equilibrium is formally defined in Appendix Lemma 5 and was discussed for the symmetric market in Section 4). Table 2 Prices, market shares, and profits comparison. Duopoly (before E’s entry) Simultaneous-move case (with an independent E) CASE 1 (E as the leader) CASE 2 (A & B as the leaders) CASE 3 (A owns E and as the leader) Paper Book (A/B) Seller A Seller B Price 18 17.724 17.742 18.153 18.559 17.979 Share 0.457 0.441 0.442 0.419 0.423 0.456 Profit 3.657 3.409 3.425 3.418 3.619 3.638E-book (E) Price 3.237 3.417 3.451 5.794 Share 0.074 0.070 0.079 0.028 Profit 0.239 0.240 0.272 0.162 Total readership 0.914 0.957 0.955 0.917 0.907 6 It would be interesting to investigate which firm(s) will move first in equilibrium (endogenous timing), but it is beyond the scope of this paper. Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 393 Author's personal copy � An offline seller of physical books selling e-books (the equilib- rium is formally defined in Appendix Lemma 6). 5.1. Effects of market asymmetries with an independent e-book seller E When an independent third party like Apple enters the book market selling e-books, then the asymmetry parameters k and m affect all prices and market shares (Appendix Lemma 3). The re- sults are best discussed by examining the effects of m and k separately. When m = 1, then one interesting equilibrium property is that A and B set equal prices, and their ratios of shares and profits (SB/SA, PB/PA) remain fixed and equal to k, as in the duopoly case. The e- book price increases in k. The prices of A and B are linear, increas- ing functions of the e-book price, so they also increase in k but only at a smaller rate. As k decreases, firm A can reach more paper book customers, but at the same time price competition intensifies, be- cause E reduces its price on e-books. Because the offline seller B also faces intensified price competition, B’s price, market share, and profit decrease. The share and profit of B increase in k, so the offline seller is better off when the market is becoming more sym- metric. Interestingly, before the entry of the e-book (Section 3), a decrease of k does not affect paper book prices, but only increases the online seller’s market share and profit. When k = 1, the price of E is a U-shaped function of m (with minimum at m� ¼ ffiffiffi 2 p � 1). The price of A increases in m if and only if the price of E increases in m, so the price of A is also a U-shaped function of m. The share and profit of A (B) increase in m if and only if the price of A (B) increases in m. The intuition is that a more asymmetric e-book market (decrease of m) decreases the demand for e-books in the neighborhood of firm B. As a result, firm E re- duces its price and so does A. Firm B benefits because it faces less competition from E, although E’s price is lower. But when m be- comes lower than a critical value m� ¼ ffiffiffi 2 p � 1, then E starts increasing its price because E is better off making a higher profit in the neighborhood of A than capturing the market in the neigh- borhood of B. E’s price change benefits B even more, but also ben- efits A because price competition is relaxed. However, the e-book market asymmetry (m) does not affect the equilibrium of the paper book duopoly before the e-book entry (Section 3) because the e- book technology is not available and thus customers’ e-book pref- erences do not affect their purchase behavior. 5.2. Effects of market asymmetries with E owned by either A or B Because the market is asymmetric, we must discuss two distinct ownership cases: the online seller A owns E (Appendix Lemma 5) and the offline seller B owns E (Appendix Lemma 6). The effects of market asymmetries are likely to be different in those two cases. 