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,113W.60th Street,New York,NY 10023,United States
a r t i c l e i n f o Article history:
Available online 1July 2010Keywords:
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.
Ó2010Elsevier 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 1500titles and features e-ink screen technology that makes reading as
pleasant as reading paper.1Using 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 technology offers 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 $113million in 2008.This is still a fraction of the $24.3billion book market,but e-book sales grew 68.4%in 2008,while total book sales decreased 2.8%(AAP 2009).In addition to purchasing a paper book through a phys-ical bookstore or an online store,customers can now download an e-book from an e-book seller.According to Publishers Weekly ,book-chains and online stores hold 32.5%and 30%shares of consumer physical book purchases in 2008(Milliot 2008).Competition be-tween online and physical sellers of products has been analyzed in the literature on e-commerce and related channel-competition
1567-4223/$-see front matter Ó2010Elsevier B.V.All rights reserved.doi:10.1016/j.elerap.2010.06.003
*Corresponding author.Tel.:+12126366131;fax:+12127655573.
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 $259as 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.
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 idea2to 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 pricesfirst.
Previous IS research on information and digital goods focused on issues of piracy and the value of digital rights management (DRM)technology(Chellappa and Shivendu2005,Smith and Telang2009,Sundararajan2004)and pricing issues such as ver-sioning and bundling(Bakos and Brynjolfsson2000).Multiple empirical studies used online book sales data and found that price dispersion does not disappear on the Internet(Brynjolfsson and Smith2000,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 only16%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 Sundararajan2006)that analyzes the value of digital rights in the context of a monopolist selling a physical and a digital book,andfinds that the monopolist should restrict certain digital rights in the presence of piracy.
Wefind 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 afirm offers both the paper books and e-books and competes with a pure paper book seller,more customers are left un-served than when bothfirms only sell paper books.In addi-tion,wefind 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:Section2defines the model whereas Sections3–5analyze and discuss the results.In particular, Section3analyzes the physical book duopoly before the entry of the e-book seller.Section4discusses the entry of an e-book seller and its impact on the market when the market is symmetric.Sec-tion5discusses the effects of market asymmetries.Section6pro-vides a few concluding remarks.
2Building on Salop’s(1979)‘‘circular”market is a well-established approach in IS
economics,e.g.the analysis of search costs(Bakos1997)and mass-customization
strategies(Dewan et al.2003).
Y.Jiang,E.Katsamakas/Electronic Commerce Research and Applications9(2010)386–3993872.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.
Thefirst 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 to1.Twofirms 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 tofirms 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 k61.
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 onefirm rather than to another,or other transaction costs or sources of disutility(Ellison and Ellison2005, Forman et al.2009).Capturing the potential asymmetry offirms 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 thanfirm 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 andflexibility(Viswanathan 2005).In addition,customers who buy offline do incur a physical transportation(travel)cost and a cost of traveling but notfinding 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 t e of buying the e-book that is either3t e1or t e2,(b)t e1 Assumption(b)means that customers of type t e1(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 t e2(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(AAP2009). 