the impacts of piracy and supply chain contracts on digital music channel performance

Decision Support Systems 52 (2012) 590–603

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Decision Support Systems

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The impacts of piracy and supply chain contracts on digital musicchannel performance

Bong-Keun Jeong a, Moutaz Khouja b,⁎, Kexin Zhao b

a SP Jain Center of Management, 10 Hyderabad Road, 119579, Singaporeb Belk College of Business, University of North Carolina at Charlotte, Charlotte, NC 28223, USA

⁎ Corresponding author.E-mail address: [email protected] (M. Khouja).

0167-9236/$ – see front matter © 2011 Elsevier B.V. Alldoi:10.1016/j.dss.2011.10.016

a b s t r a c t
a r t i c l e i n f o
Article history:Received 15 February 2011Received in revised form 5 July 2011Accepted 19 October 2011Available online 29 October 2011

Keywords:PiracyContractDigital music channelSupply chain coordination

We explore the impact of piracy on digital music supply chain profitability under different contract arrange-ments. Consumers' piracy risk cost is divided into two cases: 1) linear piracy cost and 2) fixed piracy cost. Wealso analyze two contract types: 1) fixed fee contract and 2) per song contract. Our findings indicate that themagnitude of profit loss depends on the type of consumers' piracy risk cost and the type of contract. In addi-tion, changes in consumers' piracy risk cost change the distribution of the profit between the record label andthe retailer. As the investment in piracy controls increases, the retailer keeps a larger share of the profit sur-plus leaving the record label with a smaller share. We demonstrate that a fixed fee full transfer contract willalways coordinate the supply chain, and the profitability further increases as 1) market size increases, 2) pi-racy risk cost increases, and 3) marginal cost decreases.

© 2011 Elsevier B.V. All rights reserved.

1. Introduction

Advances in the Internet and file compression technologieshave transformed the way digital products such as movies and musicare created and distributed. In the music industry, online distributionchannels have proliferated in recent years. Songs can be transmittedvia the Internet in the digitized form so that consumers can convenient-ly choose to download a single song, an entire album, or a customizedbundle from websites such as iTunes and Rhapsody. While current on-line music sales account for only 15% of total sales [18], online sales areincreasing rapidly. A report from the Recording Industry Association ofAmerica (RIAA) shows that unit sales of CD albums declined by 27.5%from 2005 to 2007 while digital album unit sales increased by 212.5%.Similarly, unit sales of single song CDs declined by 7.1% while digitalsingle song unit sales increased by 121% [36].

As online distribution channels become more popular, there is anincreasing need to re-examine contracts and coordination issues indigital music supply chains. For instance, an important question weshould ask is how do existing business models, pricing schemes,and licensing structures need to be adjusted in order to reflect thechanges caused by moving from brick-and-mortar retailing to onlinedigital sales. Traditional coordination strategies in physical productsupply chains such as buy-back and return policies may not be appli-cable due to the unique characteristics of digital experience goods [7].Marginal production cost, packaging cost, and a portion of distribu-tion cost can be eliminated by selling these products through an

rights reserved.

online digital channel. Furthermore, digital products do not requireinventory, which eliminates the risk of obsolescence and perishability[37].

The prevalence of unauthorized copying and dissemination has beena serious threat in the digital experience goods industries. In the musicindustry, rapid development of compression and file-sharing technolo-gies as well as decreasing cost of copying mediums have provided con-sumers with greater access to free music than ever before. Althoughtechnological preventive controls using software and hardware havebeen implemented, they have often had limited success, and imposedunfair restrictions on what legitimate consumers can do with thesongs they have bought [39]. Also, despite the clear articulation of digitalcopyright law and legal as well as educational deterrence efforts, piracystill exists due to the high cost of increasing consumers' awareness andof enforcing the law. Thus, it is likely that piracy will remain as a seriousproblem well into the future.

In this paper, we develop amodel to analyze the impact of piracy ondigital music supply chain profitability under different contract ar-rangements between record labels and online retailers and under dif-ferent consumer piracy risk costs. In dealing with piracy risk cost,prior empirical studies have not focused on the relationship betweenconsumers' piracy risk cost and the amount of content they pirate. Re-searchers used different measurement terms such as a single unit(“the pirated software”) [23,42], multiple units (“pirated music prod-ucts” or “copies of pirated software”) [25], or a general term (“music/software piracy”) [10], and implicitly assumed that the piracy risk costis either fixed or increasing in the amount of content pirated. In aprior study [19], we found that the magnitude of consumers' piracyrisk cost may not change with the amount of content pirated in a singlesession (consumers piracy risk costs are the same in pirating one song

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591B.-K. Jeong et al. / Decision Support Systems 52 (2012) 590–603

vs. many songs). This is in spite of the record labels' efforts to penalizeindividuals who pirate large amounts of content [32,44]. Therefore, todevelop effective anti-piracy strategy it is important to understand theimplications of fixed vs. increasing consumer piracy risk cost. One con-tribution of this paper is to explicitly incorporate heterogeneity in con-sumers' piracy behavior resulting from their piracy risk cost assessment.The rationale for the fixed risk cost is that the largest piracy risk cost oc-curs in pirating the first song, and the marginal cost of pirating moresongs diminishes very quickly after that. Our emphasis is on the impor-tance of understanding how consumers piracy risk assessment affectstheir piracy behavior and the performance of the record label, retailer,and the total supply chain.

We focus on profit maximization for newly released music al-bums. A number of studies have examined how perceived risk affectsconsumer decision and behavior [15,33]. These studies have identi-fied various aspects of risk, such as financial, performance, social,and prosecution risks, involved in ethical decision making [42]. How-ever, it is unclear how consumers assess their piracy risk cost with re-spect to the amount of content they pirate. For example, if a consumerperceives a high probability of prosecution, she is more likely to per-ceive higher risk as the number of songs she pirates increases. On theother hand, some consumers may be conscious about their image, orthey may have a desire to be identified with certain social group. Insuch a case, pirating behavior can be perceived as being unethical re-gardless of howmany songs a consumer pirates. To better understandthe implications of piracy on digital music sales, we first define twotypes of consumer piracy risk cost: 1) linear piracy cost and 2) fixedpiracy cost. In the linear cost case, we assume that a consumer's pira-cy risk cost increases linearly as the number of songs pirated in-creases. In the fixed cost case, the risk cost a consumer attaches topiracy is independent of the number of songs pirated. The piracy actmay involve a single song or a full album, but once the consumer vi-olates the law, a fixed risk cost is assigned to the act.

In addition to different types of piracy risk cost, we also examinecontractual arrangements between a record label and an online retailer.We consider two contract types: 1) fixed fee contract and 2) per songcontract. In the fixed fee contract, the record label charges the retailera fixed fee for an entire album of songs regardless of the number oftimes songs are downloaded from the retailer's website. In the persong contract, which is themost common contract type in themusic in-dustry, the record label charges the retailer a certainwholesale price foreach song downloaded. For each case, we identify an optimal Stackel-berg equilibrium and analyze how different piracy risk costs and con-tract types affect supply chain pricing, record label and retailer'sprofits, and supply chain coordination. Analytical results show that:

1. The amount of supply chain profit loss due to piracy depends onthe type of piracy risk cost of consumers as well as the contracttype between the record label and the retailer,

2. Changes in consumers' piracy risk cost not only alter total supplychain profit but also change distribution of the profit betweenthe record label and the online retailer,

3. Piracy has larger negative impact on the profitability of music al-bums containing a large number of popular songs,

4. The fixed fee full transfer contract will always fully coordinate thesupply chain, and

5. The profitability of the fixed fee contract further increases as on-line market size increases, consumer piracy risk cost increases,and marginal cost decreases.

The rest of this paper is organized as follows. Section 2 presentsrelevant literature in the area of piracy and supply chain coordination.Section 3 provides an overview of the model in which we describeconsumer purchase behavior, consumers' piracy risk costs, and con-tract types between the record label and the online retailer.Section 4 derives the optimal prices and supply chain profits in thepresence of different piracy risk costs as well as under different

contract types. Section 5 presents a number of findings. Section 6 con-tains managerial implications, conclusions, and directions for futureresearch. All proofs are shown in the Appendix A.

2. Literature review

We review relevant literature in two research streams. First, wediscuss the impact of piracy on digital experience goods, including ap-proaches to modeling consumer piracy behavior. Then, we briefly re-view the literature on supply chain coordination strategies.