5.2.1. Online seller A owns E When the online seller A owns E and maximizes the total profit by selling a paper book and an e-book, then A’s paper book market share is independent of m. This suggests that A sets its paper book and e-book price so the e-book market asymmetry does not affect its paper book market share. In addition, the strategic behavior of the offline firm B is identical to its behavior in Lemma 3, when E is independent. In particular, the formulas that give B’s price, share, and profit are identical to those in Lemma 3: B sets a price that is a mark-up over the e-book price, and k affects B’s behavior only indi- rectly through the e-book price. We can gain more insight in the strategic behavior of firms when we consider the parameters k and m separately. When m = 1, the prices of A’s electronic and paper books increase in k, be- cause c + t > V is true. Thus, firm A increases its prices as the phys- ical book market becomes more symmetric and B responds with an increase of its price and price competition is relaxed. The relation- ship between the e-book disutility parameter te1 and the produc- tion cost of physical books c determines how A’s e-book market share behaves. A’s e-book market share increases in k, if te1 > c and decreases otherwise.7 5.2.2. Offline seller B owns E When the offline seller B owns E and maximizes the total profit by selling a paper book and an e-book (Appendix Lemma 6), then the pricing and market-share behavior of the online seller A is identical to A’s behavior when E is independent: A sets a markup over the e-book price. The market share of B’s paper book is inde- pendent of k. B’s paper book market share decreases in m, which means that as the e-book market becomes more symmetric, B sells fewer physical books. When k = 1, the effect of m on the market share of B’s e-book depends on disutility and cost parameters; in particular, B’s e-book market share increases in m if and only if 4(c � te1) + t > 0. When m = 1, the prices of B’s physical book and e-book increase in k. This suggests that, as the physical book market becomes more symmetric, B increases its prices and, as a response, A increases its price as well, and therefore price competition is relaxed. The effect of k on the market share of B’s e-book depends on market param- eters; in particular, B’s e-book market share increases in k, if and only if (2 � q)te1 > V(1 � q) + c. 5.3. How ownership and market asymmetries affect total readership Now, let us consider the total readership TR (total book sales) when E is independent (TRIE), when E is owned by A (TRAE), and when E is owned by B (TRBE). The total readership is the high- est when E is independent, and the second highest when B owns E. The following figure shows the total readership ratios (TRIE/TRAE) and (TRIE/TRBE) as functions of (m, k) with parameter values, as in Figs. 3 and 4. As shown in Fig. 5, the total readership when E is independent is larger than the total readership when E is owned by the offline sell- er A or by the online seller B. A further comparison shows that the total readership when E is owned by the offline seller B is larger than the total readership when E is owned by online seller A. Inte- grated ownership is inferior with respect to total sales and social welfare because it internalizes competition and thus reduces total sales. This result is different from the IS research in ownership of Internet intermediaries that shows that integrated ownership is superior (Bakos and Katsamakas 2008), because in that literature the main effect of integrated ownership is to internalize network externalities, which tends to increase total sales and social welfare. Fig. 5 also shows that when E is owned by A, the readership reduction effect gets stronger, when the market becomes more asymmetric. However, when E is owned by B the readership reduc- tion effect gets stronger, and when the market becomes more symmetric. Owning E is a ‘‘defensive” strategy for A when there are strong market asymmetries, because the main benefit for A is avoiding competition within its large paper book market. Thus, the larger the market asymmetries, the stronger the ‘‘threat” of an indepen- dent E to A, and the stronger A’s incentive to own the e-book seller. As a result, the total readership is the lowest when the e-book sell- er is