A note on strategic piracy in the economics of software: an explanation by learning costs

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1 A note on strategic piracy in the economics of software: an explanation by learning costs Bruno Chaves and Frédéric Deroian, FORUM 1 Abstract: In a two-period model, a monopoly sells a software, the use of which necessitates learning costs In each period, the firm chooses whether to raise a protection to prevent piracy or not We show the existence of an euilibrium of the game in which the firm raises no protection in the first period; this euilibrium is positively correlated to the uality of piracy Keywords: Software Industry, Strategic Piracy, Learning Cost JEL Classification: L86, C70 As the evidence indicates, a variety of information-based industries can thrive not only despite, but because of, rampant piracy, Tehranian [003] 1 Introduction A well known fact in the economics of information is that practices evolve slower than technologies themselves, in such a way that people need to learn how to use information technology capital effectively Furthermore and specifically in the case of the software industry, the gross benefit from using a software is two-sided On the one hand, some value is created by the comparative uality and potential applications of the software with regard to competitors; the more possibilities such as multifunctions and specializations provided by the software, the more valuable the software On the other hand, the user has to spend time in learning all the aspects of the software; the more the software valuable per se, the more time and effort have to be spent in learning to use it and get effective value Expressed differently, the right good for firms is the whole system software/user, whose elements are complementary A direct conseuence for sellers is that the formation of consumers becomes a crucial determinant of their market share and much investment like interface optimization is devoted to this issue Conseuently, sellers cope with the 1 FORUM - Université Paris X - Bâtiment K - 00, avenue de la Républiue Nanterre, France BrunoChaves@univ-paris1fr; fderoian@u-paris10fr To some extent, the users formation can be considered as an input which is not internalized by the firm, which therefore sells an incomplete good 1

2 following trade off : either developing or not softwares to their best sophistication, which would induce a costly learning for the users 3 This paper focuses on firms producing highly sophisticated softwares In this context, we argue that piracy can be a strategic means to deal with this issue 4 Our argument is simple: facing the need of forming users to their softwares, firms can strategically implement low protection devices in order to attract pirates as a future demand To some extent, piracy is the ground on which the future demand will raise Specifically, we develop a simple two-stage model, in which a monopoly sells a non durable and highly specialized software for two periods 5 The monopoly chooses to raise or not a protection device at the beginning of each each period, thus preventing piracy until the end of the period On the demand side, the first period consumers buyers and eventually pirates incur a fixed learning cost At period two, those even consumers do not bear the learning cost any more, whereas the part of the demand who did nothing in period one incurs the learning cost if buying or pirating We show that the strategy consisting in establishing no protection in period one and raising a protection in period two is an euilibrium of the game Furthermore, the higher the uality of piracy, the greater the probability of the euilibrium to occur There are two reasons: firstly, the greater the proportion of pirates in period one, the greater the market share of the monopolist in period two; secondly, the greater the uality of the illegal software, the lower the price level in period one necessary to prevent the presence of piracy, and then the lower the consumer surplus captured by the monopolist in period one To sum up, a condition of emergence of a market for sophisticated softwares is the mutual adjustment of the cost of software development and the learning cost of the users specific human capital Piracy can be a means to incite the other side of the market to invest in specific human capital, thus enlarging the future demand 3 In many cases, the learning cost is a specific human capital investment: the more the software has specific functions that permit it to differentiate from competitors, the more users need to engage specific investments in human capital that cannot be redeployed without costs to other softwares 4 The 00 annual report of the Business Software Alliance on piracy shows that software piracy continues to pose challenges for the software industry In particular, the 001 piracy rate in the world is 40 percent and the loss for manufacturers amounts to 1097 billions dollars, especially in North America, Western Europe and Asia/Pacific Concerning the USA, this concerns 5 percent of all licenses and the loss is about 181 billions dollars 5 Postulating that softwares are non durable goods is consistent with the rapid obsolescence of the information technology