A large body of research has explored the impact of piracy on dig-ital experience goods industries, especially in the software and musicindustries. For example, Hong [16] found that Internet growth had asignificant negative effect on recorded music sales. However, otherstudies have shown that the negative impact of piracy on the legiti-mate demand is considerably smaller than industry estimates [17],and tolerating some piracy might even be beneficial when it createspositive network externality [13,14,27,34,41]. To better understandthe impact of digital piracy, a careful analysis of consumer piracy be-havior is needed. Previous studies incorporated various economic andbehavioral factors such as penalties and ethical propensities that in-fluence consumers' piracy tendency. Chen and Png [29] developed amodel that incorporates a penalty for copyright violation set by thegovernment. In the model, consumers are segmented into ethicaland unethical groups. While ethical consumers can choose eitherbuying a legitimate product or not using it, unethical consumers max-imize their net benefits by choosing among buying the legitimateproduct, not using it, and pirating. The results show that changes inpricing and monitoring rates have qualitatively different effects onconsumers and that from a social welfare perspective, reductions inprice are better than increases in monitoring. Similar market segmen-tation was used by Khouja and Park [21] in a model that considered aheterogeneous consumer market with three segments: ethical, indif-ferent, and pirating with each having a different affinity to piracy. Theresults indicate that the incorporation of different consumer seg-ments will cause the retailer to charge lower prices and, therefore,lead to higher legal product diffusion. The authors also show thatthe royalty system does not solve the double marginalization prob-lem and is suboptimal from a supply chain perspective. Khouja andWang [22] considered a consumer market which is divided into aretail-captive segment whose consumers are limited to the retailchannel and a hybrid segment whose consumers have access toboth retail and digital channels. They analyzed the retailer's pricingstrategy under an exclusive direct digital channel, exclusive regularretail channel, and dual channels. Khouja et al. [20] analyzed a retai-ler's pricing decision under piracy using an agent-based modelingsimulation. Bhattacharjee et al. [1] analyzed the use of “compilationalbum” which offers stronger bundling than the classic album bun-dling. Examples of compilation albums include Christmas and dancemusic albums. This type of bundling may decrease consumer searchcosts and reduce the incentive to pirate.

Chellappa and Shivendu [7] developed a model for motion pictureDVDs. The model considers two distinct types of piracy: 1) globalwhere consumers obtain illegal copies for a region other than theirown and 2) regional where consumers pirate products meant fortheir own region. Consumers differ among regions with some regionshaving consumers with higher marginal willingness to pay for theproduct (Region A) compared to other regions with lower consumerincome (Region B). The results indicate that when piracy is prevalent,losses from global piracy can be higher than when there is only re-gional piracy. Thus, maintaining separate technology standards iscritical to minimize the loss. Sundararajan [40] analyzed the optimalpricing and technological protection levels for a monopolist usingprice discrimination among consumers. In the absence of price dis-crimination, an optimal protection level is at the technologically

592 B.-K. Jeong et al. / Decision Support Systems 52 (2012) 590–603

maximum level, while it is always at a lower level in the case when aseller can price discriminate.

An interesting finding by Gopal and Sanders [15] is that deterrentcontrols that employ educational and legal campaigns to dissuade pi-rates provide more profits to the publisher than preventive controlsthat use technology to make piracy costly and difficult. Also, deterrentcontrols are shown to be superior with respect to a social welfare.Bhattacharjee et al. [2] modeled a consumer search process and retail-er strategies in the presence of online piracy. In their study, differentpricing options and licensing structures were considered. The resultindicates that the mixed pricing strategy dominates the other two op-tions, and the lump sum and percentage revenue are the better li-censing structures than the per download cost structure. However,reactions of other important players in the chain such as the manu-facture were not considered. Chen and Png [30] extended their earliermodel [29] to include a tax on copying media and equipment and agovernment subsidy for legitimate purchases in addition to the penal-ty for copying. The results indicate that taxing the copying media issuperior to imposing a penalty for piracy, and that subsidizing legiti-mate purchases is the optimal government policy from social welfareperspective.

In sum, consumer ethical attitude and perceived risk have beenwidely used in the literature as a key factor in consumer piracy be-havior. However, prior studies [2,15,21,29,30,40] mainly dealt withthe piracy of a single product (e.g. a consumer incurs a certain penaltycost if they are caught pirating a song), and did not examine whathappens if piracy risk cost increases as the amount of content piratedincreases. The implications of the risk cost structures where morethan one song is pirated in a single act may have profound impacton profitability. To better understand the effect of piracy, we comparethe fixed piracy risk cost case with the linearly increasing case. Giventhe large volume of music files available online and the option to pi-rate multiple songs in each piracy session, our approach can providenew insight into the impact of piracy on the digital music market.

The Internet has brought renewed research interest in supplychain management. Much of this research has focused on physicalproducts supply chains. A good deal of this research has found thatthe Internet has increased the power of manufacturers due to makingit possible for them to bypass retailers and sell directly to consumers[9,43]. In these e-commerce models, the physical product isunchanged but the manufacturer ships it directly to the consumer.While the Internet has given increased power to the manufacturersof physical products, it has had an opposite effect in experiencegoods industries. In the music industry, for example, the poweronce held by the record labels is undergoing a profound shift due toadvances in the technology needed to produce and distribute experi-ence goods. As described by Clemons et al. [12], the forces whichmade “stars” in the industry captive to record labels are weakening.

Digital experience goods and recorded music in particular may bedistributed through one of several channels. Premkumar [35] out-lined six distribution strategies for music, record label-retailer-customer (RLRC), record label-customer, record label-intermediary-customer (RLIC), artist-customer (AC), artist-intermediary-customer(AIC), and audio-on-demand. While the traditional supply chain con-figuration of RLRC channel remains the most common way of distrib-uting music, RLIC channel is gaining in popularity. In this channel,consumers buy songs in digital format from an intermediary such asiTunes or Rhapsody who pay the record label for the songs. Accordingto RIAA, the number of singles sold digitally on the Internet using theRLIC channel exceeds the number sold on the RLRC channel [36]. Also,the average growth/decline rates over 2005–2007 show that sales ofCD albums on the RLIC channel will well exceed the sales on theRLRC channel by 2012. The AC and AIC channels are gaining in popu-larity [3], and in some cases the music is given for free through thesechannels [31]. When music is not free, the AC channel becomes thecase of a centralized channel since the producer and the retailer are

one. This case is analyzed later in this paper. When the music is givenfree, the artists have some motives such as gaining publicity, gettingconsumers to sample their music, or increasing concert attendance.The analysis of free music model is outside the focus of this paper.

Supply chain coordination for physical products, including experi-ence goods, has been extensively studied in the area of operationsmanagement and economics. Cachon and Lariviere [4,5] showedthat revenue-sharing arrangements coordinate the supply chain inthe video rental industry and maximize overall supply chain profit.They compared revenue sharing with buy-back, quantity-flexibility,price discount, and sales rebate contracts. The authors found that rev-enue sharing is superior in its ability to coordinate many types of sup-ply chains. Revenue sharing encourages retailers to have higher orderquantities which tend to increase the overall revenue of the wholesupply chain. Chellappa and Shivendu [6,8] examined the impact ofpiracy on digital product supply chains under different contracts(fixed vs. per-copy). They found that, in the absence of piracy, boththe manufacture and retailers are indifferent to payment policiessince their profits are the same. However, in the presence of piracy,due to high fixed infrastructure cost, zero marginal cost, and uncer-tainty in market size, retailers prefer fixed-fee contract where theypay one time licensing fee. They also demonstrated that the numberof pirates and the prices are lower in the fixe-fee contract regime.These two studies are the first to examine digital supply chain coordi-nation under piracy; however, our study is different from their worksin several ways. First, the studies were limited to homogenous con-sumer segment in their taste and risk cost. Their focus was on pur-chasing/pirating a single product, consequently, did not have to dealwith the relationship between consumers' piracy risk and the amountof content pirated. Second, they assume that the quality of digitalproduct would increase as the number of features increases. Howev-er, prior studies show that consumers perceive compressed musicquality as almost the same or very good compared to legitimate CDquality [2]. Therefore, we assume consumers view a pirated copy asa perfect substitute for a legitimate copy and thus get the same utilityfrom the pirated copy. In sum, we focus on two contract arrange-ments between the record label and the online retailer: a fixed feecontract and a per song (wholesale price) contract currently used inthe music industry. In addition, we incorporate heterogeneity in theconsumers' behaviors with regard to valuation for products and riskcost assessment process. A comparison of different contract typesand their interaction with different piracy risk costs can provide bet-ter insights into digital music supply chain coordination.

3. A digital music supply chain model

We first examine consumers' purchase behavior. We assume that,for a newly released album, a consumer's valuation for songs is a non-decreasing concave function in the number of songs purchased, indi-cating that the marginal valuation is diminishing in the number ofsongs purchased from the album. This is a reasonable assumption be-cause consumers can buy their favorite songs first when using onlinestores. Consumer i's valuation for μ songs is given by:

Vi ¼ yi μκ; if μbμ0

V0i ¼ yi μκ0 ; if μ≥μ0

�ð1Þ

where

i 1, 2,…, M, a consumer index,yi a random variable satisfying α1≤yi≤β1 and α1,β1≥0.

yi has a known probability density function, pdf, fY(y) andcumulative density function, cdf, FY(y),

κ a constant satisfying 0bκb1, andμ0 the number of songs at which a consumer's marginal valua-

tion becomes zero.

Table 1Notation.