owned by the online seller A. However, owning E is an ‘‘offen- sive” strategy for B when there are strong market asymmetries, because it is an opportunity to capture the market in the neighbor- hood of A by selling e-books. The result is a larger total readership 7 The share of A’s paper book is increasing in k if and only if c > Vð1� qÞ þ qte1. When k= 1, then the market share of A’s e-book is increasing in m if and only if 2ðV þ cÞ þ t þ 4mqte1 > 4ðmqV þ te1Þ. 394 Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 Author's personal copy than the case of E owned by A, but a lower total readership than when E is independent. Overall, market asymmetries have a signif- icant effect on prices, market-shares, profits, total readership, and the incentives of the online seller A and offline seller B to own the e-book seller. Fig. 6 compares the total readership in the three cases discussed above (TRIE, TRAE, TRBE) and the total readership TRD in the duopoly market, before the e-book technology is available. When E is owned by the online seller A, the total readership is less than the total readership before the e-book entry, and this effect is enlarged the more asymmetric the e-book market is. When E is owned by the offline seller B, the readership is less than the duopoly case only if the e-book market asymmetry is small (i.e. m is large). The total readership, when E is independent, is always higher than the readership in the duopoly case. These results suggest that hav- ing an independent e-book seller enter the book market increases the total readership and leads to the highest possible readership compared to all other ownership cases. A last interesting observa- tion from Fig. 6 is that when the e-book market is perfectly asym- metric (m = 0), then B owning E also results in the highest total readership. This happens because in the perfect asymmetric case there are no e-book customers in the neighborhood of B, so B sets an e-book price that is identical to the e-book price of an indepen- dent e-book seller. 6. Conclusion The advances in Internet and IT enable the digitization of books, transforming the competitive forces in the book industry. This pa- per developed a stylized game theory model that captures the ef- fects of e-book entry on the book market. Our analysis shows that e-book entry leads to intricate price adjustments, and share and profit changes. E-book technology offers the potential for mar- ket expansion, which can be quantified in our research model. Sur- prisingly, we find that the entry of an e-book seller does not necessarily expand the total readership, and, additionally, that the price competition between the paper book sellers and the e- book seller can actually be relaxed when the e-book technology be- comes acceptable to more customers. In order to manage the entry of e-book technology (e.g., Ama- zon) or respond to that entry, managers need to consider several factors, including the differentiation and intensity of competition in the pre-existing physical book market, the cost difference be- tween e-books and physical books, the competitive ‘‘leadership”, the fraction of customers considering e-books in their purchase decisions, and the perceived ‘‘quality” of e-books for those custom- ers that consider e-books an option. In high-velocity information- goods markets, some of these factors may change fast, so optimal decisions under the current market conditions may need to be ad- justed in the near future. Most importantly, companies involved in the transformation of the book industry into digital products (e-books) and digital distri- bution channels must consider carefully the effects of ownership and market asymmetries. Expanding Salop’s circular model, this paper introduces the concepts of physical book market asymmetry (k) and e-book market asymmetry (m) and shows that these market asymmetries affect not only the market interaction when the e- book seller enters the market but also the incentives of an online book seller (A) and an offline book seller (B) to