The Japanese Economic Review Vol. 59, No. 4, December 2008

doi: 10.1111/j.1468-5876.2008.00424.x

OPTIMAL ENFORCEMENT AND ANTI-COPYING STRATEGIES TO COUNTER COPYRIGHT INFRINGEMENT*

D. ORIGINAL The S.Japanese Banerjee, ARTICLES Economic T. Chatterjee Review and A. Raychaudhuri: Optimal Enforcement And Anti-copying Strategies Blackwell Melbourne, Japanese JERE © 1352-4739 Journal XXX 2008 compilation The Economic Publishing Australia Authors Review ©Asia 2008 Japanese Economic Association

By DYUTI S. BANERJEE†, TANMOYEE BANERJEE (CHATTERJEE)‡ and AJITAVA RAYCHAUDHURI‡ †Monash University ‡Jadavpur University In this paper we study the mix of anti-copying investment strategies by an incumbent firm and the enforcement policies of a government that consists of monitoring and penalizing the copier to address the issue of commercial piracy. If monitoring is socially optimal then the subgame perfect equilibrium anti-copying investment does not guarantee the prevention of copying. If not monitoring is socially optimal then the subgame perfect equilibrium anti-copying investment may guarantee the prevention of copying. JEL Classification Numbers: K42, L11.

1.

Introduction

An interesting news item appearing in The Statesman, an English daily published in India, on 9 December 2004, read as follows. “Perhaps for the first time, film makers are getting an upper hand over pirates. Interestingly the film in question is 44 years old— Mughal-E-Azam.1 Video pirates are having a tough time making pirated CDs of the colour version of the classic.” The film is completely in a digital format and the digital standards are such that piracy will not be easy, says the project director. The story assumes significance because it suggests that producers have successfully taken antipiracy measures. This is unique because producers in developing countries generally depend on government enforcement rather than undertaking anti-copying investments to prevent piracy.2 In developing countries such as India, copyright infringement at the commercial level can take one of two forms.3 The copied product is either an imperfect or a perfect substitute of the original one. The first situation, the general assumption in the literature on piracy, * We acknowledge the comments by Rajat Acharyya, Teyu Chou and two anonymous referees. The usual disclaimer applies. 1

Mughal-E-Azam is a classic Indian blockbuster movie.

2

D. Malhotra mentions that technocrats in India are developing methodologies that can check copyright infringement. However, this is still at a nascent stage. See www2.accu.or.jp, vol. 31, no. 2. BBC (20 January 2003) reports that the music industry has been trying out different technologies to stop the unauthorized copying of CDs.

3

“Copyright infringement is the unauthorized use of copyrighted material in a manner that violates one of the copyright owner’s exclusive rights, such as the right to reproduce or perform the copyrighted work, or to make derivative works that build upon it. For electronic and audiovisual media, unauthorized reproduction and distribution is often referred to as piracy. This may occur through organized black market reproduction and distribution channels, sometimes with blatantly open commercial sale, or through purely private copying or downloading to avoid paying a purchase price. With digital technology, most modern piracy involves an exact and perfect copy of the original made from a hard copy or downloaded over the Internet.” Adopted from Wikipedia, the free encyclopedia. See http://en.wikipedia.org/wiki/ Copyright_infringement.

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implies that a consumer makes a choice regarding whether to buy the original or the copied product.4 In the second case identical copies of products like audio and visual CDs that include packaging and warranty are sold along with the legitimate ones in retail stores and at the same price to avoid detection. Therefore, consumers cannot distinguish the original from the copied product.5 The purpose of this paper is to focus on the mix of government enforcement policy and a producer’s anti-copying investment using a strategic entry deterrence framework to counter the second form of commercial copyright infringement.6 We consider a market where there is an incumbent firm, hereafter referred to as the monopolist, and a possible entrant, hereafter referred to as the fake producer, who commercially competes with the monopolist by selling identical copies of his product. The government is responsible for providing legal protection through its enforcement policies that consist of monitoring and penalizing the fake producer. The monopolist chooses an output and a level of technical protection in the form of an anti-copying investment. The higher the anti-copying investment, the lower is the probability of copying; and above a critical level of investment, copying is prevented with certainty. The monopolist may behave as a Stackelberg leader and choose the profit maximizing output and anti-copying investment, assuming that the fake producer copies his product and is competing with him. We call this the accommodating strategy. Alternatively, he may deter the fake producer’s entry either by choosing an entry deterring limit output, which we call the aggressive strategy or by choosing the critical level of investment that is sufficient to prevent copying with certainty, which we call the no copying strategy. The government’s social welfare maximizing monitoring rate endogenously determines the monopolist’s equilibrium output and anti-copying investment strategy. We show that monitoring may be the socially optimal outcome. In this case, the accommodating strategy is the subgame perfect equilibrium and the equilibrium anti-copying investment does not prevent copying with certainty. If “not monitoring” is more socially optimal than either the no copying or the accommodating strategy is the subgame perfect equilibrium. In the former case copying is prevented with certainty, which does not happen in the latter.

4

See Banerjee (2003, 2006a), Besen and Kirby (1989) and Takeyama (1994) for explanations of the assumption that the copied product is an imperfect substitute of the legitimate one.

5

Recording Industry Association of America (RIAA) in its annual record of “commercial piracy” (non-Internet) statistics and enforcement efforts released on July 13, 2005 mentions, “Because of the high quality and seeming authenticity of counterfeit CDs, this genre of illicit product is increasingly finding its way to legal music retail outlets, often at prices that approach or equal the retail price of legitimate product”. See http://www.hispanicprwire.com/news. A report published in Sify on November 11, 2005 mentions that in India fake producers have copied the latest hologram on the HP cartridge pack, making the fake cartridge almost identical to the original. See http://sify.com/printer_friendly.php?id=13940748&ctid=2&lid=1. The same report also highlights the copying of Daimler Chrysler spare parts where the copied product had similar number coding as found in the original. A report published on http://english.people.com.cn/200204/16/eng20020416_94113.shtml, on 16 April 2002 reports the destruction of pirated international brand name products like Rolex watches, Nike and Adidas sportswear and Toyota and Honda automotive parts, by Chinese customs officers in east China. These evidences suggest the existence of commercial piracy where the fake products are identical to the originals.

6

Indian Music Industry (IMI) on its web site www.indianmi.org lists three or four shops in each major city of India that have been raided and their owners arrested for the sale of pirated music CDs. This highlights the importance that IMI attaches to commercial copyright infringement and provides a justification for considering a locally oligopolistic market structure in our paper.