(p,w,μ,Π)q, sj

p: retail price, w: wholesale price, μ: number of songs, Π: profitj: piracy risk cost (N=no piracy, L=linear piracy cost, F=fixed piracy cost)q: type of contract (PS=per song contract, FC=fixed fee contract, FF=fixedfee contract with full transfer, FP=fixed fee contract with partial transfer)

s: player (CC=centralized chain, RE=retailer, RL=record label, TC=total chain)


The function given by Eq. (1) is a two-parameter utility function inwhich yi describes the taste of consumer i, with high yi indicating a con-sumerwith highwillingness to pay for a certain type ofmusic. κ is a con-stant describing the shape of the utility function. This is similar to thetwo-parameter utility function used by Chuang and Sirbu [11] to de-scribe consumers' willingness to pay for articles in a book. The functionimplies that each consumer can rank the songs on the album in decreas-ing order of preference, such that his/her favorite song is ranked first,the least favorite song is ranked last. The consumer may place novalue on some songs on the album leaving him/her with μ0 songs he/she is willing to pay some money to purchase. The consumers' willing-ness to pay for each song decreases as we move down the list. The de-crease in the willingness to pay is inversely proportional to κ.

The consumer valuation function above implies that consumershave different tastes formusic and their valuations for a given albumdi-minish at the same rate. In ourmodel, consumers are uniformly distrib-uted with respect to y. The number of songs that a consumer purchasesmust satisfy μ≤μ0 since the marginal utility becomes zero beyond μ0.We assume that μ0 is the same for all consumers to maintain analyticaltractability while allowing different consumers to prefer differentsongs. For any given price per song, consumers will purchase the num-ber of songs that maximize their net gains. In practice, a consumer buysan integer number of songs, but the use of a continuous μ allows us tobetter analyze the problem. For simplicity, we assume α1=0.

Proposition 1. The optimal number of songs consumer i purchases is

μ�i ¼ min

κyip

� � 11−κ

; μ0

!: ð2Þ

Let λ ¼ 2β1κ−1κ−2

� �1−κ , then the following proposition can beproven.

Proposition 2. If β1≤pμ1−κ

0κ then the average optimal expected number

of songs a consumer buys is

μ� ¼ λκ2p

� � 11−κ

: ð3Þ

The Proof of Proposition 2 shows the average optimal expectednumber of songs a consumer buys when the condition in the proposi-tion does not hold. However, it is reasonable to analyze the problemwhen the condition holds since consumers' utility will significantlydiminish as μ approaches μ0 (i.e. κ is small) and μ0 is relatively large.Therefore we analyze the problem when μ∗bμ0.

3.1. Impact of piracy on consumer purchase behavior

Consumers can obtain a song by purchasing a legitimate copy or bypirating it. While consumers can get songs for free (or at a negligiblecost) if they pirate, they are subject to piracy costs caused by potentialpenalties for violating copyright if they are caught, and a search costto identify and download pirated copies. In this paper, we considertwo different types of piracy risk costs: linear cost and fixed cost,which we will explain in detail in the following subsections. We use �Gto represent the proportion of consumers who will purchase a legiti-mate copy. For the no piracy case, �GN ¼ 1 because, according to our util-ity function, all consumers will purchase some quantity of songs in theabsence of piracy given the continuous μ, albeit the quantity purchasedmay be very small. Table 1 explains the notations used in this paper.

3.1.1. Linear piracy risk costIn the linear piracy risk cost case, the risk cost consumer i attaches

to piracy increases linearly in the number of songs pirated. Prior stud-ies suggest that consumers perceive compressed music quality as al-most the same or very good compared to legitimate CD quality [2].

Therefore, we assume consumers view a pirated copy as a perfectsubstitute for a legitimate copy and get the same utility from the pi-rated copy. In this scenario, consumer i will purchase μ songs if thegain from purchasing them is larger than the gain from pirating, i.e.,yiμκ−μp≥yiμκ−μziL which gives p≤zi

L. For analytical convenience,we assume that consumer i's piracy risk cost, ziL, is uniformly distrib-uted between 0 and β2. It is reasonable to assume that the upperbound on consumers' piracy risk cost is larger than price per song,β2>p. Then, the proportion of consumers who will purchase songs is

�GL ¼ ∫β10 1−∫p

01β2

dt� �

1β1

dyÞ ¼ β2−pβ2

: ð4Þ

3.1.2. Fixed piracy risk costIn this case, the risk cost of pirating μ0 songs is the same as pirating

just one song. Therefore, if consumer i chooses to pirate, she will maxi-mize her gain by illegally downloading all μ0 songs, at which the consu-mer'smarginal valuation for songs becomes zero. A consumer comparesthe net gain from purchasing any number of songs to the net gainfrom pirating μ0 songs, and purchases if yiμκ−μp≥yiμ0κ−zi

F whichgives yi(μ0κ−μκ)+μp≤zi

F. The left hand side of the inequality is theadditional utility a consumer gets from pirating μ0−μ songs plus theutility from saving the pμ that would have been spent on the legitimatepurchase of μ songs. If the piracy risk cost on the right hand side of theinequality exceeds this additional utility from pirating, then the con-sumer purchases some songs. Since it is reasonable to assume thatsome consumers' piracy risk cost is sufferingly large for the inequalityto hold, i.e. β2>yi(μ0κ−μκ)+μp holds for some consumers, the propor-tion of consumers who will purchase μ songs is

�GF ¼ ∫β10 1−∫y μκ

0−μκð Þþμp0

1β2

dt� �

1β1

dy� �

which gives,

�GF ¼ 2 β2−μpð Þ þ β1 μκ−μκ0

� �2β2

: ð5Þ

3.2. Contracts between the record label and the online retailer

In this subsection, we explore different types of contracts betweenthe record label and the online retailer. We consider two contracts: aper song contract (PS) and a fixed fee contract (FC).

3.2.1. Per song contractUnder the per song contract, the retailer will pay a wholesale price

to the record label each time a song is downloaded. The record labelacts as a Stackelberg leader in the chain, as the record label choosesthe wholesale price before the online retailer sets the retail price.The retailer takes the wholesale price as predetermined and maxi-mizes the retail profit. The record label anticipates this retail responseand maximizes its profit subject to the retail pricing decision. The re-cord label charges a wholesale price per song sold of w and incurs amarginal cost, cl. The royalty per song paid to the artist is the majorcomponent of the marginal cost incurred by the record label. Also, cris the online retailer's marginal cost, which is mainly made up by

Table 2Different scenarios.

No piracy Piracy cost

Linear Fixed

Centralized chain S1 S2 S3Per song contract S4 S5 S6Fixed fee full transfer S7 S8 S9Fixed fee partial transfer S10 S11 S12


the cost of bandwidth. If the total consumer market size is M, theretailer's profit in the per song contract is

ΠPS;RE ¼ M p−cr−wð Þμ �G: ð6Þ

The record label's profit is

ΠPS;RL ¼ M w−clð Þμ �G: ð7Þ

Let where ct=cr+cl. For centralized supply chain, the profit of thechain is

ΠPS;CC ¼ M p−ctð Þμ �G: ð8Þ

3.2.2. Fixed fee contractIn the fixed fee contract, the record label charges a lump sum fee

for an entire collection/album of songs regardless of the number oftimes songs are downloaded from the retailer's website. Dependingon who is responsible for the royalty paid to artists, two differentsub-structures can be examined. The record label may transfer theroyalty cost responsibility to the retailer so that the retailer bearsthe royalty cost. This case is referred to as fixed fee full transfer (FF).The profits of the record label and the online retailer in FF are:

ΠFF;RE ¼ M p−ctð Þμ �G−FF

ΠFF;RL ¼ FF:ð9Þ

Another possible contract is for the retailer to pay the record labela larger fee and the record label keeps the responsibility for payingthe royalty. This case is referred to as fixed fee partial transfer (FP).The profits of the record label and the online retailer in FP are:

ΠFP;RE ¼ M p−crð Þμ �G−FP: ð10Þ

ΠFP;RL ¼ FP−Mclμ �G: ð11Þ

We refer to ΔΠ as the fixed fee advantage, which is determined by:

ΔΠ ¼ ΠFC;TC−ΠPS;TC: ð12Þ

If ΔΠ is positive, the FF/FP contract is better than the PS contractfrom the supply chain perspective. The record label and the retailerhave to bargain over partitioning of the supply chain profit surplusand the actual value of FF/FP will be determined by the bargainingprocess. Many factors, such as the relative bargaining power betweenthe retailer and the record label and the risk of breakdown [26] willaffect FF. For example, in the simplest bargaining situation (i.e., oneshot game between two equally powerful firms), the Nash bargainingsolution, FF, will satisfy:

ΠFF=FP;RE−ΠPS;RE ¼ ΠFF=FP;RL−ΠPS;RL ¼ΔΠFF=FP;TC

2ð13Þ

which implies an equal division of additional profits. We do not discusshow FF/FP is determined in detail since our focus is how the contractstructures and piracy affect channel coordination.

4. Comparison of different scenarios

Based on different piracy risk costs and contract arrangements, weevaluate the scenarios shown in Table 2. Each scenario is comparedwith the benchmark case in which the supply chain is centrally coor-dinated. Closed-form expressions can't be obtained for the generalcase where κ is any value from the interval (0, 1). Therefore, wefocus on the case of κ ¼ 1

2, for which closed-form expressions can be

derived. This enables us to provide insights into the problem. Also,for β2bct, no consumers buy a legitimate product for any profitableprice. Therefore, to avoid trivial cases, we assume β2≥ct.