own the e-book seller. Combining the physical book market asymmetry and the e-book market asymmetry in the same model reveals opposing effects affecting the paper book sellers: the physical book asym- metry benefits A because it can reach more customers of physical books, but at the same time it hurts A because price competition intensifies, which also hurts B. The e-book asymmetry benefits the offline seller B because customers close to B are less likely to switch from paper books to e-books, but it may hurt or benefit A, as it affects price competition in a non-linear way. In particular, when the e-book market is not very asymmetric, price competi- tion intensifies with a decrease of m and A’s profit decreases, but price competition relaxes below a threshold, in which case A’s profit increases. The interaction of ownership and market asymmetries affect total readership, and when the market asymmetries are strong, k TRIE /TRAE m m k TRIE /TRBE Fig. 5. Total readership ratios (TRIE/TRAE) and (TRIE/TRBE) as functions of (m, k). 0.2 0.4 0.6 0.8 1.0 0.90 0.92 0.94 m TRIE TRD TRBE TRAE Fig. 6. Total readership TRD, TRIE, TRBE, TRAE as functions of e-book market asymmetry m with k = 1. Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 395 Author's personal copy ownership of E by the online seller leads to the lowest total read- ership. This suggests that Amazon’s control of the e-book market through the Kindle technology is socially inferior compared to that of an offline book seller offering e-books or that of an independent e-book seller entering the market. Two opposing forces drive these results: the physical book asymmetry benefits A, because it can reach more customers, but the e-book asymmetry hurts A because customers close to A are more likely to switch from physical books to e-books. Research and industry data (AAP 2009, Greco 2005, Oestreicher- Singer and Sundararajan 2006) suggest that the book industry is in its early stages of transformation due to IT and e-book technology. This early transformation suggests that there is a small but increas- ing fraction of consumers that consider e-books in their purchase decisions. It also indicates that the ‘‘quality” of e-book technology is currently low, but it is improving. We have shown that, as con- sumers that consider e-books in their purchase decisions increase, prices increase above a threshold of e-book disutility and decrease below the threshold. As leading technology companies like Amazon, Google and Apple are maneuvering strategically to benefit from the fast growing e-book market, power changes in the book industry’s value-chain are possible. Anecdotal evidence suggests that pub- lishers are concerned about the increasing control of e-books by Amazon’s Kindle platform and they ‘‘have turned to Apple to help them twist Amazon’s arm” (The Economist 2010). Our analysis has shown that even without considering e-book sellers’ competition, the entry of a single e-book seller has a significant impact on book markets, as e-book technology competes with the ‘‘old” book technologies. Appendix A. Proofs Lemma 1 (Duopoly pricing equilibrium). When only the physical book sellers A and B are active in the book market and (V � c)(k + 1) < kt, at equilibrium the prices, market-shares, and profits are as follows: PDA ¼ P D B ¼ Vþc2 ; S D A ¼ V�ckt ; S D B ¼ V�ct ; P D A ¼ ðV�cÞ2 2kt ; PDB ¼ ðV�cÞ2 2t . Proof. For seller A, since yDA ¼¼ ðV � P D A )/kt, taking y D A into seller A’s profit function given in Eq. (1) the second-order derivative of PDA with respect to PDA is given by �4/(kt) < 0. As the profit function is concave in price, solving the first order condition (FOC) we have PDA ¼ ðV þ cÞ=2 and yDA ¼ ðV � cÞ=ð2ktÞ. Similarly, we can solve for seller B with PDB ¼ ðV þ cÞ=2 and yDB ¼ ðV � cÞ=ð2tÞ. For the market to be uncovered it requires yDA þ yDB < 1=2, which gives the param- eter condition (V � c)(k + 1) < kt (Note: we require that this param- eter condition is satisfied in the proofs that follow). h Derivation D1 (Derivation of