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D. S. Banerjee, T. Chatterjee and A. Raychaudhuri: Optimal Enforcement and Anti-copying Strategies

These results imply that the monopolist always makes a positive anti-copying investment in equilibrium. Our findings suggest that in countries such as India and China where enforcement policies are rather weak, it is possible to prevent copyright infringement through the adoption of anti-copying investment by producers. The Mughal-E-Azam story, along with the following evidence, supports our results. A report published on www.rediff.com on 21 May 2003 read, “In a move to control music piracy that’s resulted in a Rs 18 billion loss to the Indian music industry over the last three years, Virgin Records India and Mukta Arts Ltd have introduced copy-control compact discs for the music of . . . film Joggers’ Park. . . . A copy-control CD means that the content on the CD cannot be “copied” onto another CD or be digitised.” The government of India chose Activated Content Corporation’s products and services as one of the options to combat piracy. The latter is India’s entertainment industry’s emerging technology and application services partner of choice to protect, manage and enhance digital content.7 The Indian entertainment industry accounts for approximately $US2.1bn of the country’s total economy. Mr Fritz E Attaway, executive vice president and Washington general counsel for the Motion Picture Association of America, in his speech to the USA–China Trade: Preparations for the Joint Commission on Commerce and Trade, Subcommittee on Commerce, Trade, and Consumer Protection, mentions that “China has recently unveiled a new DVD format. It is important that this format contain copy protection to insulate prerecorded content on DVDs from widespread copying.”8 In a recent paper Park and Scotchmer (2005) compare the pricing of contents under legal protection to that with technical protection, both of which prevent copying with certainty. They show that the price under technical protection is lower than that under legal protection because in the former case the users’ cost of circumvention acts as the upper bound on the price. The prices resulting from technical protection depend on whether or not the protection standards are independent or are shared between the producers—and on the sharing rule. Unlike Park and Scotchmer (2005), in our paper, legal protection is represented by the monitoring rate which is the probability of detecting the fake producer. Therefore, legal protection cannot guarantee the prevention of copyright infringement with certainty.9 Even technical protection, which is captured by the anti-copying investment, below a critical level cannot prevent copying with certainty.10 Furthermore, we endogenize the legal protection, which in turn determines the subgame perfect equilibrium level of technical protection an issue not addressed in Park and Scotchmer (2005). The literature on copyright infringement by end-users and that at the commercial level generally focuses on legal protection through enforcement policies rather than the mix of

7

See http://findarticles.com/p/articles/mi_qn4175/is_20040315/ai_n12931435, 15 May 2004.

8

See http://energycommerce.house.gov/108/hearings/03312004Hearing1239/Attaway 1915.htm, 31 March 2004.

9

As Becker and Stigler (1974) mention, detection with certainty is difficult because malfeasant agents try to circumvent detection.

10

Banerjee (2003) treats technical protection as an anti-copying investment, which is a fixed cost incurred by the monopolist that prevents copying with certainty.

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technical and legal protection. In the context of commercial software piracy, Banerjee (2003) shows that if monitoring is the socially optimal outcome then piracy is prevented and the monopoly outcome is restored. Banerjee (2006a), using a strategic entry deterrence framework, shows that lobbying by the monopolist is a necessary but not a sufficient condition that may result in monitoring as the socially optimal outcome, in which case commercial piracy may be prevented with certainty. The restoration of the monopoly results is only a special case. These findings differ from those in our paper where the socially optimal monitoring rate does not guarantee the prevention of copyright infringement with certainty. Copying is prevented with certainty only if not monitoring is socially optimal and the no copying strategy is the subgame perfect equilibrium. In this case, although the monopoly price is restored the monopolist’s profit is less than that in the monopoly case. This paper is arranged as follows. In Section 2 we present the model and in Section 3 we analyse the equilibrium no copying, accommodating and aggressive strategies. Section 4 sets out the social welfare analysis and in Section 5 we provide the concluding remarks.

2.

The model

We begin our analysis by describing the monopoly situation. For simplicity we assume a linear demand function of the form, p(q) = 1 – q, where q and p denote the quantity and the price. We assume an installed monopolist. This allows us to avoid the fixed cost of developing the product, and the marginal cost of production is assumed to be zero. The monopoly results are p*m = 1/ 2, q*m = 1/ 2 and π *m = 1/ 4. Let us introduce the fake producer in our model, who counterfeits and sells unauthorized identical reproductions of the monopolist’s product. The government’s role is to monitor the illegal activities of the fake producer. If detected, the fake producer pays a penalty at an institutionally given level G. The game played between the government, the monopolist and the fake producer is specified in an extensive form as follows. Stage 1: The government chooses a monitoring rate, α. Stage 2: The monopolist chooses a quantity qm and an anti-copying investment x. Stage 3: The fake producer makes his entry decision and chooses a quantity qf .12 Let us now discuss the behaviour of each of the agents in our model. In many countries such as India, identical pirated copies of products like audio and video CDs that include

11

End-user piracy refers to the situation where users make copies of legitimate software for personal consumption. Cheng et al. (1997) and Noyelle (1990) mention that the high price of software products is the dominant reason for piracy. Chen and Png (1999) show that pricing rather than monitoring is a better strategy for a firm to deal with end-user piracy. Harbaugh and Khemka (2000) compare targeted enforcement to extensive enforcement and show that the latter is better than the former. Oz and Thisse (1999) show that in the presence of network externalities non-protection against piracy is an equilibrium. Takeyama (1994), Conner and Rumelt (1991) and Nascimento and Vanhonacker (1988) also discuss the role of network externalities on the marketing of software. Commercial software piracy refers to a situation where a firm illegally reproduces and sells copies of legitimate software, thereby, competing with the original producer. Banerjee (2003, 2006a), explores the impact of government action on commercial software piracy where the government is solely responsible for identifying and punishing software pirates for selling inferior substitutes of licensed software.

12

The pricing game is discussed in Appendix B.