4.1. Centralized supply chain

The decision maker chooses the price which maximizes the totalprofit of the integrated supply chain. This case includes the AC chan-nel since the artist acts as both the producer and retailer. Althoughthis supply chain configuration is not yet common in the music indus-try, it provides the maximum profit for the supply chain, and is usedas the benchmark to which other contracts are compared.

Proposition 3. The optimal prices for a centralized supply chain are:

S1. No piracy:

pN�CC ¼ 2ct ð14Þ

S2. Linear piracy cost:

pL�CC ¼ 2ctβ2

ct þ β2ð15Þ

S3. Fixed piracy cost:

pF�CC ¼ λ2−2β1λþ 8ηct þ ζ t

8ηð16Þ

where η ¼ 2β2−λffiffiffiffiffiffiμ0

pand ζ t ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiλ2 λ−2β1ð Þ2 þ 8ηct 8ηct−λ λ−2β1ð Þð Þ

q:

Proposition 3 shows that if μ∗bμ0, the centralized supply chain re-sponds to piracy under the linear piracy cost by decreasing the priceby pN�CC−pL�CC ¼ 2c2t

ctþβ2. This implies that piracy has a limited effect on

the optimal price when piracy risk cost is high. More interestingly,for products with low marginal cost, the supply chain can lower theprice considerably to encourage legitimate sales and discourage pira-cy while still being profitable. For fixed piracy cost, the optimal pricedepends on μ0. This is because consumers will pirate all μ0 songswhen they pirate and therefore they compare the net gain of anypurchase of μ∗bμ0 songs to the net gain from pirating μ0 songs.The analysis indicates that piracy reduces the optimal price inthe fixed cost case as well. This is intuitive since firms need tolower price to keep consumers from pirating [39].

However, the amount of price declines in the fixed piracy cost casemay be less or more than the decrease in the linear case dependingon problem parameters. For example, for β2=6, λ=3, and μ0=2,pCCF ∗ bpCC

L ∗ for ctb0.428. If μ0=5, then pCCF ∗bpCC

L ∗ for ctb0.508. Therefore,when the marginal cost is small, the decrease in the optimal pricefor the fixed piracy cost case is larger than in the linear case. Table 3summarizes results for the centralized chain optimum.

4.2. Decentralized supply chain with per song contract

In a decentralized chain with per song contract, the retailer paysthe record label a wholesale price for each song sold. The recordlabel pays a portion of this wholesale price to the artists in royalty.

Table 3Summary of centralized chain optimums, μ∗bμ0.

Centralized chain

No piracy pCCN ∗ 2ct

μCCN ∗ λ8ct

� 2ΠCC

N ∗ Mλ2

64ct

Linear piracy cost pCCL ∗ 2ctβ2

ctþβ2

μCCL ∗λ ctþβ2ð Þ8ctβ2

� 2ΠCC

L ∗ Mλ2 ct−β2ð Þ264ctβ2β2

Fixed piracy cost pCCF ∗ λ2−2λβ1þζ tþ8ηct

8η

μCCF ∗4η2λ2

λ λ−2ϕð Þþ8ηctþζ tð Þ2

ΠCCF ∗ Mη2λ2 λ λ−2ϕð Þþζ tð Þ 8ηctþζ tð Þ

4β2 λ λ−2ϕð Þþ8ηctþζ tð Þ3

Table 4Summary of decentralized supply chain optimums with per song contract, μ∗bμ0.

Decentralized chain with per song contract

No piracy pPSN ∗ 2(w+cr)

μPSN ∗ λ8 wþcrð Þ� 2

wPSN ∗ 2cl+cr

ΠPS, REN ∗ Mλ2

128ct

ΠPS, RLN ∗ Mλ2

256ct

ΠPS, TCN ∗ 3Mλ2

256ct

Linear piracy cost pPSL ∗ 2 wþcrð Þβ2

wþcrβ2

μPSL ∗λ wþcrþβ2ð Þ8 wþcrð Þβ2

� 2wPS

L ∗ β22ϕ − ϕ

3−cr

ΠPS, REL ∗ Mλ2 ϕ2þ3β2ϕ−3β2

2ð Þ2−192β2β2 ϕ3−3ϕβ2

2ð Þ

ΠPS, RLL ∗ Mλ2 ϕ2þ3ctϕ−3β2

2ð Þ ϕ4−15β22ϕ

2þ9β42ð Þ

192ϕβ2β2 ϕ2−3β22ð Þ2

ΠPS, TCL ∗ Mλ2 ϕ2þ3 ϕ−β2ð Þβ2ð Þ 2β2 ϕ2−3β2

2ð Þþct 3β2 ϕþβ2ð Þ−ϕ2ð Þð Þ−64β2β2 ϕ2−3β2

2ð Þ2

Fixed piracy cost pPSF ∗ λ2−2β1λþ8ηρþ1

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4 λ2−2β1λþ8ηρð Þ2−96ηλρ λ−2β1ð Þ

q8η

μPSF ∗4η2λ2

λ2−2β1λþ8ηρþ12

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4 λ2−2β1λþ8ηρð Þ2−96ηλρ λ−2β1ð Þ

q� 2

wPSF ∗ No closed form solution

ΠPS, REF ∗ Mη2λ2 8ηρþτð Þ λ2−2β1λþτð Þ

4β2 λ2−2β1λþ8ηρþτð Þ3

ΠPS, RLF ∗ No closed form solution

ΠPS, TCF ∗ No closed form solution

where τ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiλ4−4β1λ

3 þ 4 β21−2ηρ

� λ2 þ 16ηρβ1λþ 64η2ρ2

r:


This is the most common contract arrangement between record labelsand retailers [3]. The retailer's margin per song is quite small since thewholesale price averages about $ 0.70 [28].

Proposition 4. Under the per song contract, the optimal retail andwholesale prices for a decentralized supply chain are:

S4. No piracy1:

pN�PS ¼ 2 wþ crð Þ ð17Þ

wN�PS ¼ 2cl þ cr ð18Þ


pL�PS ¼2β2 wþ crð Þwþ cr þ β2

ð19Þ

wL�PS ¼

β22

φ−φ

3−cr ð20Þ

where φ ¼ 3θð Þ13 and θ ¼ −9ctβ22 þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi81c2t β

42 þ 3β6

2

qS6. Fixed piracy cost2:

pF�PS ¼λ2−2β1λþ 8ηρþ 1

2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4 λ2−2λβ1 þ 8ηρ� �2−96ηλρ λ−2β1ð Þ

q8η

ð21Þ

where ρ=w+cr.

Table 4 summarizes the results for the decentralized chain with

per song contract. An interesting result from Table 4 is thatΠN�

PS;RE

ΠN�PS;RL

¼ 2

in the no piracy case which implies that the retailer makes twiceas much profit as the record label. This is the opposite of the classicsupply chain profit distribution under a Stackelberg equilibrium andlinear demand where the manufacturer makes twice as much profitas the retailer [9]. The reason for the retailer keeping larger share ofsupply chain profits is the demand curvature. In decentralized supplychains, as demand convexity with regard to price increases, the retail-er keeps a larger share of supply chain profits and the decentralizedsupply channel on the whole improves [38]. For example, for expo-nential demand, the retailer keeps half of the supply chain profits.For the case of no piracy in Proposition 4, consumer demand is

given by M λκ2p

� 11−κ ¼ M λκð Þ2

4p2 which is strongly convex and the retailer

keeps two thirds of supply chain profits. One can view the high

1 w* is obtained under the condition, μ*bμ0.2 We're unable to obtain the closed-form solution in the fixed piracy cost case.

demand sensitivity to price as giving more power to the retailer dueto the increased importance of the retail price decision and enablingher to keep larger share of supply chain profits.

Another noteworthy finding is that changes in the piracy risk cost,β2, not only change total supply chain profit but also change the dis-tribution of profit between the retailer and the record label. As β2 in-creases (through increasing efforts to combat piracy), total supplychain profit will increase. However, the retailer gets a larger shareof the surplus profit leaving the record label a smaller share. Thechange in the profit distribution occurs because in the linear piracyrisk cost case, the demand function is given by M λκð Þ2

4p2β2−pβ2

¼M λκð Þ2

4p2 − λκð Þ24pβ2

� which reduces the convexity of the demand function

due to the term − λκð Þ24pβ2

. As β2 increases, λκð Þ24pβ2

decreases and demandsensitivity to price increases which enables the retailer to keep a larg-er share of supply chain profits. When β2 becomes very large, λκð Þ2

4pβ2be-

comes close to zero, the demand function becomes the same as inthe no piracy case in which the retailer makes twice the profit ofthe record label.

4.3. Decentralized supply chain with fixed fee contract

If a fixed fee contract is used in the decentralized chain, the re-tailer pays the record label a fixed fee in exchange for being able tosell songs from a record label's album/collection to the public.Depending on who is responsible for the royalty payment to art-ists, two fixed fee contract types, full transfer and partial transfer,can be considered.

