A Strategic Approach to Software Protection U

Transcription

1 Â Â Strategic pproach to Software Protection U OZ SHY University of Haifa, Israel and Stockhol School of Econoics, Sweden ozshy@econ.haifa.ac.il JCQUES-FRNCË OIS THISSE CORE, Universite Catholique de Louvain, elgiu and CERS, Ecole Nationale des Ponts et Chaussees, France thisse@core.ucl.ac.be This paper deonstrates that there is a strategic reason why software firs have followed consuers desire to drop software protection. We analyze software protection policies in a price-setting duopoly software industry selling differentiated software packages, where consuers preference for particular software is affected by the nuber of other consuers who ( legally or illegally) use the sae software. Increasing network effects ake software ore attractive to consuers, thereby enabling firs to raise prices. However, it also generates a copetitive effect resulting fro feircer copetition for arket shares. We show that when network effects are strong, unprotecting is an equilibriu for a noncooperative industry. 1. Introduction Since the widespread introduction of personal coputers in the early 1980s, software firs have gradually reoved protection against copying. We see at least two reasons for this policy change on the part of firs. First, firs realized that consuers were annoyed by the protective devices, which coproised the effectiveness of their products. 1 Second, as we argue in this paper, when the arket expands and copetition intensifies, due to large network effects, *We thank Hal Varian, two anonyous referees, and a coeditor for useful coents on earlier drafts. 1. For exaple, see announceents ade by MicroPro International Corp. to drop the copy protection fro WordStar 000 in order to eliinate hardware incopatibility probles and siplify the installation procedure ( PC Week, February 19, 1985 ), and by shton-tate to iediately end copy protection on its ost popular Dbase progra ( Coputerworld, ugust 5, 1986 ). Q 1999 Massachusetts Institute of Technology. Journal of Econoics & Manageent Strategy, Volue 8, Nuber, Suer 1999, 163 ] 190

2 164 Journal of Econoics & Manageent Strategy firs have strategic incentives to reove protection in order to increase the nuber of consuers using their packages. Specifically, we explicitly address the issue of price copetition in a differentiated software industry in which firs can choose whether to ake their software easy to copy or prohibitively costly to copy. We then study the strategic incentives for firs to protect or not to protect their software against piracy. Our odel rests on the assuption that the value of using a software package increases with the nuber of people who legally and illegally use the sae package. There are several epirical studies confiring the existence of software-specific network effects ( see, e.g., rynjolfsson and Keerer, 1996, and Gandal, 1994 ). For exaple, Gandal finds that users of spreadsheet software highly value Lotus file copatibility. In the sae vein, rynjolfsson and Keerer suggest that network-externality-type variables play an iportant role in the deterination of software prices. s observed by Conner and Ruelt ( 1991 ), piracy has two econoic effects on software firs. First, piracy leads to a fall in direct sales. However, by increasing the size of the installed base, it ay also boost the deand for the particular software. In this respect, Givon et al. ( 1995) report that pirates generated about 80% of the unit sales of spreadsheets and word processors in the UK. Installing protection in software has therefore two opposite effects, which have been analyzed by Conner and Ruelt in a onopoly setting. They found that, absent any network externality, a onopoly software developer increases price and profit when the exogenously chosen protection technology increases software protection. In contrast, when network externalities are present, profit can rise or fall as the level of piracy protection is increased. The goal of our paper is to investigate related issues by introducing price copetition aong firs producing differentiated software packages. We deonstrate that protection can be used strategically, since protection reoval enhances clientele just like strategic price cutting. In order to accoplish this analysis, we graft the network-externality odel onto the Hotelling-type spatial copetition odel. In addition, we consider two groups of consuers: those who need the services provided by the software suppliers, and those who do not ( support-independent consuers ). For siplicity we assue that by protecting, firs can fully prevent all consuers fro pirating their software. Our ain results are as follows. First, when firs protect their software, a low-price equilibriu eerges if network effects are