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D. S. Banerjee, T. Chatterjee and A. Raychaudhuri: Optimal Enforcement and Anti-copying Strategies

packaging and warranty are sold through small retail channels. To circumvent detection and given that the products are identical, the fake products are sold at the same price as the original ones. The consumer cannot distinguish the fake product from the legitimate. Only specially trained experts can distinguish the original product from the fake. Such experts may be hired by the government to monitor illegal activities. So in our model we assume that the government is responsible for monitoring the illegal activities of a fake producer. Let α denote the monitoring rate, which is the probability of detecting the illegal activities of the fake producer, and G be the institutionally given penalty that the fake producer has to pay if his illegal activities are unearthed.13 It may be partly redistributed to the monopolist to cover for the damages that he incurs due to the sell of fake products. Let c(α) be the monitoring cost with the properties, c′(α) > 0 and c′′(α) > 0. The monopolist’s strategy consists of choosing a quantity qm and a level of investment, x, that may prevent copying. Let h (x) be the probability that the fake producer can copy when the anti-copying investment is x. We assume that copying is completely prevented if x ≥ x, i.e. h(x) = 0 for x ≥ x. We further assume that h′(x) < 0 and 0 ≤ h(x) < 1 for 0 ≤ x < x. h′(x) = 0, for x ≥ x. For x < x we get the following events and the probability of their occurrences. Probability that the fake producer can copy and is detected = αh(x), Probability that the fake producer can copy and is not detected = (1 − α)h(x) and Probability that the fake producer cannot copy = (1 − h(x)).

(1)

The fake producer’s output is zero if he cannot copy or if he copies and is detected when trying to sell his product. This occurs with probability, (1 – h(x)) + αh(x). Table 1 summarizes the market demand, the monopolist’s and the fake producer’s profits for each of the events described in Equation (1). Table 1 Events, demand and profits Events

Market demand

Monopolist’s profit

Fake producer’s profit

Fake producer copies and is detected. Fake producer cannot copy.

p = 1 – qm because qf = 0. p = 1 – qm because qf = 0. p = 1 – qm – qf

qm − qm2 − x

–G

qm − qm2 − x

0

Fake producer copies and is not detected.

2 m

qm − q − qm q f − x

q f − q 2f − qm q f

Using Table 1 and the probability of the occurrences of the different events described in Equation (1) we get the monopolist’s profit function πm as follows,

π m (qm , q f , x, α ) = (1 − α )h( x)(qm − qm2 − qm q f − x) + (1 − (1 − α )h( x))(qm − qm2 − x)

13

(2)

It is possible that the government monitors but cannot detect the fake producer. This means that the government knows that fake products are sold in the market but cannot detect the seller. One explanation can be that the fake producer may get some prior information of a possible police raid and may decide to remove the fake products from the store.

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The monopolist chooses from the following three strategies. He may decide to deter the fake producer’s entry by choosing, x = x. We call this the no copying strategy (nc-strategy). Alternatively, he may choose to deter the fake producer’s entry through a limit output strategy, which we call the aggressive strategy (ag-strategy). The monopolist may choose to behave as a Stackelberg leader and choose the profit maximizing output and anticopying investment assuming that the fake producer copies his product and is competing with him. We call this the accommodating strategy (ac-strategy). Let π mi and π fi denote the monopolist’s and the fake producer’s profit for the monopolist’s strategy, i ∈ {nc, ac, ag}. We assume that the fake producer enters only if he makes positive profit. The fake producer’s expected profit if he copies the monopolist’s product, which occurs with probability h(x), is

π f (qm , q f , x, α ) = h( x)((1 − α )(q f − q2f − qm q f ) − αG).

3.

(3)

Equilibrium no copying, aggressive and accommodating strategies

In this section we discuss the equilibrium nc-, ag- and ac-strategies. We solve for the equilibrium accommodating and the aggressive strategies by using the method of backward induction. The fake producer’s reaction function is, qf = (1 − qm)/2. 3.1

No copying strategy (NC)

In this case the monopolist chooses x = x which, by assumption, is sufficient to prevent copying. The equilibrium results are pmnc* = 1/ 2, qmnc* = 1/ 2 and π mnc* = 1/ 4 − x . For the rest of the analysis we assume, π mnc* = 1/ 4 − x  > 0, that is, x < 1/ 4. 3.2

Aggressive strategy (AG)

In this case the monopolist strategically deters the fake producer’s entry by choosing a limit output such that it is not profitable for the fake producer to enter the market given that he can copy the monopolist’s product. Substituting the fake producer’s reaction function in his expected profit function yields πf (qm, qf, x, α) = h(x)[(1 − α)(1 − qm)/2]2 − αG ). The fake producer’s entry is deterred if πf (qm, qf, x, α) ≤ 0. So the entry deterrence condition is (1 − (2√(αG)/(1 − α))) ≤ qm. Suppose the entry deterrence condition holds with strict inequality. Then the monopolist can reduce the quantity and increase his profit without disturbing the entry deterrence condition as long as the output is less than the monopoly level. Since the fake producer’s entry is deterred if his profit is zero, the entry deterrence condition holds with strict equality. At α = αmax, where αmaxG/(1 − αmax) = 1/16, qm = 1/2. For monitoring rates above αmax, the monopolist will continue producing qm = 1/2 and not reduce his output any more because that will reduce his profit. Therefore, for the rest of the paper we will consider monitoring rates in the range of α ∈ [0, αmax]. Since the fake producer’s entry is deterred, the issue of detecting him does not arise. Also the issue of the fake producer copying the monopolist’s product does not arise because it is only the monopolist’s product that exists in the market. So the market demand is p = 1 – qm. The monopolist’s profit if he does not make the anti-copying investment is π m = qm − qm2 . If he makes the anti-copying investment then his profit is – 524 – © 2008 The Authors Journal compilation © 2008 Japanese Economic Association

D. S. Banerjee, T. Chatterjee and A. Raychaudhuri: Optimal Enforcement and Anti-copying Strategies

π m = qm − qm2 − x . Clearly, not making the anti-copying investment is the dominant strategy. The results for the equilibrium ag-strategy are summarized in Proposition 1 and the proof is given in Appendix A. Proposition 1. The equilibrium entry deterring limit output and the anti-copying investment are (qmag*, x ag* ) = (1 − (2√αG /(1 − α )), 0), for 0 ≤ α ≤ αmax where, αmaxG/(1 − αmax) = 1/16 · qmag* is non-increasing in α, for 0 ≤ α ≤ αmax, and G. αmax is decreasing in G. The monopolist’s profit for the equilibrium aggressive strategy is

π mag* = qmag* − qmag*2.