4.3.1. Fixed fee full transfer contract

Proposition 5. The optimal retail prices for a decentralized supply chainwith fixed fee full transfer contract are:

Table 5Summary of fixed fee full transfer contract optimums, μ∗bμ0.

Fixed fee full transfer contract

No piracy pFFN ∗ 2ct

μFFN ∗ λ8ct

� 2ΠFF, RE

N ∗ Mλ2

64ct−FF

ΠFF, RLN ∗ FF

ΠFF, TCN ∗ Mλ2

64ct

Linear piracy cost pFFL ∗ 2ctβ2

ctþβ2

μFFL ∗λ ctþβ2ð Þ8ctβ2

� 2ΠFF, RE

L ∗ Mλ2 ct−β2ð Þ264ctβ2β2

−FF

ΠFF, RLL ∗ FF

ΠFF, TCL ∗ Mλ2 ct−β2ð Þ2

64ctβ2β2

Fixed piracy cost pFFF ∗ λ2−2β1λþ8ηctþζ t

8η

μFFF ∗4η2λ2

λ2−2β1λþ8ηctþζ tð Þ2

ΠFF, REF ∗ Mη2λ2 λ λ−2β1ð Þþζ tð Þ 8ηctþζ tð Þ

4β2 λ λ−2β1ð Þþ8ηctþζ tð Þ3 −FF

ΠFF, RLF ∗ FF

ΠFF, TCF ∗ Mη2λ2 λ λ−2β1ð Þþζ tð Þ 8ηctþζ tð Þ

4β2 λ λ−2β1ð Þþ8ηctþζ tð Þ3

Table 6Summary of fixed fee partial transfer contract optimums, μ∗bμ0.

Fixed fee partial transfer contract

No piracy pFPN ∗ 2cr

μFPN ∗ λ8cr

� 2ΠFP, RE

N ∗ Mλ2

64cr−FP

ΠFP, RLN ∗ FP−Mλ2cl

64c2r

ΠFP, TCN ∗ Mλ2

64cr1− cl

cr

� Linear piracy cost pFP

L ∗ 2crβ2crþβ2

μFPL ∗λ crþβ2ð Þ8crβ2

� 2ΠFP, RE

L ∗ Mλ2 cr−β2ð Þ264crβ2β2

−FP

ΠFP, RLL ∗ Mcl c2r −β2

2ð Þλ2

64c2r β2β2þ FP

ΠFP, TCL ∗ Mλ2

64crβ2β2

� cr−β2ð Þ2− cl c2r −β2

2ð Þcr

� �

Fixed piracy cost pFPF ∗ λ2−2β1λþ8ηcrþζ r

8η

μFPF ∗4η2λ2

λ2−2β1λþ8ηcrþζ rð Þ2

ΠFP, REF ∗ Mη2λ2 λ λ−2β1ð Þþζ rð Þ 8ηcrþζ rð Þ

4β2 λ λ−2β1ð Þþ8ηcrþζ rð Þ3 −FP

ΠFP, RLF ∗ FP− 2Mη3λ2cl 8ηcrþζ rð Þ

β2 λ λ−2β1ð Þþ8ηcrþζ rð Þ3

ΠFP, TCF ∗ Mη2λ2 λ λ−2β1ð Þ−8ηclþζ rð Þ 8ηcrþζ rð Þ

4β2 λ λ−2β1ð Þþ8ηcrþζ rð Þ3


S7. No piracy:

pN�FF ¼ 2ct ð22Þ


pL�FF ¼2β2ctct þ β2

ð23Þ


pF�FF ¼ λ2−2β1λþ 8ηct þ ζ t

8η: ð24Þ

Proposition 5 shows that the optimal retail price under the FF con-tract is the same as the optimal retail price of the fully coordinatedchain. Consequently, the total supply chain profit under the FF con-tract is the same as the profit in the centrally coordinated supplychain. In the no piracy case, the range of lump sum payment thatyields the same or greater profits for the decentralized record labeland retailer than under the per song contract is:

Mλ2

256ct≤FF≤ Mλ2

128ct: ð25Þ

Since Mλ2

128ct− Mλ2

256ct¼ Mλ2

128ct> 0, there exists a fixed fee payment

under which both parties are better off. Table 5 summarizes resultsin the fixed fee full transfer contract.

4.3.2. Fixed fee partial transfer contract

Proposition 6. The optimal retail prices for a decentralized supply chainwith fixed fee partial transfer contract are:

S10. No piracy:

pN�FP ¼ 2cr ð26Þ


pL�FP ¼ 2β2crcr þ β2

ð27Þ


pF�FP ¼ λ2−2β1λþ 8ηcr þ ζ r

8ηð28Þ

where ζ r ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiλ2 λ−2β1ð Þ2 þ 8ηcr 8ηcr−λ λ−2β1ð Þð Þ

q:

Note that the optimal prices for this contract are independent ofthe marginal cost of the record label. For the fixed fee partial transfercontract, the fee that yields the same or greater supply chain profitthan the per song contract in the no piracy case is:

Mλ2

1282clc2r

þ 12ct

� �≤FP≤Mλ2

1282cr− 1

ct

� �: ð29Þ

Eq. (29) implies that if 0bclb 12 cr then there is a fixed fee under

which the fixed fee partial transfer contract can leave both the retailerand the record label better off than in the per song contract. Sincethere is no wholesale price under this contract, and the retailer isnot responsible for the royalty, the fixed fee partial transfer contractis better than the per song contract when the royalty (the major com-ponent of cl) is small relative to cr. In this case, the retailer chargeshigher price due to the large cr and sells less songs which reducesthe royalty cost paid by the record label. Given p∗ and μ∗ for each

scenario, we can show that total supply chain profit under fixed feefull transfer contract is always greater than the total supply chainprofit in per song and fixed fee partial transfer contracts. Table 6 sum-marizes the results for the fixed fee partial transfer contract.

5. Analysis

There are a number of interesting results related to managing adigital music channel under piracy. We begin by introducing the gen-eral findings. Some results cannot be proved for the general case due

(a) Per song contract(b) Fixed fee full transfer contract

π π

ββ

Fig. 1. Total chain profits vs. piracy cost (cr=0.15, cl=0.25, α1, α2=0, β1=1, μ0=10, M=10).


to the lack of closed-form for w∗ in the fixed piracy cost. We presentthese results as findings which are demonstrated numerically.

Corollary 1. Piracy will reduce the total profit of the supply chain. Thedecrease in supply chain profits depends on the type of piracy risk costof consumers.

Corollary 1 indicates that the type of piracy risk costs determinesthe magnitude of supply chain profit loss. As shown in Fig. 1, whenthe upper limit on piracy cost, β2, is relatively small, the total chainprofit under the linear piracy cost is greater than the profit underthe fixed piracy cost for both the per song and fixed fee full transfercontract. However, as β2 increases, the total chain profit under thefixed piracy cost becomes closer to the linear case. This result indi-cates that, if consumers' piracy risk costs are low, the supply chainsuffers more under the fixed piracy cost.

In addition to β2, profits also depend on β1 and μ0. Fig. 2 showsthat for the per song contract, when β1 is large, i.e. high valuationfor songs, and/or μ0 is large which is the case for popular artists,total supply chain profit is greater in the linear piracy cost case. Inother words, popular artists suffer more from piracy when consumershave fixed piracy cost. In the case of no piracy and linear piracy, μ0does not affect total chain profit because consumers buy only thesongs which maximize their net gain. However, when the piracycost is fixed, consumers pirate all μ0 songs where their marginal val-uation for songs becomes zero. Popular artists usually have higherμ0, which, in turn, makes pirating even more attractive for consumers.Another interesting result is the shape of total chain profit vs. β1 inthe fixed piracy cost. Unlike the other two cases, the total chain profitunder the fixed piracy cost increases for a range of β1 and then start

β

Fig. 2. Total chain profits vs. β1 and μ0 under per song contract (c

decreasing. A closer examination shows that although consumers'valuation for songs increases, the price stays relatively constant inthe fixed piracy cost case. Hence, consumers who decide to purchasesongs would purchase more songs and the total chain profit increases.However, as β1 increases further, piracy becomes more preferable byconsumers which reduces the pricing power of the retailer and de-creases total chain profit.

Corollary 2. For any κ∈ (0,1), fixed fee full transfer contract willalways fully coordinate the supply chain.

We numerically examine the fixed fee advantage where the totalsupply chain is better off relative to the per song contract for twofixed fee structures and the two piracy risk costs. If this advantage ispositive, we assume the record label and the retailer can find a satis-factory division of the profit surplus.

Finding 1. Changes in the piracy risk cost not only change total supplychain profit but also change the distribution of the profit betweenthe retailer and the record label.

Fig. 3 shows that as β2 increases, the profits of the retailer, the re-cord label, and the supply chain all increase. Total chain profit is aconcave increasing function of β2 indicating that the positive margin-al impact of β2 is decreasing. This is because the proportion of con-sumers purchasing a legitimate product becomes close to 1 for highβ2, thus most consumers will buy a legitimate product rather than pi-rate. However, Fig. 3a shows that for small values of β2, the profit ofthe record label increases more than the profit of the retailer underthe linear piracy cost. For larger values of β2, the profit of the retailerincreases more under both fixed and linear piracy costs. Let β2 be the

μ

r=0.15, cl=0.25, α1, α2=0, β1=1, β2=3, μ0=10, M=10).