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 offirm A’s consumers are likely to consider e-books thanfirm 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 Brynjolfsson2000).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(Viswanathan2005),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.Table1summarizes the modeling notations. 3.Duopoly market of physical book sellers Let us consider the book market in which only the physical book sellers A and B are active and e-books are not available.We use the superscript D to represent results of this duopoly market.Let P D A be the price charged byfirm A and c be the common marginal cost.The net valuation of a customer located at distance x apart fromfirm A is given by VÀP D A Àktx.Similarly,the net valuation of a customer lo- cated at distance x apart fromfirm B is given by VÀP D B Àtx. 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 3This discrete distribution significantly simplifies our model analysis versus even the simple uniform distribution case(Dewan et al.2000),without loss of generality. 388Y.Jiang,E.Katsamakas/Electronic Commerce Research and Applications9(2010)386–399potential 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 y D A be the location of a customer who is indifferent be-tween purchasing the title from A and not participating in the mar- ket.Since VÀP D A Àkty D A ¼0,we deduce that y D A ¼ðVÀP D A Þ=kt.Firm A will choose the optimal price P D A to maximize its net profit,which is given by: P D A ¼2y D A P D A Àc :ð1ÞThe duopoly pricing equilibrium(Lemma1)states that custom- ers located within(V–c)/(2kt)distance fromfirm A or(V–c)/(2t) fromfirm B will purchase the physical book,and customers located further away from thefirms 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(VÀc)(k+1) twofirms isfixed:S D B =S D A ¼k and P D B=P D A¼k.Because in general the market asymmetry parameter k61,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(S D A þS 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: Case1:Entry of an independent e-book seller,who sets the price on e-booksfirst,whereas physical book sellers set the prices second. Case2:Entry of an independent e-book seller when physical book sellers set the pricesfirst,and the e-book seller sets the price second;and, Case3:Entry of an e-book seller,who is integrated with the physical book seller A,and A sets the pricesfirst. 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 Table1 Table of modeling notation. Notation Definition Comments b,D,1,2,3Superscripts representing results of the simultaneous move benchmark,duopoly market,Case1,Case2,and Case3, respectively c Paper book sellers’marginal production an d distribution cost i Subscript index i=A,B,representing paper book sellers A and B, respectively k k61is 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 m61is 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,m q of seller B’s consumers will consider e-books whereas q of seller A’s consumers will consider e-books P i Price charged by paper book seller i When P A=P B,we occasionally use P A/B to stand for the price charged by sellers A and B P e Price charged by the e-book seller E S i 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 S i+S e S e Market shares of the e-book seller E t Consumers’unit-distance disutility of purchasing a paper book t e Consumers’disutility of purchasing an e-book,and t e is either t e1 or t e2with t e1 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 y D A represents the location of a customer who is indifferent between purchasing the title from A and not participating in the duopoly market y p The location on the circle of the customer who is indifferent between purchasing the paper book and the e-book G i 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 G i+G e G e The e-book seller’s profit q The mass of paper book seller A’s consumers who have a low disutility t e1on e-books The mass of paper book seller B’s consumers who have a low disutility t e1on e-books is m q 4As