(4)

At α = 0, qmag* = 1 and π mag*(α ) = 0. This means that in the absence of monitoring the market becomes contestable in the sense that the equilibrium entry deterring limit output equals the perfectly competitive outcome, which is 1, since the marginal cost is assumed to be zero. At α = αmax, the monopolist’s equilibrium profit is the same as that in the monopoly case, that is, π mag*(α max ) = 1/ 4 . 3.3

Accommodating strategy (AC)

In this case the monopolist behaves like a leader in a Stackelberg game and chooses the profit maximizing quantity and anti-copying investment assuming that the fake producer copies his product. Let qmac*, x ac* and qac f * be the monopolist’s output and anti-copying investment and the fake producer’s output for the equilibrium ac-strategy and the results are summarized in Proposition 2. The proof is given in Appendix A. Proposition 2. (i) The fake producer cannot enter if α ∈ [αmax, 1]. (ii) The monopolist’s equilibrium output and anti-copying investment and the fake producer’s equilibrium output are (qmac*, x ac*) = (1/ 2, x ac*) and qac f * = 1/ 4 for 0 ≤ α ≤ αmax. xac∗ is the solution to h′(x) = −(8/(1 − α)) and (αmaxG/(1 − αmax)) = 1/16. At α = αmax, (qmac*, x ac*) = (1/ 2, 0) and qac f * = 0. (iii) The equilibrium anti-copying investment xac∗ is strictly less than x and decreasing in α for 0 ≤ α ≤ αmax. From Proposition 2 we see that in case of the ac-strategy the monopolist retains its market share as in the monopoly case, that is qmac* = 1/ 2 and, therefore, is unaffected by the monitoring rate. The equilibrium anti-copying investment level xac* cannot prevent copying with certainty because xac* < x and is decreasing in the monitoring rate. This means that as the monitoring rate increases, the monopolist free rides and decreases the equilibrium level of anti-copying investment. Since xac* satisfies h′(x) = −(8/(1 − α)), an increase in the monitoring rate increases the absolute value of h′(x). This means that an increase in the monitoring rate decreases the equilibrium level of anti-copying investment but at the same time decreases the probability of copying. This is because dh(x ac*)/dα = h′(x ac*)x ac*′(α) > 0 since h′(x ac*) < 0 and x ac*′(α) < 0. At α = αmax the issue of detecting the fake producer and whether he can copy or not does not arise because he cannot enter the market. Therefore, at α = αmax, there is no anticopying investment in equilibrium and the monopolist’s profit is π mac*(α max ) = qmac* − qmac*2 – 525 – © 2008 The Authors Journal compilation © 2008 Japanese Economic Association

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which on substituting qmac* = 1/ 2 yields π mac*(α max ) = 1/ 4. So at α = αmax the monopoly results hold. The monopolist’s equilibrium profit is ⎧ 1 (1 − α )h( x ac*) − x ac*, ⎪⎪ − 8 π mac*(α ) = ⎨ 4 ⎪ 1, ⎪⎩ 4

3.4

if 0 ≤ α < α max ,

(5) at α = α max .

Comparative static analysis

In this section we provide a comparative static analysis of the monopolist’s equilibrium profits for the ag- and ac-strategies with respect to the monitoring rate and penalty. This allows us to compare the properties of the equilibrium profits with respect to the monitoring rate, which is later used to determine the monopolist’s subgame perfect equilibrium strategy for the socially optimal monitoring rate. The comparative static analysis with respect to the penalty allows us to discuss the effects of a penalty on the socially optimal monitoring rate. The results are summarized in Proposition 3 and the proof is given in Appendix A. Proposition 3. (i) For a given positive penalty G, there exists a monitoring rate £, £ ∈ (0, αmax), such that π mag*(£ ) = π mac*(£ ), π mac*(α ) > π mag*(α ) for α ∈ [0, £) and π mac*(α ) < π mag*(α ) for α ∈ (£, α max). (ii) For a given positive monitoring rate α, there exists a penalty G, G ∈ (0, Gmax), such that π mag*(G ) < π mag*(G ), π mac*(G ) > π mag*(G ) for G ∈ [0, G) and π mac*(G ) < π mag*(G ) for G ∈ (G, Gmax), where Gmax satisfies αGmax /(1 − α) = 1/16. (iii) £ is decreasing in G. Proposition 3 (i) implies that π mag*(α ) is steeper than π mac*(α ) in the interval, α ∈ [0, αmax) and the single crossing property is satisfied. Let α be the monitoring rate at which π mag*(α ) = π mnc*. A diagrammatic representation of Proposition 3 (i) is provided in Figures 1 and 2 which consider the cases, π mac*(α = 0) > π mnc* and π mac*(α = 0) < π mnc* .

Figure 1. Comparative static analysis of monopolist’s profit and monitoring rate (π mac*(α = 0) < π mnc*). – 526 – © 2008 The Authors Journal compilation © 2008 Japanese Economic Association

D. S. Banerjee, T. Chatterjee and A. Raychaudhuri: Optimal Enforcement and Anti-copying Strategies

Figure 2. Comparative static analysis of monopolist’s profit and monitoring rate (π mac*(α = 0) < π mnc*).

Figure 3. Comparative static analysis of monopolist’s profit and penalty.

Proposition 3 (ii) shows that π mac*(G ) is independent of G in the interval, G ∈ [0, Gmax). The fake producer cannot enter if G ≥ Gmax and the monopoly results are restored. Therefore, we only consider a penalty in the interval G ∈ [0, Gmax] for any given positive monitoring rate. In this interval π mag*(G ) is increasing in G with π mag*(G = 0) = 0 and π mag*(Gmax ) = π *m . So the single crossing property is satisfied in the interval, G ∈ (0, Gmax) and this is diagrammatically represented in Figure 3. Proposition 3 (iii) summarizes the effects of a change in the penalty on the properties of the profit functions with respect to the monitoring rate. From Proposition 1 we know that an increase in the penalty decreases αmax. Therefore, the slope of π mag* with respect to α increases due to an increase in G. π mac* is independent of the penalty in the interval α ∈ [0, αmax) and, therefore, its slope with respect to the monitoring rate is unaffected by changes in G. Hence, an increase in G, causes π mac* and π mag* to intersect at a lower monitoring rate. This is illustrated in Figure 4. – 527 – © 2008 The Authors Journal compilation © 2008 Japanese Economic Association

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Figure 4. Effects of a change in penalty on the comparative static analysis of the monopolist’s profit and the monitoring rate.

4.

Social welfare analysis

In this section we perform the welfare analysis and determine the socially optimal monitoring rate, which in turn determines the monopolist’s subgame perfect equilibrium strategy. Social welfare (SW ) is defined as the surplus of every agent in the model, that is SW i (α ) = CS i (α ) + π mi*(α ) + π if*(α ) + αG − c(α ), i ∈ {nc, ag, ac}.

(6)

αG – c(α) is the government’s expected revenue and CS i(α), i ∈ {nc, ag, ac} is the consumer surplus. We begin by determining the consumer surplus for the monopolist’s different strategies. Since the market demand curve is linear with unit slope, the consumer surplus is ((1 − p)q)/2 = q2/2, where p and q are the market price and quantity. The consumer surplus for the equilibrium nc- and ag-strategies where there are no fake products in the market are CS nc = 1/8 and CS ag = 1/2[1 − √αG/(1 − α)]2. The social welfare functions in these two cases are SW nc =

3 − x − c(α ), 8

and SW ag (α ) =

(7) 2qmag*

− 2

qmag*2

− c(α ).