3 This paper is complementary to some previous works Conner and Rumelt 1991 show that a monopolist can have a strategic opportunity to allow for piracy in the presence of network externalitites Similar findings are in Takeyama 1994 and Slive and Bernhardt 1998 Notably, the two papers argue that piracy can be viewed as a form of price discrimination in which the manufacturer sells some of the software at a price of zero In the presence of significant network externalities for the software, it may be profit maximizing for the software manufacturer to tolerate piracy by home consumers, most of whom have a low willingness to pay, because they contribute to the valuation of the good made by legal users Our results can also be interpreted in terms of price discrimination, but the reason for an increased demand is different In our setting, piracy originates a future rent, since by enabling the formation of illegal users, the future demand is enlarged In a competitive market, Shy and Thisse 1999 show that not protecting is a possible strategic action in the presence of network externalities, in order to reduce competition piracy induces less demand for other firms We note that this trend of literature, linking network externalities and strategic piracy, is contradicted by Poddar 00 who argues that these results are strongly model specific Lastly, Banerjee 003 and Chen and Png 003 study the policy implications of piracy Banerjee shows that the optimal level of tracking set up by the government is not always high, while Chen and Png show that an increase in detection can affect welfare more negatively than price cuts Section develops the model, section 3 gives the result under the form a proposition The proof of the proposition is given in section 4 The model We build a two-period 6 game, in which a monopolist 7 sells a software to heterogenous consumers Consumers heterogeneity is captured by the parameter θ [θ l, θ h ], representing the gross benefit from using the software 8 We denote = θ h θ l At period t = {1, }, 6 Reasoning in two or any finite period does not change the nature of the results Another possibility would be to model an infinite-period game with time preference 7 This is like in Conner and Rumelt 1991 and Banerjee 003 Note that this hypothesis is consistent with the traditional view that many information and technology-related businesses have cost structures with large fixed costs and small, or even zero, marginal costs They are, to use the textbook term, natural monopolies Varian [001] 8 In the introduction, we relied the intrinsic interest of the software depends on the formation of the user Hence, a general formulation would assume that the gross benefit is positively correlated to the level 3

4 the price of the good is denoted p t and the legal demand for the good is denoted D t In each period, the consumers have the following choices: buying the software, pirating the software if the firm raises no protection, doing nothing At period one, buying and pirating originates a fix cost c ]0, θ h [ of learning At period two, consumers who did nothing in period one and who buy or pirate incur this cost, whereas consumers who bought or pirated in period one do not support this cost any more if they buy or pirate in period two In each period, the monopolist can raise a protection, which completely prevents piracy during the period In order to focus on pure strategic effects, there is no cost of protection, and protecting does not deserve the utility of legalist consumers 9, ie the technology used for protecting does not does not diminishes the uality of the software or its ergonomic properties, Furthermore, it is assumed for simplicity that the marginal costs are eual to zero, and we model an installed monopolist, which allows us to avoid incorporating the fixed cost of producing the software An unregistered copy is not fully reliable, which is captured by the parameter [0, 1] 10 Hence, at period one, the utility of consumer of type θ is: θ p 1 c if the consumer buys the product θ c if the consumer pirates 0 if the consumer does nothing At period two, the utility of consumer θ is: θ p if the consumer buys the product and bought or pirated it in period one θ θ p c θ c if the consumer pirates and bought or pirated it in period one if the consumer buys and neither bought nor pirated it in period one if the consumer pirates and neither bought nor pirated it in period one 0 if the consumer does nothing We study in the next sections the subgame perfect euilibria of this two-stage game of formation of the user Clearly our hypothesis is more constraining with regard to the possibility of originating an euilibrium with no protection in period one 9 This is like in Banerjee 003, Conner and Rumelt 1991 and Shy and Thisse 1999 Another means to protect is the tracking of illegal users, which would involve a model of monitoring 10 We stipulate that pirated software is not fully reliable, like Banerjee 003 Rather, in Shy and Thisse 1999 the pirated software is fully reliable, but only legal users can access complementary services 4

5 3 Results This section provides, through a proposition, the condition under which it is rational for the monopolist to cope with piracy in period one The proof is given in the next section Proposition In this two-stage game, the monopolist s best strategy is No Protection, No Protection if and only if θ h < c + c Indeed, in this case there is no piracy On the opposite, the monopolist s best strategy is No Protection, Protection if and only if θ h c + c Remarks: 1 The monopolist is in presence of piracy when θ h c + c, and then it always chooses to avoid protection We note that this expression is more likely when the uality of piracy is high There are two reasons: firstly, the greater the proportion of pirates in period one, the greater the market share of the monopolist in period two; secondly, the greater the uality of the illegal software, the lower the price level in period one necessary to prevent the presence of piracy, and then the lower the consumer surplus captured by the monopolist in period one We do not include in the model a parameter of time preference due to space restriction, so our analysis focuses on the limiting case where there is no time preference Of course, when integrating such a parameter, it is easily shown that when θ h c +, No protection, Protection is the euilibrium for sufficiently low value of time preference, whereas Protection, Protection is the euilibrium otherwise 4 Appendix In this appendix, we prove the proposition by backward induction compute three marginal consumers We need first to Indifference between pirating and buying: θ p1 = p 1 1 Indifference between doing nothing and pirating: θ 0p = c Indifference between doing nothing and buying: θ 01 = p 1 + c The first part of the proposition is easily shown: if θ h < c +c, then the marginal consumer who is indifferent between buying the software and not buying in the case of monopoly without piracy which turns to be, after little calculation, eual to θ h c is smaller than the marginal consumer who is indifferent between pirating and doing nothing c In that case, piracy does not exist Therefore, No protection, No protection is the euilibrium 5