(a) Linear piracy risk cost (b) Fixed piracy risk cost

π π

β β

Supply chain Retailer Label Supply chain Retailer Label

Fig. 3. Profits vs. piracy cost under linear and fixed risk costs for the per song contract (cr=0.15, cl=0.25, α1, α2=0, β1=1, μ0=10, M=10).


value of β2 at which ΠPS, REL ∗ =ΠPS, RL

L ∗ , i.e. each party gets 50% of thechain's profits. For values of β2 satisfying β2bβ2, the record labelgets more than 50% of the supply chain profit. Suppose f(β2) is a con-vex increasing function denoting the amount of investment in deter-rent and preventive piracy controls needed to increase piracy riskcost (i.e. increase to β2). If β2bβ2 then, Fig. 4a shows that under thelinear piracy cost, the label keeps a large share of the supply chainprofit, which Fig. 3a indicates is increasing quickly. Therefore, the re-cord label has a strong incentive in investing to combat piracy. As β2

increases, Fig. 3a shows that its effect on total supply chain profits de-creases, demand becomes more sensitive to price, and Fig. 4a showsthat the retailer's share of supply chain profits increases. This reducesthe record's label incentive to invest in combating piracy. When β2

becomes very large, the retailer's share of the supply chain profits ap-proaches two thirds leaving the record label with one third of thechain's profit and much lower incentive to combat piracy relative tothe retailer. Under the fixed piracy cost, the profit distribution be-tween the retailer and record label is mostly constant with abouttwo thirds of the profit kept by the retailer.

Finding 2. In the fixed piracy risk cost case, supply chain profitdecreases in μ0, the number of songs where the consumer's marginalvaluation becomes zero.

In the case of fixed piracy cost, μ0 has a significant impact on theprofits of the retailer, record label, and supply chain. As shown inFig. 5, the profits of both the record label and retailer under the persong contract decrease as μ0 increases, which is counter-intuitive.

(a) Linear piracy risk cost (

ββ

π π

π π

Fig. 4. Profit distribution vs. piracy cost for the per song contra

According to this result, an album with 4 popular songs will resultin less profits for the record label and retailer than an album with 2popular songs. This is due to the fact that consumers in this casewill pirate all μ0 songs when they pirate, thus large μ0 gives con-sumers high utility and their fixed piracy risk cost makes the netgain from pirating larger than from purchasing and the supply chainmakes less profit.

If everything is held constant except for μ0 and β2, then settingΠFF, TC

F ∗ equal to zero gives the curve of zero supply chain profitsunder the fixed fee full transfer contract in Fig. 6. This figure showsthat as β2 increases, more consumers buy rather than pirate, thusthe total chain's profit increases. On the other hand, since consumerspirate all μ0 songs when they pirate, the profitable region shrinks as μ0increases.

As β2 and M increase, Fig. 7a and b, respectively, shows that thefixed fee full transfer advantage increases most in both the linearand fixed piracy cost cases. It is interesting to note from Fig. 7a thatmost of the benefit from increasing β2 (i.e. combating piracy) occursover a short range of its values and that for high values of β2 thetype of consumer piracy cost becomes less important. Fig. 7b showsthat selecting the right contract is more important when the marketsize is large and consumers have linear piracy risk cost.

As cr and cl increase, Fig. 8a and b, respectively, shows that thefixed fee advantage decreases in both the linear and fixed piracycost cases. The royalty paid to artists is the major component of cl,and therefore it is likely that the record label's marginal cost wouldn'tchange drastically in the future. On the other hand, major compo-nents of cr such as the bandwidth cost can be reduced gradually as

b) Fixed piracy risk cost

β

π π

π π

ct (cr=0.15, cl=0.25, α1, α2=0, β1=1, μ0=10, M=10).

μ

Fig. 5. Profits vs. μ0 under fixed piracy risk cost and per song contract (cr=0.15,cl=0.25, α1, α2=0, β1=1, β2=3, M=10).

β 2

μ0

Fig. 6. Profitable values of β2 and μ0 under fixed piracy risk cost and fixed fee full trans-fer contract (cr=0.15, cl=0.25, α1, α2=0, β1=1, M=10).


technology advances. The fixed fee full transfer contract is significantlybetter than the per song contract as the retailer's marginal costsdecrease. An interesting finding is the shape of fixed fee advantage vs.cr in the fixed fee partial transfer case. As shown in Fig. 8, the fixed feeadvantage becomes positive and increasing for a range of cr and then

Full Transfer / Linear

Fixed Fee Advantage Fixe

Full Transfer / Fixed

PartialTransfer / Fixed

0 2 4 6 8 10β0.00

0.05

0.10

0.15

0.20

Partial Transfer / Linear

a

Fig. 7. Fixed fee advantage vs. β2 and M (cr=0

0.0 0.2 0.4 0.6 0.8 1.0Cr0.00

0.05

0.10

0.15

0.20


Full Transfer / FixedPartial Transfer / Linear


aFixed Fee Advantage Fixe

Fig. 8. Fixed fee advantage vs. cr and cl (β1=

decreases. We suspect that this is due to the unique characteristics offixed fee partial transfer contract as well as the non-linear demand. Un-like full transfer, the online retailer in the partial transfer contract onlytakes cr into account in her pricing decision. Therefore, at low valuesof cr, the retailer sets the price at a low value to maximize her profit,and large number of songs is sold. The royalty cost paid by the recordlabel is large enough to wipe out the record label's profit and thereforethere is no feasible FP contract for low values of cr. As cr increases, theretailer raises the price causing a sales decline large enough to reducethe royalty cost which makes the FP contract feasible. As cr increasesfurther, the fixed fee advantage starts decreasing due to decline in theretailer's profit. Fig. 8b also shows that the FF advantage diminishesquickly as cl increases. When cl is large, the retailer, who is responsiblefor cl in this contract, has to charge high price and piracy becomes prev-alent, which erodes the contract's advantage.

6. Discussion and conclusion

We developed a model for analyzing the impacts of piracy and sup-ply chain contracts on the performance of supply chains for one type ofdigital experience goods—music. In ourmodel, the product is transmit-ted digitally through a pure online channel. The consumer's risk cost ofpiracy is divided into two cases: 1) linear risk cost and 2) fixed risk cost,based on whether the risk cost a consumer attaches to piracy dependson the amount of content pirated or not.We also examine two differentcontract types that record labels and online retailers may enter into, afixed fee contract and a per song contract.

From the perspective of a manager, understanding consumers' riskcostwith respect tomusic piracy is critical since it hasmany implicationsfor pricing and piracy control strategies. For example, consistent withthe finding in [21], we show that the optimal price in the presence of pi-racy is always lower than or equal to the price assuming no piracy. Thissuggests that it is optimal for record labels and online retailers to priceproducts with full consideration of piracy. In addition, we demonstrate


Full Transfer / Fixed

Partial Transfer / LinearPartialTransfer / Fixed

0 2 4 6 8 10M0.00

0.02

0.04

0.06

0.08

0.10d Fee Advantage

b

.35, cl=0.15, α1, α2=0, β1=1, μ0=10).


Full Transfer / FixedPartial Transfer / Linear


0.0 0.2 0.4 0.6 0.8 1.0Cl0.00

0.05

0.10

0.15

0.20

bd Fee Advantage

1, β2=3, μ0=10, M=10, α1, α2=0).


that themagnitude of supply chain profit loss is related to the type of pi-racy risk cost. Assuming that consumers' propensity toward piracy iscurrently low, changing consumers' perception of piracy risk cost to-ward the linear case (e.g. charging a penalty based on the amount ofsongs pirated) can provide more profits to the chain. Also, retailersshould pursue different strategies depending on the popularity of art-ists/songs. When the fixed piracy risk cost is dominant, popular songsand/or artists suffer more from piracy. Hence, different pricing policiesthrough subscription, quantity discount, and bundling can be an effec-tive strategy for popular artists since they encourage legitimate saleswhile discouraging piracy.

We also find that increasing consumers' piracy risk cost through pre-ventive and deterrent controls does not equally benefit both record labelsand retailers under the per song contract. As consumers' piracy risk costincreases through piracy controls, the record label's share of supplychain profit decreases while the retailer's share increases. Interestingly,most evidence suggest that the record labels have led the effort in com-bating digital piracy [32,44], which may be due to the fact that they be-lieve the consumers' risk cost is currently very low and they benefit themost from increasing it. However, record labels should adjust their strat-egies as the piracy risk cost changes. If consumers' piracy risk cost is be-yond certain threshold, it will be better for the record label not to makean investment in piracy control and leave it up to the retailer to do so.

We show that the fixed fee full transfer contract dominates partialtransfer and per song contracts suggesting a need for new licensingmodels for digitalmusic sales. This dominance increaseswhen the piracyrisk cost and the market size for online music increase, and when mar-ginal costs decrease. Unlike other industries in the digital goods business,such as movie rental chains, which engaged in improving market condi-tions through contractual innovation (e.g. revenue-sharing [5,24]), themusic industry's response has been limited. Optimal supply chain perfor-mance can be achieved if firms coordinate by contracting using fixed feepayments. The per song contract is currently themost common contracttype in the music industry, but we demonstrate the superiority of fixedfee full transfer contract relative to the per song contract.