In case of the equilibrium ac strategy, in the interval α ∈ [0, αmax), the fake product exists in the market with probability (1 – α)h(x) in which case the consumer surplus is 9/32 and the monopolist’s and the fake producer’s profits are π mac* = 1/8 − x ac* and π ac f * = 1/16 . With probability αh(x) the fake producer copies and is detected. So there is no fake product in the market. In this case, the consumer surplus and the monopolist’s and fake producer’s profits are CS = 1/8, π mac* = 1/ 4 − x ac* and π ac f * = −αG, respectively. The fake producer cannot copy the product with probability (1 − h(xac*)) in which case the consumer surplus, the monopolist’s and the fake producer’s profits are CS = 1/8, π mac* = 1/ 4 − x ac* and π ac f * = 0 . So the ex ante expected social welfare for the equilibrium ac-strategy is – 528 – © 2008 The Authors Journal compilation © 2008 Japanese Economic Association

D. S. Banerjee, T. Chatterjee and A. Raychaudhuri: Optimal Enforcement and Anti-copying Strategies

⎛1 ⎞ 1 9 SW ac (α ) = (1 − α )h( x ac*) ⎜ − x ac* + + − c(α )⎟ + 16 32 ⎝8 ⎠ ⎛1 ⎞ 1 αh( x ac*) ⎜ − x ac* − G + + G − c(α )⎟ + 8 ⎝4 ⎠

(8)

⎛1 ⎞ 3 3h( x ac*)(1 − α ) 1 (1 − h( x ac*) ⎜ − x ac* + − c(α )⎟ = + − x ac* − c(α ). 8 32 ⎝4 ⎠ 8

Let α i* be the monitoring rate that maximizes SW i(α), i ∈ {nc, ac, ag}. Let α* be the socially optimal monitoring rate. Proposition 4 summarises the results for the socially optimal monitoring rate and the monopolist’s subgame perfect equilibrium strategy which is the main finding of this paper. The proof is given in Appendix A. Proposition 4. (i) If x ≥ (h(xac*(α = 0))/8) + xac*(α = 0) then there exists a socially optimal monitoring rate only if αac* ∈ [0, £]. The socially optimal monitoring rate is α* = α ac* and the ac-strategy is the subgame perfect equilibrium; and (ii) If x < (h(xac*(α = 0))/8) + xac*(α = 0) then not monitoring is the socially optimal outcome, that is, α* = 0 and the nc-strategy is the subgame perfect equilibrium. An intuitive explanation of Proposition 4 requires an understanding of the properties of the social welfare functions for the different strategies with respect to the monitoring rate. The social welfare function corresponding to the no copying strategy is monotonically decreasing in the monitoring rate because the anti-copying investment is sufficient to prevent copying irrespective of the level of monitoring. So the cost of monitoring is a deadweight loss. Therefore, α nc* = 0. The social welfare function corresponding to the aggressive strategy is also monotonically decreasing in the monitoring rate. This is because the positive effect of a higher monitoring on the monopolist’s profit is outweighed by the negative effect of a higher monitoring on the consumer surplus. Therefore, α ag* = 0. However, in the case of the social welfare function corresponding to the accommodating strategy, the sign of SW ac′(α) is ambiguous as shown in the proof of Proposition 4 in Appendix A. The ambiguity results from the positive effect of a higher monitoring rate on the monopolist’s profit and the negative effects of a higher monitoring rate on the fake producer’s profit and consumer surplus. Hence, 0 ≤ α ac* ≤ αmax. Since α ag* = 0 and ag π ag m *(α * = 0) = 0, the monopolist never chooses the aggressive strategy. Suppose x is such that the situation represented in Figure 1 holds. In this case the accommodating strategy is the subgame perfect equilibrium because it dominates the no copying strategy irrespective of whether α ac* = 0 or α ac* > 0. The socially optimal monitoring rate is α* = α ac*. This implies that the pirate’s entry is not prevented in equilibrium. Suppose x is such that the situation represented in Figure 2 holds. In this case the socially optimal monitoring rate is α * = α nc* = 0. The formal proof is provided in Appendix A. This means that no monitoring is the socially optimal policy and the no copying strategy is the subgame perfect equilibrium which implies that piracy is prevented. Therefore, Proposition 4 shows that monitoring may or may not be the socially optimal policy. If not monitoring is the socially optimal outcome then either the nc-strategy that guarantees the prevention of copying with certainty or the ac-strategy is the subgame – 529 – © 2008 The Authors Journal compilation © 2008 Japanese Economic Association

The Japanese Economic Review

perfect equilibrium strategy. In the latter case the equilibrium anti-copying investment does not guarantee the prevention of copying with certainty. This is because from Proposition 2 we know that the equilibrium anti-copying investment, xac* (α* = 0) that satisfies h′(xac* (α* = 0)) = –8, is strictly less than x. Alternatively, if monitoring is the socially optimal outcome then the ac-strategy is the subgame perfect equilibrium and, using Proposition 2, the equilibrium anti-copying investment is xac*(α*) that satisfies h′(x ac*(α*)) = –(8/(1 − α*)). However, xac*(α*) does not guarantee the prevention of copying with certainty because from Proposition 2 we know that x ac*(α*) < x. Proposition 4 implies that the monopolist always makes a positive anti-copying investment in equilibrium and there may be a combination of enforcement policy and anti-copying investment in equilibrium. It may also be the case that the fake producer cannot copy the monopolist’s product in the absence of monitoring. Thus it is possible to prevent copyright infringement through anti-copying investment rather than depending on enforcement infringement policies, which are rather weak or lacking in developing countries. The Mughal-E-Azam case mentioned in the Introduction is an example that supports our results. Further, we also see that the entry deterring limit output aggressive strategy is never a subgame perfect equilibrium. Let us now discuss the effects of a change in the penalty on the optimal monitoring rate in the case where monitoring is socially optimal. SW nc is independent of G, therefore G = 0 maximizes SW nc. The same result holds for SW ag because it is non-increasing in G, ag ag ag since dSW ag / dG = (1 − q ag m *)dq m */ dG ≤ 0 because 1 − q m * ≥ 0 and dq m */ dG < 0. From ac Equation (8) we observe that G does not appear in SW since it is a transfer payment from the fake producer to the government. From Proposition 2 we know that x ac* is independent of G in the interval α ∈ [0, α max). Therefore, SW ac(α) and hence, α ac* is independent of G. From Propositions 1 and 3 we know that α max and £ are inversely related to G. These have the following implications. If the conditions specified in Proposition 4 (i) hold then the socially optimal monitoring rate is α* = α ac*. Any change in G will not affect this monitoring rate since α ac* is independent of G, provided the conditions for the existence of equilibrium are not violated. That is, if an increase in G, which results in a fall in £, causes α ac* to exceed £ then equilibrium does not exist according to Proposition 4 (i). This implies that though a change in G does not affect α* = α ac*, it may affect the existence of the equilibrium monitoring rate. This analysis highlights the role of a penalty in determining the existence of a socially optimal monitoring rate.