a benchmark,we also derived the pricing equilibrium when the paper book sellers and the e-book seller set prices simultaneously(Appendix Lemma2).We use the superscript b to represent results of this simultaneous price move scenario. Y.Jiang,E.Katsamakas/Electronic Commerce Research and Applications9(2010)386–39934.1.Entry of an independent e-book seller Let us consider the samefirms 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 P e and the customer’s disutility t e,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 point0;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 and1=4Ày where y=(VÀP)/t,representing the location of the marginal cus- tomer for seller A.First,consider the1=4Ày 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 t e1in this segment may purchase the e-book.Since a customer’s transaction cost t e is independent of her location,the demand for e-book in the 1=4Ày segment is given by2q(1=4Ày).Next,consider the y segment. We only focus on the case with P e+t e1>P,which means thatfirm 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 y p=(P e+t e1ÀP)/t since VÀPÀty p=VÀP eÀt e1.Thus,the demand for the e-book in this segment is given by2q(yÀy p). The profit functions for the paper book sellers and the indepen- dent e-book seller can be simplified as: P A¼P B¼2ðPÀcÞ½ðVÀPÞ=tÀqðVÀP eÀt e1Þ=t ð2ÞP e¼4q P e½1=4ÀðP eþt e1ÀPÞ=t :ð3ÞPaper 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 movesfirst (Case1),or the physical book sellers movefirst(Case2).4.1.1.Case1:the independent e-book seller anticipates the move of physical book sellers In thefirst case,the e-book seller sets the pricefirst,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 onfirm E’s electronic device.We use the superscript1to represent results of Case1.The pricing equilibrium of this Stackelberg game is presented in Appendix Lemma3. Comparing P b e ,the e-book price when all players move simulta- neously,with P1 e ,the e-book price when the independent E moves first,wefind that P1 e >P b e .That is,when E movesfirst,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(S1 e ).However,the profit comparison shows that P1 e >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 (P1 A=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 (S1 A=B >S b A=B ).Thus,the paper book sellers also benefit when the e-book seller actsfirst 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,P1 A=B A=B .However,the market shares of the paper book sellers are reduced(S1 A=B ),even with re-duced prices.Thus,the paper book sellers’profits are lower as well (P1 A=B A=B ). We illustrate the impact of the entry of an independent e-book seller on the book market in a numerical example.Fig.3represents the one-quarter circular market in Case1withfirm A located at zero.Parameter values for this example are:V=26,c=10,t=35, t e1=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 t e1on 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 390Y.Jiang,E.Katsamakas/Electronic Commerce Research and Applications9(2010)386–399lower 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 y p represents the marginal customers who are indifferent between the paper book and e-book.Forfirm A,customers located in[y p,y]and with type t e1will 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 t e1 customers(located between the dotted line and0.25),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 Case1consumer surplus and social welfare increase with the entry of an independent e-book seller. 4.1.2.Case2:the physical book sellers anticipate the entry of the independent e-book seller In the second case,the paper book sellers movefirst.This spe-cial case enables the study of e-book entry under adverse market conditions for the entrantfirm.We use the superscript2to repre-sent results of case2.The pricing equilibrium of this Stackelberg game is presented in Appendix Lemma4.This case is similar to Case1in 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,P2 A=B >P b A=B and P2 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 Proposition1(Conditions for prices to increase and readership to decrease after e-book entry in Case2).