demand for e-book and physical books): We derive the demand for e-book and A’s and B’s physical books for the article’s model defined in Section 2. Customerspref- erences are defined in Section 2, and the e-book market asymmetry mathematically implies that a customer’s e-book disutility te is te1 with probability f ðdÞ ¼ q; 0 6 d < 1=4 mq; 1=4 6 d 6 1=2 � and te2 with proba- bility 1 � f(d), where d is the customer’s distance from firm A’s location, 0 6 q 6 1, 0 < m 6 1, and F is the c.d.f. of f. Consider the half-circle market with A located at 0 and B at ½. The indifferent consumers of paper book located at yA, yB for A and B, respectively, satisfy yA = (V � PA)/kt and ½ � yB = (V � PB)/t. Cus- tomers in the segment [yA, yB] will not purchase physical books, but a mass of customers equal to F(yB) � F(yA) may purchase the e-book. We only focus on the case with Pe + te1 > Pi (i = A, B), which means A and B always have some loyal customers who prefer pa- per book even though they have a low disutility of e-book. Consider the [0, yA] segment. The marginal customer who pre- fers A’s paper book over the e-book is located at ypA = (Pe + - te1 � PA)/kt since V � PA � ktypA = V � Pe � te1. Thus, the demand for the e-book in this segment is F(yA) � F(ypA) and the demand for A’s physical book is yA � (F(yA) � F(ypA)). Next consider the [yB, 1/2] segment. In this segment, the mar- ginal customer ypB who prefers B’s paper book over the e-book sat- isfies ½ � ypB = (Pe + te1 � PB)/t since V � PB –t(½ � ypB) = V � Pe � te1. Thus, the demand for the e-book in this segment is F(ypB) � F(yB) and the demand for B’s physical book is ½ � yB � (F(ypB) � F(yB)). In summary, the total demand for A’s physical book is SA ¼ 2ðyA � ðFðyAÞ � FðypAÞÞÞ; ðA1Þ the total demand for B’s physical book is SB ¼ 2ð1=2� yB � ðFðypBÞ � FðyBÞÞÞ; ðA2Þ and the total demand for the e-book is Se ¼ 2ðFðypBÞ � FðypAÞÞ: ðA3Þ the profit from A’s physical book is ðPA � cÞSA; ðA4Þ the profit from B’s physical book is ðPB � cÞSB; ðA5Þ and the profit from the e-book is PeSe: ðA6Þ Lemma 2 (Simultaneous-move pricing equilibrium with the entry of an independent e-book seller). When an independent e-book seller enters the market and makes pricing decision simultaneously with the paper book sellers, at equilibrium the prices and market- shares are as follows8: PbA ¼ P b B ¼ 8c þ tqþ 4te1qþ 8V � 8Vq 16� 4q ; Pbe ¼ 2c þ t � 4te1 þ 2te1qþ 2V � 2Vq 8� 2q ; SbA ¼ S b B ¼ 8V � 8c þ 4cqþ qðt þ 4te1 � 8VÞ ð8� 2qÞt ; Sbe ¼ 2qð2c þ t � 4te1 þ 2te1qþ 2V � 2VqÞ ð4� qÞt : Proof. In the simultaneous-move pricing game, the profit func- tions for the paper book sellers and the e-book seller are described in Eqs. (2) and (3). All three firms set prices simultaneously to max- imize their profit. The equilibrium prices and market-shares follow. h Lemma 3 (Pricing equilibrium with the independent e-book seller as the leader in the pricing game). When an independent e-book seller enters the market anticipating the price response of physical book sellers, at equilibrium the prices and market-shares are as follows: 8 This lemma is proved only for the symmetric market with k = 1 and m = 1, since it is applicable only to the discussion of the symmetric market in Section 4. 396 Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 Author's personal copy If the market is symmetric (k = m = 1), the equilibrium is simplified to the following: P1A ¼ P 1 B ¼ 8Vþ8c�2cq�qð10V�t�4te1Þþ2q2ðV�te1Þ 16�8q ; P 1 e ¼ 2ð1�qÞðV�te1Þþtþ2c�2te1 8�4q ; S 1 A ¼ S 1 B ¼ 8V�8cþ6cqþqðtþ4te1�10VÞþ2q2ðV�te1Þ ð8�4qÞt ; S 1 e ¼ qð2Vþ2c�2Vqþt�4te1þ2te1qÞ 2t . Proof. We consider the Stackelberg game in which an indepen- dent e-book seller E sets its price in the first stage, and firms A and B set their prices simultaneously in the second stage. All firms are maximizing their profits. The game is solved backwards for the subgame perfect Nash equilibrium.In stage 2, firms A and B set prices to maximize the profits from selling physical books defined in (A4) and (A5), respectively, taking the price