5.

Conclusion

The literature on software piracy predominantly focuses on enforcement policies targeted towards piracy and its effectiveness in preventing copyright infringement. The general assumption in this literature is that the pirated products are imperfect substitutes of the legitimate ones. Unlike the literature, in this paper we addressed the issue of commercial copyright infringement where the copied product is identical to the legitimate one. While the government is responsible for anti-copying enforcement policies, we allowed the monopolist to play an active role in the prevention of copyright infringement by considering an entry deterrence framework and introducing an anti-copying investment by the monopolist. We assumed that the probability of copying is inversely related to the anti-copying investment and above a certain critical level it guarantees the prevention of copying with certainty. – 530 – © 2008 The Authors Journal compilation © 2008 Japanese Economic Association

D. S. Banerjee, T. Chatterjee and A. Raychaudhuri: Optimal Enforcement and Anti-copying Strategies

The monopolist’s strategies consisted of output and anti-copying investment that either allowed or deterred the fake producer’s entry, or prohibited copying with certainty. We called them the accommodating, aggressive and no copying strategies. The government’s social welfare maximizing monitoring rate endogenously determined the monopolist’s subgame perfect equilibrium strategy. We showed that if monitoring is not socially optimal then either the accommodating or the no copying strategies are the subgame perfect equilibrium. In the former case the equilibrium anti-copying investment does not guarantee the prevention of copying while in the latter case copying is prevented with certainty. If monitoring is socially optimal then the accommodating strategy is the subgame perfect equilibrium and copying is not prevented with certainty. In our model the government is responsible for detecting copyright infringement. Alternatively, firms may initiate the detection procedure. Banerjee (2006b) addresses this issue in the context of commercial software piracy where a monopolist is responsible for monitoring the illegal activities of a pirate and the government chooses a social welfare maximizing penalty, which the pirate, if detected, pays to the monopolist. Banerjee (2006b) shows that the socially optimal penalty, which depends on the government’s stance toward piracy, may result in monitoring as the subgame perfect equilibrium and consequently the deterrence of piracy. Promotion of socioeconomic institutions may be an alternative to detection and anti-copying strategies to reduce copyright infringement. In a recent paper, Banerjee et al. (2005) show that that economic development, more openness, less corrupt governments, softening of political and civil rights results in a reduction in software piracy. Openness reduces tariffs and quotas, which in turn reduces the price of legitimate software and as a result piracy decreases. Political rights as defined in the United Nations International Covenant on Civil and Political Rights (1966) include the rights to self-determination and to freely dispose of natural wealth and resources. The institution of democracy ensures protection of political rights. Civil liberties promote liberty and guarantee that due process of law will be observed, striking a balance between the freedom of the individual and the right not to have one’s freedom infringed by others’ abuse. Let us discuss some of the possible extensions of this paper. First, to analyse the mix of enforcement policies and anti-copying investment strategies where the fake product is an inferior substitute of the monopolist’s product. We believe that the findings of this paper will hold in this case because the properties of the monopolist’s profit functions with respect to the monitoring rate corresponding to the different strategies discussed in this paper are similar to those in Banerjee (2006a) where the fake product is assumed to be an inferior substitute of the legitimate one. Second, to consider a model of ex post detection. In this case the probability of detection depends on the quantity of illegal copies sold in the market. Third, this paper assumes a single fake producer. However, there may be multiple fake producers. In this case it is possible that a subset of fake producers is detected while the others are not. A detailed analysis of such a model will have to take into consideration all various combinations of fake producers who are detected which in turn depends on the number of fake producers assumed in the model.14

14

Yao (2005) considers a model of commercial counterfeiting with multiple counterfeiters. The counterfeit market is assumed to be perfectly competitive and the detection of one counterfeiter leads to the detection of all. Yao (2005) do not consider the detection of a subset of counterfeiters.

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APPENDIX I Proof of Proposition 1 In case of the ag-subgame, the equilibrium entry deterring limit output is q ag m* = 1 − * is decreasing in α and G, since 2√αG/(1 − α), for 0 ≤ α ≤ α max, α maxG /(1 − α max ) = 1/16 ⋅ q ag m 2 * / / / αG/(1 − α) is increasing in α and G. At α = αmax, q ag = 1 2 ⋅ d α dG = − 1 16 α m max max < 0 .  Proof of Proposition 2 = 1/ 2 and q acf * = 1/ 4 , if the fake producer can copy which occurs with probability h(x). Substituting this in the fake producer’s expected profit we get π ac f * = (1 − α )/16 − αG . The fake producer cannot enter the market given that he can copy if π ac f * = ((1 − α)/ 16)h(x) − αh(x)G ≤ 0 which on rearrangement becomes αG/(1 − α) ≥ 1/16. Let αmax be the monitoring rate that satisfies the no-entry condition with equality. The fake producer cannot enter if the monitoring rate satisfies the condition αmax ≤ α ≤ 1 because α/(1 − α) is increasing in α, 0 ≤ α < 1. However, the relevant range of the monitoring assumed is α ∈ [0, αmax]. Let us consider the range α ∈ [0, αmax). Substituting qmac* = 1/ 2 in the monopolist’s expected profit function given in Equation (2) and maximizing it with respect to x, that is dπ m /dx = −[(1 − α)h′(x)/8] − 1 = 0, yields the solution xac*. Now xac* cannot guarantee that the fake producer cannot copy with certainty because h′(xac*) = −(8/(1 − α )) < 0 which implies that x ac* < x. By assumption h′(x) < 0 for x < x. Now maximization requires d2πm/dx2 = −(1 − α)/8h″(x) < 0. This implies that it must be the case that, h′′(x) > 0. From h′(xac*) = −(8/(1 − α)) we get dxac*/dα = −[8/(h″(xac*)(1 − α)2)] < 0, since h′′(x ac*) > 0. At α = α max the issue of detecting the fake producer and whether he can copy or not does not arise because he does not enter and αmax is independent of x. Therefore, xac* = 0 at α = αmax and hence the monopolist’s profit is π mac*(α max ) = qmac* − qmac*2 which on substituting qmac* = 1/ 2 yields, π mac*(α max ) = 1/ 4 .  q ac m*