The proposed model has several limitations. First, the model focuseson the relationship between the record label and online retailer, anddoes not consider other important players in the chain such as artistsand government. Second, while our model considers heterogeneousconsumer valuations for songs, we assume that the valuation diminishesat the same rate. Third, our model does not consider different pricingstrategies such as subscription pricing, quantity discounts, and non-linear pricing. Lastly, while we propose that the fixed fee full transferwill fully coordinate the supply chain, our model does not considerthe exact lump sum paid by the record label. Other factors, such astheir relative bargaining power in the market, will determine FF/FP.

The above limitations guide us to several areas for future research. Inour model, two different types of consumer risk costs are assumedbased on the amount of content pirated. Therefore, it would be interest-ing to empirically explore how consumers actually evaluate the risk costof piracy. Also, simulation techniques such as an agent-based modeling(ABM) can be promising to relax some of the limiting assumptions thatwementioned. The use of ABMmay enable us to analyze agents' (i.e. re-tailer, record label, and consumers) behavior, motives, and interactionsand to examine their consequences in terms of aggregate systembehav-ior. It would also help us to incorporate various coordination strategiessuch as different pricing schemes and approaches to combat piracy.

Appendix A

Proof of Proposition 1. Consumer i's net gain from purchasing μsongs is

gi ¼ yi μκ−μp; if μbμ0

yi μκ0−μ0p; if μ≥μ0

:

�

For μbμ0,d2gidμ2 ¼ κ−1ð Þκμκ−2yi≤0. Therefore, the optimal quantity

of songs to purchase is given by the solution to the first order condi-tion which gives (given the assumption that the upper limit is μ0)

μ�i ¼

κyip

� � 11−κ

:

Proof of Proposition 2. Solving μ0 ¼ κyip

� 11−κ gives yi ¼ pμ1−κ

0κ . One of

the following two cases will occur.

1. If β1 >pμ1−κ

0κ then κ iyi

p

� 11−κð Þ

> μ0 for some consumers who will

maximize their utility by purchasing μ0 songs. The optimal averageexpected number of songs a consumer buys is:

μ� ¼ ∫pμ1−κ

0κ

01β1

dx

!∫

pμ1−κ0κ

0

yκp

� 11−κ

β1dyþ μ0 ∫β1

pμ1−κ0κ

1β1

dx

!

which gives

μ� ¼1−κð Þ κ

p

� 11−κ pμ1−κ

0κ

� 11−κþ2

β21 2−κð Þ − pμ2−κ

0

β1κþ μ0:

If β1≤pμ1−κ

0κ then κ iyi

p

� 11−κð Þ

≤μ0 for all consumers and no consumer

will maximize her utility by purchasing μ0 songs or more. The optimalaverage expected number of songs a consumer buys is:

μ� ¼ ∫β10

yκp

� 11−κ

β1dy ¼

1−κð Þ β1κp

� 11−κ

2−κ:

Proof of Proposition 3. Centralized chain

1. No piracy: Substituting the first part of μ∗ into ΠCCN and taking the

first derivative gives:

dΠNCC

dp¼ −Mλ2 p−2ctð Þ

16p3:

The necessary condition for optimality dΠNCC

dp ¼ 0 gives p1=2ct. Also,

d2ΠNCC

dp2¼ Mλ2 p−3ctð Þ

8p4

1) For p≤3ct,d2ΠN

CCdp2 ≤0 andΠCC

N is concave and therefore p1=2ct isa local maximum on 0≤p≤3ct.

2) For p>3ct,d2ΠN

CCdp2 > 0 and dΠN

CCdp b0, thus ΠCC

N is convex decreasing.

From (1) and (2), p1=2ct is the unconstrained optimal if μp1≤μ0.

2. Linear piracy costSubstituting the first part of μ∗ and �GL into ΠCC

L and taking the firstderivative gives:

dΠLCC

dp¼ −Mλ2 ct p−2β2ð Þ þ pβ2ð Þ

16p3λ:

The necessary condition for optimality dΠLCC

dp ¼ 0 givesp1 ¼ 2ctβ2ctþβ2

. Thesecond derivative of ΠCC

L w.r.t p is

d2ΠLCC

dp2¼ Mλ2 ct p−3β2ð Þ þ pβ2ð Þ

8p4λ

1) For p≤ 3ctβ2ctþβ2

, d2ΠL

CCdp2 ≤0 andΠCC

L is concave and therefore p1 ¼ 2ctβ2ctþβ2

is a local maximum on 0≤p≤ 3ctβ2ctþβ2

.

2) For p > 3ctβ2ctþβ2

, d2ΠLCC

dp2 > 0 and dΠLCC

dp b0, thus ΠCCL is convex

decreasing.

From (1) and (2), p1 ¼ 2ctβ2ctþβ2

is the unconstrained optimal if μp1≤μ0.


3. Fixed piracy costSubstituting the first part of μ∗ and �GF into ΠCC

F and taking the firstderivative gives:

dΠFCC

dp¼ Mλ2

256p4 α2−β2ð Þ�ct 3λ2−32pβ2−2 α1 þ β1ð Þ 3λ−8p

ffiffiffiffiffiffiμ0

p� ��

þ2p −λ2 þ 8pβ2 þ 2 α1 þ β1ð Þ λ−2pffiffiffiffiffiffiμ0

p� �� :

The necessary condition for optimality dΠFCC

dp ¼ 0 gives two roots

p1 ¼ λ2−2β1λþ8ηct−ζ t8η and p2 ¼ λ2−2β1λþ8ηctþζ t

8η , let η ¼ 2β2−α1 þ β1ð Þ ffiffiffiffiffiffi

μ0p

.

1) When η>0, p2>p1.Mλ2

256 α2−β2ð Þ is negative, the second part of the first derivative can

be written as 8ηp−2 þ −2λ2 þ 4 α1 þ β1ð Þλ−32ctβ2þ�

16ct α1 þ β1ð Þ ffiffiffiffiffiffiμ0

p Þp−3 þ 3λ2ct−6λct α1 þ β1ð Þ�

p−4. Since

η>0, dΠFCC

dp increases and approaches zero as p goes to positive

infinity. This implies that ΠCCF decreases on (−∞,p1), increases

on (p1,p2), and decreases on (p2,+∞). Therefore, p2 is the globaloptimal.

2) When ηb0, p1>p2.Mλ2

256 α2−β2ð Þ is negative, the second part of the first derivative can

be written as 8ηp−2 þ −2λ2 þ 4 α1 þ β1ð Þλ−32ctβ2þ�

16ct α1 þ β1ð Þ ffiffiffiffiffiffiμ0

p Þp−3 þ 3λ2ct−6λct α1 þ β1ð Þ�

p−4. Since

ηb0, dΠFCC

dp decreases and approaches zero as p goes to positive

infinity. This implies that ΠCCF increases on (−∞,p2), decreases

on (p2,p1), and increases on (p1,+∞). According to Eq. (5),there is an upper limit of p, �p, in order to make the purchaseprobability non-negative, and ΠF

CC �pð Þ ¼ 0. Therefore, p2 is theglobal optimal.

Proof of Proposition 4. Per song contract

1. No piracySubstituting the first part of μ∗ into ΠPS, RE

N and taking the firstderivative gives:

dΠNPS;RE

dp¼ −Mλ2 p−2w−2crð Þ

16p3:

The necessary condition for optimality dΠNPS;REdp ¼ 0 gives p1=2(w+

cr). The second derivative of ΠPS, REN w.r.t p is

d2ΠNPS;RE

dp2¼ Mλ2 p−3w−3crð Þ

8p4

1) For p≤3(w+cr),d2ΠN

PS;RE

dp2 ≤0 and ΠPS, REN is concave and therefore

p1=2(w+cr) is a local maximum on 0≤p≤3(w+cr).

2) For p>3(w+cr),d2ΠN

PS;RE

dp2 > 0 anddΠN

PS;REdp b0, thus ΠPS, RE

N is convexdecreasing.From (1) and (2), p1=2(w+cr) is the unconstrained optimal.Substituting the first part of μ∗ and p∗ intoΠPS, RL

N and taking thefirst derivative w.r.t w gives (assuming that μ≤μ0):

dΠNPS;RL

dw¼ Mλ2 −wþ 2cl þ crð Þ

64 wþ crð Þ3 :

The necessary condition for optimality dΠNPS;RLdw ¼ 0 gives

w1=2cl+cr. The second derivative of ΠPS,RLN w.r.t w is

d2ΠNPS;RL

dw2 ¼ Mλ2 w−3cl−2crð Þ32 wþ crð Þ4

1) For w≤3cl+2cr,d2ΠN

PS;RL

dw2 ≤0 and ΠPS, RLN is concave and therefore

w1=2cl+cr is a local maximum on 0≤w≤3cl+2cr.