of E’s e-book as given. Substituting these prices into E’s profit function (A6) we can solve for the optimal price for E in stage 1. There exists a unique equilibrium for which the prices and market-shares follow. h Lemma 4 (Pricing equilibrium with the physical book sellers as the leader in the pricing game). When the physical book sellers anticipate firm E’s market entry and set prices first, at equilibrium the prices and market-shares are as follows9: P2A ¼ P 2 B ¼ 8V þ 8c � 4cq� 8qV þ tqþ 4te1q 16� 8q ; P2e ¼ 2ð1� qÞðV � te1Þ þ t þ 2c � 2te1 þ te1q� cq� tq=4 8� 4q ; S2A ¼ S 2 B ¼ 8V � 8c þ 4cqþ qðt þ 4te1 � 8VÞ 8t ; S2e ¼ q½ð1� qÞð8V þ 4c þ t � 12te1Þ þ 4c þ 3t � 4te1� ð8� 4qÞt : Proof. The profit functions for the paper book sellers and the e- book seller are described in Eqs. (2) and (3). Since in Case 2 the paper book sellers act as the leader in the Stackelberg pricing game, they will set their prices on the paper book first, anticipating the price response of the e-book seller. It is straight forward to show that each player’s profit function is concave in its own price. Thus we can derive the equilibrium prices by solving the FOCs. For the e-book seller E, its FOC is given by: FOC of E qð4P2 þ t � 4te1 � 8P2e Þ=t ¼ 0: ðA7Þ Here, the superscript 2 represents Case 2, and we omit the subscript A (B) of paper book price to simplify notation. From (A7), we can de- rive that the e-book price is given by P2e ¼ ð4P 2 þ t � 4te1Þ=8. Since the paper book sellers move first, they will take P2e into Eq. (2) and solve through the FOC for the optimal paper book price, which is given by P2 ¼ 8Vþ8c�4cq�8qVþtqþ4te1q16�8q . When the e-book seller enters it will set its price in response to the paper book price P2e ¼ ð4P 2 þ t � 4te1Þ=8. The market share of each player can be derived accordingly, based on their profit functions. h Proof of Proposition 1 (Conditions for prices to increase and reader- ship to decrease after e-book entry in Case 2). In Case 2 with a sym- metric market (k = m = 1), a price comparison between P2 and PD shows that PD � P2 ¼ qð4V � 4te1 � tÞ=ð16� 8qÞ, which can be negative when V < te1 + t/4. That is, an entry of an independent e- book seller can lead to a high price on paper book. Accordingly, the paper book market shrinks. h Proof of Proposition 2 (Effect of q on prices in Case 2). In Case 2 with a symmetric market (k = m = 1), @P2=@q ¼ ð8te1 � 8V þ 2tÞ= 8ð2� qÞ2 which means the paper book price is increasing in q when V < te1 + t/4. h Lemma 5 (Pricing equilibrium with seller A also selling e-books and as the leader in the pricing Game). When firm A owns the e- book seller E and it anticipates firm B’s price response to the introduc- tion of e-book, at equilibrium prices and market-shares are as follows: If the market is symmetric (k = m = 1), the equilibrium is simplified to the following: P1e ¼ 2cð1þ kmÞ þ 2ðVð1� qÞ � ð2� qÞte1Þ þ kðð1þmÞt þ 2mðte1ðmq� 2Þ þ Vð1�mqÞÞ 4ð2� qþ kmð2�mqÞÞ ; P1A ¼ ð1=2Þðc þ qte1 þ Vð1� qÞ þ qP 1 e Þ; P1B ¼ ð1=2Þðc þmqte1 þ Vð1�mqÞ þmqP 1 e Þ; S 1 A ¼ 2ðP1A � cÞ kt ; S1B ¼ 2ðP1B � cÞ t ; S1e ¼ qð2� qþ kmð2�mqÞÞ t P1e : P3e ¼ 2ckmþ 4ð1� qÞðV � te1Þ þ kðð1þmÞt þ 2mðte1ðmq� 2Þ þ Vð1�mqÞÞ 4ð2� 2qþ kmð2�mqÞÞ ; P3A ¼ 2cð2ð1� qÞ þ kmð2þ ð1�mÞqÞ þ 4Vð1� qÞ þ kð4mV þ qð1þmÞðt � 2mVÞÞ 4ð2� 2qþ kmð2�mqÞÞ ; P3B ¼ ð1=2Þðc þmqte1 þ Vð1�mqÞ þmqP 3 e Þ; S3B ¼ 2ðP3B � cÞ t ; S3A ¼ Vð1� qÞ þ qte1 � c kt ; S3e ¼ qð2cð2þ kmÞ � 4te1 þ kðð1þmÞt þ 2mðð1�mqÞV � te1ð2�mqÞÞÞ 4kt : 9 This lemma is proved only for the symmetric market with k = 1 and m = 1, since it is applicable only to the discussion of the symmetric market in Section 4. Y. Jiang, E. Katsamakas / Electronic Commerce Research and Applications 9 (2010) 386–399 397 Author's personal copy P3A ¼ 4V þ 4c � 2cqþ tq� 4qV 8� 6q ; P3e ¼ 3ð1� qÞðV � te1Þ þ t þ c � te1 8� 6q ; P3B ¼ cð8� 5qÞ þ qðt þ 4te1 � 11VÞ þ 3q2ðV � te1Þ þ 8V 16� 12q ; S3A ¼ V � c þ qðte1 � VÞ t ; S3e ¼ qðV þ 3c � Vqþ t � 4te1 þ te1qÞ 2t ; S3B ¼ 8V � 8c þ 7cqþ qðt þ 4te1 � 11VÞ þ 3q2ðV
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