Proof of Proposition 3 (i) dπ mac*(α )/ dα = h( x ac*)/8 − ((1 − α )/8)h′( x ac*)(dx ac*/ dα ) − (dx ac*/ dα ) = h( x ac*)/8 > 0 for α ∈ [0, αmax). We get this using the first-order condition −(1 − α)h′(x)/8 − 1 = 0 ⇒ h′(xac*) = −(8/(1 − α)). d 2π mac*(α )/ dα 2 = h′( x ac*)/8(dx ac*/ dα ) > 0 because h′(xac*) and dxac*/dα are both negative. So in the interval α ∈ [0, αmax), π mac*(α ) = 1/ 4 − ((1 − α )h( x ac*)/8) − x ac* is strictly increasing and a convex function of α. At α = 0, π mac*(0) = 1/ 4 − (h( x ac*)/8) − x ac*. The monopolist’s profit for the equilibrium ag-strategy is π mag* = qmag* − qmag*2 which equals the monopoly profit at α = αmax. Now dπ mag*/ dα = (1 − 2qmag*)dqmag*/ dα ≥ 0 because dqmag*/ dα ≤ 0 and (1 − 2qmag*) ≤ 0 since 1/ 2 ≤ qmag*) ≤ 1. So π mag*(α ) is maximized at αmax. At α = 0, π mag*(α ) = 0. So π mac*(0) > π mag*(0) and at α = αmax, π mac*(α max ) = π mag*(α max ) =1/ 4 so π mag*(α ) is steeper than π mac*(α ) and, therefore, the single crossing property is satisfied in the range α ∈ (0, αmax). (ii) dπ mac*/ dG = 0 because qmac* and xac* is independent of G. At Gmax where Gmax satisfies αGmax/ ag ag ag ag (1 − α) = 1/16, π mac* = π * m =1/ 4. dπ m */ dG = (1 − 2qm *)dqm */ dG ≥ 0 because dqm */ dG ≤ 0 ag*) ag* ag*( and (1 − 2qm ≤ 0 since 1/ 2 ≤ qm ≤ 1. So π m G ) is maximized at Gmax since π mag*(Gmax ) = π *m =1/ 4. At G = 0, π mag*(G = 0) = 0 . So π mac* > π mag*(G = 0). Therefore, π mag*(G ) is steeper than π mac*, and the single crossing property is satisfied in the range G ∈ (0, Gmax). (iii) Since π mac* is independent of G in the interval G ∈ [0, Gmax) and α ∈ [0, αmax) therefore, – 532 – © 2008 The Authors Journal compilation © 2008 Japanese Economic Association

D. S. Banerjee, T. Chatterjee and A. Raychaudhuri: Optimal Enforcement and Anti-copying Strategies

dπ mac*/ dα is also independent of G in the same intervals. From Proposition 1 we know that αmax is decreasing in G. This means that an increase in G restores the monopoly outcome at a lower monitoring rate but the property of dπ mac*/ dα remains unaffected. An increase in G results in π mag* attaining its maximum value π *m at a lower αmax. This means the slope of π mag* with respect to α increases and therefore, π mag* intersects π mac* at a lower £. Thus £ is decreasing in G. 

Proof of Proposition 4

α * = 0 because SW nc′(α) = −c′(α) < 0. SW ag ′(α ) = (1 − qmag*)qag*′ (α ) − c′(α ) < 0 since qmag*′ (α ) < 0 , (1 − qmag*) ≥ 0 and c′(α) > 0. So α ag* = 0. SW ac′(α) = [(3/32)(1 − α)h′ (xac*)xac*′(α) − x ac*′(α)] − [(3/32)h(xac*) + c′(α)]. The first expression is positive because h′(xac*) < 0 and xac*′(α) < 0, and the second expression is negative for α ac ∈ [0, αmax). Therefore, the sign of SW ac′(α) is ambiguous. So α ac* ∈ [0, αmax). Parts (i) and (ii) of Proposition 4 are proved using Figures 1 and 2. π mac*(α = 0) ≥ π mnc* ⇒ x ≥ [h( x ac*(α = 0))/8] + x ac*(α = 0) . So the ac-strategy weakly dominates the nc-strategy. This is represented in Figure 1. An equilibrium does not exist if αac* > £ because of the following reason. Suppose α ac* > £ . Then if the government chooses α ac*, the monopolist chooses the ag-strategy which does not maximize SWag. If the government chooses αag* = 0 then the monopolist chooses the ac-strategy which does not maximize SW ac(α). Therefore, an equilibrium exists only if αac* ∈ [0, £]. In this range the ac-strategy weakly dominates the ag-strategy and αac* also maximizes social welfare. Therefore, α* = αac*, αac* ∈ [0, £] is the socially optimal monitoring rate and the ac-strategy is the subgame perfect equilibrium. Part (ii) of the proposition follows from the fact that, π mac*(α = 0) ≤ π mnc* ⇒ x ≤ [h( x ac*(α = 0))/8] + x ac*(α = 0) . In the range α ∈ [0, !] the nc-strategy dominates the ac-strategy. If αac* ∈ [£, αmax) then the government will not choose αac* even if SW ac(α ac*) > SW nc for the reasons explained above. Therefore, α* = 0 is socially optimal and the nc-strategy is the subgame perfect equilibrium.  nc

APPENDIX II15 Let us consider a price game where the monopolist chooses his own price and the fake producer chooses the same price to avoid detection. The extensive form representation of this game is as follows. Stage 1: The government chooses a monitoring rate α. Stage 2: The monopolist chooses a price p and an anti-copying investment strategy x. Stage 3: The fake producer makes his entry decision and chooses the same price p. If the fake producer enters the market then the monopolist’s quantity is (1 − p)/2. Otherwise, the monopolist’s quantity is 1 – p. So the demand for the monopolist’s product is ⎛ (1 − p) ⎞ qm = (1 − (1 − α )h( x))(1 − p) + (1 − α )h( x)⎜ ⎟. ⎝ 2 ⎠

15

(A1)

The authors would like to thank one of the referees for suggesting this pricing game.