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 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 fromfirm A can then purchase and consume e-books offered by A. 4.2.1.Case3:the integratedfirm A sets its prices(P A and P e) anticipating the move offirm B Clearly,e-books compete directly with A’s paper book,raising cannibalization concerns.However,firm A may gain by taking market share fromfirm B and serving previously un-served customers.The analysis of the e-book and paper book sellers’markets discussed in Section4.1still 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)whilefirm A’s(4)includes a term of profit from e-books as well,andfirm A will decide both P e and P A: P A¼2ðP AÀcÞ½ðVÀP AÞ=tÀqðVÀP eÀt e1Þ=t þ2q P e D e;ð4ÞP B¼2ðP BÀcÞ½ðVÀP BÞ=tÀqðVÀP eÀt e1Þ=t ;ð5Þwhere D e=½À(p e+t e1ÀP A)/tÀ(P e+t e1ÀP B)/t.We focus on the Stackelberg game withfirm 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 offirm B.We use the superscript3to represent results of Case3.The pricing equilib-rium of this Stackelberg game is presented in Appendix Lemma5.In this case,the two paper book sellers may charge different prices for the paper book. Y.Jiang,E.Katsamakas/Electronic Commerce Research and Applications9(2010)386–399391 Whenfirm 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,P3 A >P D A=B >P3 B .This suggests that the introduction of e- books by an integratedfirm 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 statics5of Cases1–3.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 t e1,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(t e1)on e-books, and this is in favor of the e-book seller. When the independent e-book seller E is the leader(Case1),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(Case2),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 =@q>@P2e=@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>t e1+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(@P2 i =@q<@P2e=@q<0(i=A,B)). Proposition2(Effect of q on prices in Case2).When physical book sellers anticipate the entry of an independent e-book seller,all sellers’prices increase in q if V Research and industry data(AAP2009,Greco2005,Oestreicher-Singer and Sundararajan2006)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 t e1is high and decreasing. Given these conditions,Proposition2suggests that as more con-sumers consider e-books in their purchase decisions,prices in the book market increase above a t e1threshold and decrease below the same threshold. In Case3,when the fraction of customers considering e-books increases,we have@P3 A =@q>0,@P3e=@q>0,@S3A=@q<0,and @S3 e =@q>0.That is,when q increases,the integratedfirm 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(@ðS3 e þS3 A Þ=@q>0)and are higher than the duopoly case(S3 e þS3 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(@P n j =@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 (@P n i =@t>0;i=A,B and n=1,2,3).In response,the e-book seller will also increase the price of e-books(@P n e =@t>0;n=1,2,3).As a result,the market shares of both paper books and e-books de- crease in t,(@S n j =@t<0;j=A,B,e and n=1,2,3). As consumers’disutility of e-book t e1decreases 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 t e1de-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(@P n i =@t e1P0;@P n e =@t e1<0;and @S n i =@t e1>0,@S n e =@t e1<0,i=A,B and n=1,2,3). When seller A owns the e-book seller,A’s price on paper book is independent of the disutility parameter t e1(@P3 A =@t e1¼0).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 t e1)does not affect Amazon’s physical book prices.The market share of paper books decreases and the share of e-books increases as t e1de-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(@ðS3 e þS3 A Þ=@t e1<0).This happens because,as t e1decreases,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. Proposition3(Effects of q and t e1in Case3).Whenfirm A owns the e-book seller,its total market share decreases in t e1,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 Sections4.1and4.2, 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 Table2.This numerical example illustrates some interesting results.First,in Case3the integratedfirm A’s total profit is given by3.781—the sum of profits 5A summary of the comparative statics formulas is provided in Appendix Table A1.