6 strategy Next, we examine the case where there is effective piracy The period-two subgame We assume until the end of the proof that piracy exists This means notably that θ h < c + c and p 1 1 > c Furthermore, a nonnegative profit entails θ h > k Since the cost of protection is negligible, and since there is no future market, the monopolist has clearly interest to protect his software in period two: protection is always better than allowing piracy for the original developer So, we just have to find the optimal price proposed in period two, given the state of consumers in terms of learning cost Actually, in period one, part of them have either bought or pirated the software, in such a way that they do not have to bear the learning cost Of course, this concerns agents with highest θ This means that there exists a value k [θ l, θ h ] such that every agent θ k has either bought or pirated in the first period and every agent θ < k did nothing in period one We denote by π k the profit in period two given k case 1: p k Then the demand is D = θ h p only consumers who do not bear the learning cost buy the good and the profit of the monopolist is π = p D The first order condition induces that ˆp = θ h subcase 1: θ h k Then ˆp = θ h and ˆπ = θ h subcase : θ h 4 < k Then we obtain a constrained solution for clarity a single hat means a first best optimum, whereas a double hat means a constrained optimum; ˆp = k and ˆπ = k θh k That is, the whole first period buyers and pirates buy the good in period two case : p ]k c, k] Then the demand is D = θ h k, ie no agent who did nothing in period one can buy the product The profit is linear in p : π = p θh k Hence, ˆp = k and ˆπ = k θ h k case 3: p k c Then the demand is D = θ h p c entailing ˆp = θ h c subcase 1: θ h+c < k Then ˆp = θ h c θ subcase : h +c k c θh k first period and ˆπ = θ h c 4 The profit is π = p θh p c, k Then we obtain a constrained solution; ˆp = k c and ˆπ = That is, the whole buyers in period two are the buyers and pirates of the From his little analysis we derive the optimal strategy of the firm in period two according to the magnitude of parameter θ h with regard to other parameters: 1 θ h k: if p > k, then ˆπ = θ h 4 ; if p ]k c, k], then ˆπ = k θh k ; if p k c, then ˆπ = k c θh k ; 6

7 Thus, the firm chooses ˆp = θ h and ˆπ = θ h 4 θ h ]k c, k[: if p > k, then ˆπ = k θh k if p k c, then ˆπ = k c θh k ; Thus, the firm chooses ˆp = k and ˆπ = k θh k ; if p ]k c, k], then ˆπ = k θh k ; 3 k < θ h k c: if p > k, then ˆπ = k θh k ; if p ]k c, k], then ˆπ = k θh k ; if p k c, then ˆπ = θ h c Now, θ h c 4 < k θh k 4 ; iff θ h ]k, k + 1[ Note that k c k is not possible, because this would imply that θ h < k If k c k + 1, the firm s best profit is k θh k when θ h > k + 1 and θ h c 4 if θ h ]k, k + 1[; if k c [k, k + 1], then θ h ]k, k + 1[ and the optimal profit is k θh k if k < θ h k + 1, the firm s profit is θ h c 4 Euilibria of the two-stage game To sum up, if k + 1 < θ h k c, the firm s profit is k θh k ; We first examine the strategy no protection, protection Then we turn to the strategy protection,protection Finally, we compare the two strategies Not protecting in period one If the firm does not protect its software in period one, it is exposed to piracy As mentioned before, if p 1 c 1, then there is no piracy, so that this case does not arise at all Then we are ensured that in the case we examine, p 1 > c 1 ˆp 1 = 1 θ h, ˆπ 1 = 1 θ h 4 and k = c Then, as θ h > c + c, At this step, we can determine the optimal profit: the best price is ˆp 1 = 1 θ h, and it leads to the following optimal profit adding the profits of the two periods - we use for this the result of the preceding subsection of the second period subgame- : ˆπ = θ h 4 Indeed, k = c, and we want θ h c + c Then in the preceding analysis of optimal profit in period, we are ensured to be in the first case, ie ˆp = θ h and ˆπ = θ h 4 To sum up, No protection, Protection leads to the following strategy: ˆp 1 = 1 θ h ˆp = θ h and ˆπ = θ h 4 Protecting in period one, In this case, the firm does not bear the illegal competition from piracy We just have to consider one marginal consumer: θ 01 = p 1 + c, which induces the following profit in period one: π 1 = p 1θ h p 1 c 7