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The monopolist’s and the fake producer’s expected profits are ⎛ p(1 − p) ⎞ π m ( p, x, α ) = (1 − (1 − α )h( x))( p(1 − p) − x) + (1 − α )h( x)⎜ − x⎟ 2 ⎝ ⎠ and p(1 − p) π f ( p, x, α ) = h( x)((1 − α ) − αG ). 2

(A2)

We begin our analysis with the ag-strategy. The fake producer’s entry is strategically deterred if π f (p, x, α) = h(x)((1 − α)(p(1 − p)/2) − αG) ≤ 0. This yields the equilibrium entry deterring limit price, which is, pag* =

1 1 8αG − 1− . 2 2 1−α

(A3)

new satisfy this equality, that is, Now, pag* = 1/2 when √(1 − 8αG/(1 − α)) = 0. Let α max new new new , the monopolist does not reduce 1/8 = α max G /(1 − α max ). For monitoring rates above α max its price any further because it does not change the entry deterrence condition but reduces its profit. So for the rest of the analysis, we will consider monitoring rates in the range, new α ∈ [0, α max ]. In this case also α ag* = 0. The monopolist’s profit is π mag* = pag*(1 − pag*). The consumer surplus and the social welfare functions for the equilibrium ag-strategy are

CS ag =

(1 − pag*)2 2

(A4)

and SW ag

1 − pag*2 = − c(α ). 2

dSW ag/dα = −pag*(dpag*/dα) − c′(α) < 0 because dpag*/dα = 2G[1 − 8αG/(1 − α)]−1/2 new 1/(1 − α)2 > 0 for α ∈ [0, α max ]. So the property of SW ag for the pricing game is the same as that in the quantity game and α ag* = 0 maximizes SW ag. Let us now consider the accommodating strategy where the monopolist chooses the profit maximizing price and anti-copying investment assuming that the fake producer copies his product. The first-order conditions yield the solutions which are dπ m 1 = 0 ⇒ pac* = dp 2

(A5)

dπ m 8 = 0 ⇒ h′( x ac*) = − dx 1−α

(A6)

and

The monopolist’s and the pirate’s equilibrium profits are,

π mac*(α ) =

1 (1 − α )h( x ac*) − − x ac* 4 8

(A7)

and 1 ac − αG ). π ac f *(α ) = h( x *)((1 − α ) 8 – 534 – © 2008 The Authors Journal compilation © 2008 Japanese Economic Association

D. S. Banerjee, T. Chatterjee and A. Raychaudhuri: Optimal Enforcement and Anti-copying Strategies

From Equation (A7) we see that the monopolist’s profit is the same as in the quantity game new new new and the fake producer cannot enter if α satisfies α ≥ α max where 1/8 = α max G /(1 − α max ). ac* *( This we get by equating π ac so the monopoly results α ) = h ( x )(( 1 − α ) 1 / 8 − α G ) = 0 f new are restored at α ≥ α max . Irrespective of the fake producer’s entry decision, the equilibrium quantity sold in the ac market is qac* = qmac* + qac f * = 1/ 2 because p * = 1/2. Therefore, the consumer surplus and social welfare functions for the equilibrium ac-strategy are CSac = 1/8 and SWac = 3/8 − > ac xac* − c(α). dSW ac / dα = −(dx ac*/ dα ) − c′(α ) = < 0, because dx */dα < 0. Therefore, the ac property of SW for the pricing game is the same as in the quantity game and new ] maximizes SWac. α ac* ∈ [0, α max Since the properties of SW ag and SW ac for the pricing game are the same as that in the quantity game therefore, the results for the social welfare maximizing monitoring rate is the same as that specified in Proposition 4. The only difference between the two games is new new new because 1/8 = α max α max < α max G /(1 − α max ) > α maxG /(1 − α max ) = 1/16. This means that the monitoring rate at which the monopoly outcome is restored in the pricing game is higher than that in the quantity game. Final version accepted 19 January 2007.

REFERENCES Banerjee, D. S. (2003) “Software Piracy: a Strategic Analysis and Policy Instruments”, International Journal of Industrial Organization, Vol. 21, No. 1, pp. 97–127. –––– (2006a) “Lobbying and Commercial Software Piracy”, European Journal of Political Economy, Vol. 22, No.1, 139–155. –––– (2006b) “Enforcement Sharing and Software Piracy”, Review of Economic Research on Copyright Issues, Vol. 3, No. 1, pp. 83–97. ––––, A. Khalid and J. E. Sturm (2005) “Socio-Economic Development and Software Piracy: An Empirical Assessment”, Applied Economics, Vol. 37, pp. 2091–1097. Becker, G. and G. Stigler (1974) “Law Enforcement, Malfeasance and Compensation”, Journal of Legal Studies, Vol. 3, pp. 1–18. Besen, S. M. and S. N. Kirby (1989) “Private Copying, Appropriability, and Optimal Copying Royalties”, Journal of Law and Economics, Vol. 32, pp. 255–280. Chen, Y. and I. Png (1999) “Software Pricing and Copyright Enforcement: Private Profit vis-à-vis Social Welfare’ End-Users”, Proceedings of the 20th International Conference in Information Systems, December, pp. 119–123. Cheng, H. K., R. R. Sims and H. Teegen (1997) “To Purchase or Pirate Software: An Empirical Study”, Journal of Management Information Systems, Vol. 13, No. 4, 49–60. Conner, K. R. and R. P. Rumelt (1991) “Software Piracy: An Analysis of Protection Strategies”, Management Science, Vol. 37, No. 2, pp. 125–137. Harbaugh, R. and R. Khemka (2000) “Does Copyright Enforcement Encourage Piracy?”, Working Paper, Claremont McKenna College. Nascimento, F. and W. R. Vanhonacker (1988) “Optimal Strategic Pricing of Reproducible Consumer Products”, Management Science, Vol. 34, No. 8, pp. 921–937. Noyelle, T. (1990) “Computer Software and Computer Services in Five Asian Countries”, in United Nations Conference on Trade and Development/United Nations Development Programme (UNCTAD/UNDP), Services in Asia and the Pacific: Selected Papers, Vol. 1. New York: United Nations. Oz, S. and J. F. Thisse (1999) “A Strategic Approach to Software Protection”, Journal of Economics and Management Strategy, Vol. 8, No. 2, pp. 163–190. Park, Y. and S. Scotchmer (2005) “Digital Rights Management and the Pricing of Digital Products”, NBER working paper 11532. Takeyama, L. (1994) “The Welfare Implications of Unauthorized Reproduction of Intellectual Property in the Presence of Network Externalities”, Journal of Industrial Economics, Vol. 62, No. 2, pp. 155–166. Yao, J. T. (2005) “Counterfeiting and an Optimal Monitoring Policy”, European Journal of Law and Economics, Vol. 19, No. 1, pp. 95–114.

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