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 Case3with Cases1and2,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 Case1with Case2,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-Or1985),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 Cases1and2.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 3actually 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 Section5.3. 5.Effects of market asymmetries Section4provided 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 Section2,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 Laudon2010). 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 Sundararajan2006)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,andfinally 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 Lemma3and was dis-cussed for the symmetric market in Section4). An established online seller like Amazon selling e-books(the equilibrium is formally defined in Appendix Lemma5and was discussed for the symmetric market in Section4). Table2 Prices,market shares,and profits comparison. Duopoly (before E’s entry)Simultaneous-move case (with an independent E) CASE1 (E as the leader) CASE2 (A&B as the leaders) CASE3 (A owns E and as the leader) Paper Book(A/B)Seller A Seller B Price1817.72417.74218.15318.55917.979 Share0.4570.4410.4420.4190.4230.456 Profit 3.657 3.409 3.425 3.418 3.619 3.638 E-book(E) Price 3.237 3.417 3.451 5.794 Share0.0740.0700.0790.028 Profit0.2390.2400.2720.162 Total readership0.9140.9570.9550.9170.907 6It would be interesting to investigate whichfirm(s)will movefirst in equilibrium (endogenous timing),but it is beyond the scope of this paper. 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 (S B /S A ,P B /P A )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 à ¼ffiffiffi 2p À1).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 à ¼ffiffiffi2p À1,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 t e 1and 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 t e 1>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 Àt e 1)+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 (2Àq )t e 1>V (1Àq )+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 (TR IE ),when E is owned by A (TR AE ),and when E is owned by B (TR BE ).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 (TR IE /TR AE )and (TR IE /TR BE )as functions of (m ,k )with parameter values,as in Figs.3and 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.5also 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 >V ð1Àq Þþq t e 1.When k =1,then the market share of A’s e-book is increasing in m if and only if 2ðV þc Þþt þ4m q t e 1>4ðm q V þt e 1Þ. 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.6compares the total readership in the three cases discussed above (TR IE ,TR AE ,TR BE )and the total readership TR D 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.6is 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 TR IE /TR AE m m k TR IE /TR BE Research and industry data(AAP2009,Greco2005,Oestreicher-Singer and Sundararajan2006)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 Economist2010).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 Lemma1(Duopoly pricing equilibrium).When only the physical book sellers A and B are active in the book market and(V Àc)(k+1) A ¼P D B¼Vþc 2 ;S D A ¼VÀc kt ;S D B ¼VÀc t ;P D A¼ðVÀcÞ2 2kt ; P D B ¼ðVÀcÞ2 2t . Proof.For seller A,since y D A ¼¼ðVÀP D A )/kt,taking y D A into seller A’s profit function given in Eq.