2) For w>3cl+2cr,d2ΠN

PS;RL

dw2 > 0 anddΠN

PS;RLdw b0, thus ΠPS, RL

N is convexdecreasing.From (1) and (2), w1=2cl+cr is the unconstrained optimal.

2. Linear piracy costSubstituting the first part of μ∗ and �GL into ΠPS, RE

L and taking thefirst derivative gives:

dΠLPS;RE

dp¼ Mλ2 pwþ cr p−2β2ð Þ þ p−2wð Þβ2ð Þ

16p3β2:

The necessary condition for optimality dΠLPS;REdp ¼ 0 gives

p1 ¼ 2β2 wþcrð Þwþcrþβ2

. The second derivative of ΠPS, REL w.r.t p is

d2ΠLPS;RE

dp2¼ Mλ2 pwþ cr p−3β2ð Þ þ p−3wð Þβ2ð Þ

8p4β2

1) For p≤ 3β2 wþcrð Þwþcrþβ2

,d2ΠL

PS;RE

dp2 ≤0 and ΠPS, REL is concave and therefore

p1 ¼ 2β2 wþcrð Þwþcrþβ2

is a local maximum on 0≤p≤ 3β2 wþcrð Þwþcrþβ2

.

2) For p > 3β2 wþcrð Þwþcrþβ2

,d2ΠL

PS;RE

dp2 > 0 anddΠL

PS;REdp b0, thus ΠPS, RE

L is convexdecreasing.From (1) and (2), p1 ¼ 3β2 wþcrð Þ

wþcrþβ2is the unconstrained optimal.

Substituting the first part of μ∗, �GL, and p∗ intoΠPS, RLL and taking

the first derivative gives assuming that μ≤μ0):

dΠLPS;RL

dw¼

Mλ2 w3 þ 3wc2r þ c3r þ w−2clð Þβ22 þ cr 3w2−β2

2

� � 64 wþ crð Þ3β2β2

:

The necessary condition for optimality dΠLPS;RLdw ¼ 0 gives

w1 ¼ β22φ − φ

3−cr. The second derivative of ΠPS, RLL w.r.t w is

d2ΠLPS;RL

dw2 ¼ Mλ2 w−3cl−2crð Þβ2

32 wþ crð Þ4β2

1) For w≤3cl+2cr,d2ΠL

PS;RE

dp2 ≤0 and ΠPS, RLL is concave. Also, w1b3cl

+2cr. Therefore w1 is a local maximum on 0≤w≤3cl+2cr.

2) For w>3cl+2cr,d2ΠL

PS;RL

dw2 > 0 anddΠL

PS;RLdw b0, thus ΠPS, RL

L is convexdecreasing.From (1) and (2), w1 is the unconstrained optimal.

3. Fixed piracy costSubstituting the first part of μ∗ and �GF into ΠPS, RE

F and taking thefirst derivative gives:

dΠFPS;RE

dp¼ Mλ2

256p4 α2−β2ð Þ8ηp2−2 8wηþ λ λ−2β1ð Þð Þpþ 3wλ λ−2β1ð Þ

þ 3λ λ−2β1ð Þ−16ηð Þcr

Þ:


The necessary condition for optimality dΠFPS;REdp ¼ 0 gives two roots

p1 ¼ λ2−2β1λþ8ηρ−12

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4 λ2−2λβ1þ8ηρð Þ2−96ηλρ λ−2β1ð Þ

p8η and

p2 ¼ λ2−2β1λþ8ηρþ12

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4 λ2−2λβ1þ8ηρð Þ2−96ηλρ λ−2β1ð Þ

p8η , let

η ¼ 2β2− α1 þ β1ð Þ ffiffiffiffiffiffiμ0

p.

1) When η>0, p2>p1.Mλ2

256 α2−β2ð Þ is negative, the second part of the derivative can be

written as 8ηp−2 þ −2λ2 þ 4α1λþ 4β1λ−32wβ2−�

32crβ2þ16w α1 þ β1ð Þ ffiffiffiffiffiffi

μ0p þ 16cr α1 þ β1ð Þ ffiffiffiffiffiffi

μ0p Þp−3 þ 3wλ2 þ 3crλ

2−�

6wα1λ−6wβ1λ−6cr α1 þ β1ð ÞλÞp−4. Since η>0, dΠFPS;REdp in-

creases and approaches zero as p goes to positive infinity. Thisimplies that ΠPS, RE

F decreases on (−∞,p1), increases on (p1,p2), and decreases on (p2,+∞). Therefore, p2 is the globaloptimal.

2) When ηb0, p1>p2.Mλ2

256 α2−β2ð Þ is negative, the second part of the derivative can be

written as 8ηp−2 þ −2λ2 þ 4α1λþ 4β1λ−32wβ2−�

32crβ2 þ16w α1 þ β1ð Þ ffiffiffiffiffiffi

μ0p þ 16cr α1 þ β1ð Þ ffiffiffiffiffiffi

μ0p Þp−3 þ 3wλ2þ

�3crλ2−

6wα1λ−6wβ1λ−6cr α1 þ β1ð ÞλÞp−4. Since ηb0, dΠFPS;REdp de-

creases and approaches zero as p goes to positive infinity. Thisimplies that ΠPS, RE

F increases on (−∞,p2), decreases on (p2,p1), and increases on (p1,+∞). According to Eq. (5), there isan upper limit of p, �p, in order to make the purchase probabilitynon-negative, and ΠF

PS;RE �pð Þ ¼ 0. Therefore, p2 is the global op-timal. Also, please note that, in the fixed piracy risk cost case,the closed form solution for w can't be obtained.

Proof of Proposition 5. Fixed fee full transfer contractThe optimal solutions under the fixed fee full transfer contract can

be derived by following similar arguments in previous proofs.

Proof of Proposition 6. Fixed fee partial transfer contractThe optimal solutions under the fixed fee partial transfer contract

can be derived by following similar arguments in previous proofs.

Proof of Corollary 1. In the non-piracy case, the probability of pur-chase, if the net gain is positive, is �GN ¼ 1 which is always greaterthan the linear piracy cost probability of purchase �GL and the fixed pi-racy cost probability of purchase �GF . Thus, the following condition issatisfied regardless of the contract type:

M pL�or F�−ct�

μ �GL or FbM pL�or F�−ct�

μ �GN:

Also, for any p, the following condition is satisfied as well.


μ �GNbM pN�−ct�

μ �GN:

The above two inequalities yield


μ �GL or FbM pL�or F�−ct�

μ �GNbM pN�−ct�

μ �GN:

Therefore, piracy will reduce the profit of the supply chain.

Proof of Corollary 2. In a fully coordinated supply chain, the optimalretail price (p∗) satisfies the following condition:

dΠCC

dp�¼ dM p−ctð ÞμCC

�Gdp�

¼ 0

d2ΠCC

dp�2¼ d2M p−ctð ÞμCC

�Gdp�2

b0:

And the profit of centralized supply chain is:

Π�CC ¼ M p�CC−ct

� �μ�CC

�G:

If the retailer and record label adopts the fixed fee full transfer con-tract, the optimal retail price (i.e., pFF∗ ) satisfies the following condition:

dΠFF;RE

dp�FF¼ dM p−ctð ÞμFF

�Gdp�FF

¼ 0

d2ΠCC

dp�2FF¼ d2M p−ctð ÞμFF

�Gdp�2FF

b0:

And, the total supply chain profit is:

Π�FF;TC ¼ M p�FF−ct

� �μ�FF�G:

Therefore, pCC∗ =pFF∗ , and ΠCC

∗ =ΠFF, TC∗ .

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Bm
ong-Keun Jeong is an Assistant Professor of Global BBA at SP Jain Center of Manage-ent. He received his Ph.D. degree from the University of North Carolina at Charlotte.
His research interests include digital piracy, information technology investment,emerging technology adoption, and data mining. His publications have appeared in In-ternational Journal of Electronic Commerce, Information & Management, Journal of Theo-retical and Applied Electronic Commerce Research, and Data & Knowledge Engineering.

Moutaz Khouja is a Professor in the Department of Business Information Systems andOperations Management at the University of North Carolina at Charlotte. He received aB.S. in Mechanical Engineering, an MBA from the University of Toledo, and a Ph.D. inOperations Management from Kent State University. His research interests are in theareas of inventory management, pricing, forecasting, and agent-based modeling. Hispublications have appeared in many leading journals, including Decision Sciences, IIETransactions, European Journal of Operational Research, International Journal of Produc-tion Research, Journal of Management Information Systems, and Omega.

Kexin Zhao is an Assistant Professor of Management Information Systems in the BelkCollege of Business at the University of North Carolina at Charlotte. She received herPh.D. degree from the University of Illinois at Urbana-Champaign. Her research inter-ests include economics of information systems, e-business standardization, and elec-tronic commerce. Her papers have been published in journals such as Journal ofManagement Information Systems, Decision Support Systems, International Journal ofElectronic Commerce, and Electronic Markets.

http://www.thembj.org/mbdb/lets-get-digital

http://www.thembj.org/mbdb/lets-get-digital

http://www.riaa.com/keystatistics.php

http://www.riaa.com/keystatistics.php

the impacts of piracy and supply chain contracts on digital music channel performance

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