8 The problem of the monopolist is therefore: p1 θ h p 1 c max p1 It turns out immediately that: i if p > p 1 + c, then when θ h ii if p ]p 1, p 1 + c], ˆπ = p 1+cθ h p 1 c iii if p p 1, then when θ h+c + π p 1 + c > p 1 + c, ˆπ = θ h 4 ; when θ h p 1 + c, ˆπ = p 1+cθ h p 1 c ; when θ h+c p 1 +c, ˆπ = p 1θ h p 1 c < p 1 +c, ˆπ = θ h c 4 This analysis can be categorized in terms of the parameter θ h in three cases: 1 if θ h > p 1 + c: then ˆp 1 = θ h c and ˆπ = θ hθ h c Indeed, we have to compare under the constraint 1 max p1 θ h p 1 c p1 max p1 +cθ h p 1 c p1 solution: ˆp 1 = θ h c and with maxp1 p1 θ h p 1 c + θ h 4 with The first leads to the constrained and ˆπ = θ hθ h c The second entails the same price and profit The third induces ˆp 1 = θ h c and ˆπ = θ hθ h c The result follows if θ h ]p 1 + c, p 1 + c]: then ˆp 1 = θ h 3c 4 and ˆπ = θ h c 8 Indeed, we have to compare with each other under the constraint max p1 θ h p 1 c p1 and max p1 p1 +cθ h p 1 c ˆπ = θ h c 8 The first optimization entails ˆπ = θ h c and the second Straightforward calculation shows that the first is greater than the second iff θ h < 3c 4, which is not compatible with constraint 3 if θ h < p 1 + c: then, in one case θ h < c, ˆp 1 = θ h c, that is θ h = p 1 + c, so the profit is at most 0 θ h < k in a second case θ h c, ˆp 1 = θ h c and ˆπ = θ h c Indeed, we have to compare under the constraint 3 max p1 θ h p 1 c p1 The first leads to ˆπ = θ h c + θ h c 4 and max p1 +cθ h p 1 c p1 and the second ˆπ = θ hθ h c 4 But the former profit is better off iff θ h cθ h c > 0 Recalling that by definition θ h > c, the result follows Comparing the results of the three cases, it follows that the best price is ˆp 1 = θ h 3c 4 and ˆπ = θ h c 8 Thus, this profit is the maximal payoff that the monopolist can obtain when protecting its software in both periods one and two Comparing the strategies We are now able to compare the two strategies, according to three cases with regard to parameter θ h 1 θ h > c + c: the monopolist has interest to avoid protection in period one iff θ h c 1 θ h c 1 + > 0 Since Indeed, θ h 4 > θ h c 8, we are done because θ h > c Protection < 1 The euilibrium strategy is then No Protection, 8

9 θ h < c + c: then the euilibrium monopoly price is less than the effective cost of pirating and piracy does not exist Therefore, No Protection, No Protection is the euilibrium strategy References Banerjee, D S, 003, Software piracy: a strategic analysis and policy instruments, International Journal of Industrial Organization, 1, Chen, Y and I Png, 003, Information Goods Pricing and Copyright Enforcement: Welfare Analysis, Information Systems Research, 14 Conner, K R and R P Rumelt, 1991, Software piracy: an analysis of protection strategies, Management Science, 37, Poddar, S, 00, Economics of software piracy and it s global impact, National University of Singapore Seventh Annual BSA Global Software - Piracy Study, june 00 Shy, O and J-F Thisse, 1999, A strategic approach to software protection, Journal of Economics and Management Strategy, 8, Slive, J and D Bernhardt, 1998, Pirated for profit, Canadian Journal of Economics, 31, Takeyama, L N, 1994, The welfare implications of unauthorized reproduction of intellectual property in the presence of demand network externalities, Journal of Industrial Economics, 6, Tehranian, J, 003, Optimizing piracy: the uses and limits of intellectual property enforcement in the cyberage, SSRN Working Paper Varian, H R, 001, Economics of Information Technology, the Raffaele Mattioli Lecture, delivered at Bocconi University, Milano, Italy, on November 15-16, 001 9