(1)the second-order derivative of P D A with respect to P D A is given byÀ4/(kt)<0.As the profit function is concave in price,solving thefirst order condition(FOC)we have P D A ¼ðVþcÞ=2and y D A ¼ðVÀcÞ=ð2ktÞ.Similarly,we can solve for seller B with P D B ¼ðVþcÞ=2and y D B ¼ðVÀcÞ=ð2tÞ.For the market to be uncovered it requires y D A þy D B <1=2,which gives the param- eter condition(VÀc)(k+1) q;06d<1=4 m q;1=46d61=2 and t e2with proba- bility1Àf(d),where d is the customer’s distance fromfirm A’s location,06q61,0 Consider the[0,y A]segment.The marginal customer who pre-fers A’s paper book over the e-book is located at y pA=(P e+-t e1ÀP A)/kt since VÀP AÀkty pA=VÀP eÀt e1.Thus,the demand for the e-book in this segment is F(y A)ÀF(y pA)and the demand for A’s physical book is y AÀ(F(y A)ÀF(y pA)). Next consider the[y B,1/2]segment.In this segment,the mar-ginal customer y pB who prefers B’s paper book over the e-book sat-isfies½Ày pB=(P e+t e1ÀP B)/t since VÀP B–t(½Ày pB)=VÀP e Àt e1.Thus,the demand for the e-book in this segment is F(y pB)ÀF(y B)and the demand for B’s physical book is ½Ày BÀ(F(y pB)ÀF(y B)). In summary,the total demand for A’s physical book is S A¼2ðy AÀðFðy AÞÀFðy pAÞÞÞ;ðA1Þthe total demand for B’s physical book is S B¼2ð1=2Ày BÀðFðy pBÞÀFðy BÞÞÞ;ðA2Þand the total demand for the e-book is S e¼2ðFðy pBÞÀFðy pAÞÞ:ðA3Þthe profit from A’s physical book is ðP AÀcÞS A;ðA4Þthe profit from B’s physical book is ðP BÀcÞS B;ðA5Þand the profit from the e-book is P e S e:ðA6ÞLemma2(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: P b A ¼P b B ¼ 8cþt qþ4t e1qþ8VÀ8V q 16À4q ; P b e ¼ 2cþtÀ4t e1þ2t e1qþ2VÀ2V q 8À2q ; S b A ¼S b B ¼ 8VÀ8cþ4c qþqðtþ4t e1À8VÞ ð8À2qÞt ; S b e ¼ 2qð2cþtÀ4t e1þ2t e1qþ2VÀ2V qÞ ð4ÀqÞt : 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 threefirms set prices simultaneously to max-imize their profit.The equilibrium prices and market-shares follow.h Lemma3(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: 8This lemma is proved only for the symmetric market with k=1and m=1,since it is applicable only to the discussion of the symmetric market in Section4.If the market is symmetric(k=m=1),the equilibrium is simplified to the following:P1 A ¼P1 B ¼ 8Vþ8cÀ2c qÀqð10VÀtÀ4t e1Þþ2q2ðVÀt e1Þ 16À8q ;P1 e ¼2ð1ÀqÞðVÀt e1Þþtþ2cÀ2t e1 8À4q ;S1 A ¼S1 B ¼ 8VÀ8cþ6c qþqðtþ4t e1À10VÞþ2q2ðVÀt e1Þ q ;S1 e ¼qð2Vþ2cÀ2V qþtÀ4t e1þ2t e1qÞ. Proof.We consider the Stackelberg game in which an indepen-dent e-book seller E sets its price in thefirst stage,andfirms A and B set their prices simultaneously in the second stage.Allfirms are maximizing their profits.The game is solved backwards for the subgame perfect Nash equilibrium.In stage2,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 stage1.There exists a unique equilibrium for which the prices and market-shares follow.h Lemma4(Pricing equilibrium with the physical book sellers as the leader in the pricing game).When the physical book sellers anticipatefirm E’s market entry and set pricesfirst,at equilibrium the prices and market-shares are as follows9: P2 A ¼P2 B ¼ 8Vþ8cÀ4c qÀ8q Vþt qþ4t e1q 16À8q ; P2 e ¼ 2ð1ÀqÞðVÀt e1Þþtþ2cÀ2t e1þt e1qÀc qÀt q=4 8À4q ; S2 A ¼S2 B ¼ 8VÀ8cþ4c qþqðtþ4t e1À8VÞ 8t ; S2 e ¼ q½ð1ÀqÞð8Vþ4cþtÀ12t e1Þþ4cþ3tÀ4t e1 ð8À4qÞt : Proof.The profit functions for the paper book sellers and the e-book seller are described in Eqs.(2)and(3).Since in Case2the paper book sellers act as the leader in the Stackelberg pricing game,they will set their prices on the paper bookfirst,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 qð4P2þtÀ4t e1À8P2eÞ=t¼0:ðA7ÞHere,the superscript2represents Case2,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 P2 e ¼ð4P2þtÀ4t e1Þ=8.Since the paper book sellers movefirst,they will take P2 e into Eq.(2) and solve through the FOC for the optimal paper book price,which is given by P2¼8Vþ8cÀ4c qÀ8q Vþt qþ4t e1q 16À8q . When the e-book seller enters it will set its price in response to the paper book price P2 e ¼ð4P2þtÀ4t e1Þ=8.The market share of each player can be derived accordingly,based on their profit functions.h Proof of Proposition1(Conditions for prices to increase and reader-ship to decrease after e-book entry in Case2).In Case2with a sym-metric market(k=m=1),a price comparison between P2and P D shows that P DÀP2¼qð4VÀ4t e1ÀtÞ=ð16À8qÞ,which can be negative when V If the market is symmetric(k=m=1),the equilibrium is simplified to the following: P1 e ¼ 2cð1þkmÞþ2ðVð1ÀqÞÀð2ÀqÞt e1Þþkðð1þmÞtþ2mðt e1ðm qÀ2ÞþVð1Àm qÞÞ q q; P1 A ¼ð1=2Þðcþq t e1þVð1ÀqÞþq P1eÞ; P1 B ¼ð1=2Þðcþm q t e1þVð1Àm qÞþm q P1eÞ;S1A¼ 2ðP1 A ÀcÞ ; S1 B ¼ 2ðP1 B ÀcÞ t ;S1 e ¼ qð2Àqþkmð2Àm qÞÞ t P1 e : P3 e ¼ 2ckmþ4ð1ÀqÞðVÀt e1Þþkðð1þmÞtþ2mðt e1ðm qÀ2ÞþVð1Àm qÞÞ 4ð2À2qþkmð2Àm qÞÞ ; P3 A ¼ 2cð2ð1ÀqÞþkmð2þð1ÀmÞqÞþ4Vð1ÀqÞþkð4mVþqð1þmÞðtÀ2mVÞÞ q q; P3 B ¼ð1=2Þðcþm q t e1þVð1Àm qÞþm q P3eÞ; S3 B ¼ 2ðP3 B ÀcÞ ;S3 A ¼ Vð1ÀqÞþq t e1Àc ; S3 e ¼ qð2cð2þkmÞÀ4t e1þkðð1þmÞtþ2mðð1Àm qÞVÀt e1ð2Àm qÞÞÞ 4kt : 9This lemma is proved only for the symmetric market with k=1and m=1,since it is applicable only to the discussion of the symmetric market in Section4. P3 A ¼ 4Vþ4cÀ2c qþt qÀ4q V 8À6q ; P3 e ¼ 3ð1ÀqÞðVÀt e1ÞþtþcÀt e1 8À6q ; P3 B ¼ cð8À5qÞþqðtþ4t e1À11VÞþ3q2ðVÀt e1Þþ8V q; S3 A ¼ VÀcþqðt e1ÀVÞ t ; S3 e ¼ qðVþ3cÀV qþtÀ4t e1þt e1qÞ 2t ; S3 B ¼ 8VÀ8cþ7c qþqðtþ4t e1À11VÞþ3q2ðVÀt e1Þ q: Proof.We consider the Stackelberg game in whichfirm A sets prices for its physical book and its e-book in thefirst stage,and thenfirm B sets its physical book price in the second stage.All firms are maximizing their profits:firm A maximizes the sum of its profit from its physical book(A4)and its e-book(A6),andfirm B maximizes its profit from its physical book(A5).The game is solved backwards for the subgame perfect Nash equilibrium.In stage2,firm B sets its optimal price taking the prices of the e-book and A’s physical book as given.Substituting B’s price into A’s profit function we can solve for the optimal prices for A set in stage1. There exists a unique equilibrium for which the prices and mar-ket-shares follow.h Proof of Proposition3(Effects of q and t e1in Case3).In Case3 with a symmetric market(k=m=1),the total market share of seller A satisfies@ðS3 e þS3 A Þ=@t e1¼ðÀ2qþq2Þ=2t<0and@ðS3eþ S3 A Þ=@q¼ð3cþtÀ2t e1þ2q t e1ÀVÀ2V qÞ=2t>0(because param-eters satisfy V wefind@P3 B =@q¼@S3B=@q,which could be positive or negative depending on parameter conditions.h Lemma6(Pricing equilibrium with seller B also selling e-books and as the leader in the pricing game).When the seller B owns E and it anticipatesfirm A’s response to the introduction of e-book,at equilibrium prices and market-shares are as follows: Proof.We consider the Stackelberg game in whichfirm B sets prices for its physical book and its e-book in thefirst stage,and then firm A sets its physical book price in the second stage.We use superscript4to represent this case.Allfirms are maximizing their profits:firm B maximizes the sum of its profit from its physical book(A5)and its e-book(A6),andfirm A maximizes its profit from its physical book(A4).The game is solved backwards for the sub-game perfect Nash equilibrium.In stage2,firm A sets its optimal price taking the prices of the e-book and B’s physical book as given. Substituting A’s price into B’s profit function we can solve for the optimal prices for B set in stage1.There exists a unique equilibrium for which the prices and market-shares follow(see Table A1).h P4 A ¼1=2ðcþq t e1þVð1ÀqÞþq P4eÞ; P4 e ¼ 2cþktð1þmÞþ2t e1ðqÀ2þ2kmðm qÀ1ÞÞþ2Vð1À2qþ2kmð1Àm qÞÞ 4ð2Àqþ2kmð1Àm qÞÞ ; P4 B ¼ 2cð2Àqð1ÀmÞþ2kmð1Àm qÞÞþ2Vð2Àqð1þmÞÞþkmð4Vþqðtð1þmÞÀ4mVÞÞ 4ð2Àqþ2kmð1Àm qÞÞ ; S4 A ¼ 2ðP4 A ÀcÞ kt S4 e ¼ qðcð2þ4kmÞþkðtð1þmÞÀ4mt e1Þþ2ðVð1ÀqÞÀt e1ð2ÀqÞÞ ; S4 B ¼ Vð1Àm qÞþm q t e1Àc t : Table A1 Summary of comparative statics(with k,m=1). Parameter Case1Case2Case3 c@P i/@c>@P e/@c>0@P i/@c>@P e/@c>0@P A/@c>@P B/@c>@P e/@c>0 t@P e/@t>@P i/@t>0@P e/@t>@P i/@t>0@P e/@t>@P A/@t>@P B/@t>0 t e1@P i=@t e1>0;@P e=@t e1<0and@P i=@t e1 @t e1>0,@S e/@t e1<0.@P i/ @t e1<|@P e/@t e1|,if q<4/5; otherwise@P i/@t e1>|@P e/@t e1|P A is independent of t e1,@P B/@t e1>0, @P e/@t e1<0and@P B/@t e1<|@P e/ @t e1|,@S e/@t e1<0,@S A/@t e1>0, @(S e+S A)/@t e1<0,@S B/@t e1>0 q@P e/@q>0,@S e/@q>0,@P i/@q=@S1/@q could be positive or negative@P i/@q=2@P e/@q,@S i/@q<0,@P i/ @q>@P e/@q>0if V 398Y.Jiang,E.Katsamakas/Electronic Commerce Research and Applications9(2010)386–399References Agarwal,R.,and Lucas,H.C.The information systems identity crisis:focusing on high-visibility and high-impact research.MIS Quarterly,29,3,2005,381–398. Association of American Publishers.Industry Statistics.Published on March31,2009. Available at http://www.publishers.org/main/IndustryStats/IndStats/2008/ 2008_Stats.htm. 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