3 Strategic pproach to Software Protection 165 strong, whereas a high-price equilibriu arises under weak network effects. Therefore, all firs are better off with software protection when network effects are weak. In contrast, firs prefer not to protect their software when network effects are strong. The next set of results deals with a arket situation where firs choose to protect or not, prior to price copetition. For very weak network effects, both firs choose to protect their software because the ipact of piracy on sales is insignificant. For interediate value of the network effects, one fir chooses to protect whereas the other does not. This is because the network effects are now strong enough to induce one fir not to protect, thereby benefiting fro the larger network size, whereas these effects are still too low for the other fir to be able to afford to do it. Furtherore, the nonprotecting fir earns a higher profit than the protecting fir. This suggests that the nonprotecting fir, because of its network size, builds a large network fored not only by pirates but also by legal users. Finally, our ain result shows that, when network effects are sufficiently strong, both firs choose nonprotection, since such a policy is now associated with large network sizes, consequent high consuers valuations, and high profit levels. This result extends the onopoly result obtained by Conner and Ruelt ( 1991) to the case of a ultistrategic oligopoly. The literature on copying focuses on arkets with no network effects, thereby aking their analyses ore applicable to journal, book, and usic copying than to software ( see Novos and Waldan, 1984; Johnson, 1985; Liebowitz, 1985; and esen and Kirby, 1989 ). These papers show that even if consuer preferences for journals and books do not exhibit network externalities, publishers ay still earn higher profits when photocopying of originals is allowed. In this case, restrictions on photocopying ay reduce total welfare. These results were obtained under the assuption that publishes can price-discriinate between individual subscribers and libraries ( or other types of dealers ), by charging the libraries higher subscription rates that take into account the nuber of photocopies norally ade fro these journals. More precisely, the arguent relies on the assuption that a library s willingness to pay for journals should increase when photocopying is done on the preises because the availability of photocopying causes library users to value the library s journal holdings ore highly so that library funding will increase accordingly. Thus, these papers odel the arket for legal subscribers and photocopying as a arket for durable goods, where photocopying is odeled as siilar to a secondary arket for used durable goods. In contrast, our paper provides an alternative approach to the literature

4 166 Journal of Econoics & Manageent Strategy by ignoring the issue of appropriability of value fro copies, and focusing instead on network effects. esen and Kirby ( 1989) suarize these odels and argue that the differences in conclusions regarding the effects of private copying on social welfare result fro differences in ( 1) the extent to which the sellers of originals can appropriate the value placed on the by all users, ( ) the relative arket sizes for used and new copies, and ( 3) the degree of substitution between originals and copies. In the present paper we depart fro the literature in two ways. First, we introduce price copetition. Second, instead of focusing on appropriability, we introduce users network externalities and heterogeneity across consuers with respect to the level of utility they derive fro the support offered by software firs to their legal custoers. Hence, one can say that one of the contributions of the present paper is that it provides a rational, other than the ability to appropriate, for firs to ake copying r pirating easy. natural question to ask is why software piracy differs fro journal and book photocopying, or even audio- and video-cassette duplication. Pirating software differs fro journal and book photocopying in several aspects. 1. When software is not protected, any copy and copies of copies will be identical to the original. In contrast, paper and cassette copies are not equal to the originals, and copies of copies tend to be unreadable. Moreover, paper copying always loses inforation such as fine lines, fine print, and color iages ( even in color copying ).. Therefore, in the case of photocopying, the nuber of copies ade depends on the nuber of originals purchased in the arket, whereas software piracy can potentially originate fro a single diskette. 3. Journal and book publishers find it difficult and costly to physically protect their rights against illegal photocopying, whereas software developers can install protective devices that ake piracy very difficult, and soeties ipossible. 4. Software users depend on services and docuentation provided by developers, whereas copied journal articles and books can be. Consequently, our paper does not focus on the cost of duplication ( assued to be negligible for software) as a factor deterining the ratio of copies to originals. Instead, we concentrate on the service provided by software fir to legal users.

5 Strategic pproach to Software Protection 167 read without reference to the original publishers. Siilarly, listening and viewing audio and video cassettes does not require the use of any operating instructions fro the anufacturer. ecause of these differences, the law treats photocopying and software piracy in different ways. For exaple, Section 170 of Copyright ct states:... the fair use of copyrighted work... for purposes such as criticis, coent, newsreporting, teaching ( including ultiple copies for classroo use ), scholarship, or research, is not an infringeent of copyright. In contrast the Coputer Software Copyright ct does not have the equivalent fair-use doctrine. Therefore, the law recognizes that the arket consequences of photocopying for journal and book publishers are different fro those of software piracy. For this reason, we liit the scope of this paper to analyzing the software industry. The paper is organized as follows. Section develops a duopoly odel for the software industry where consuers value of a software package increases with the nuber of other consuers using the sae software. Section 3 solves for equilibriu software prices when firs do not protect their software. Section 4 solves for equilibriu when firs protect their software. Section 5 investigates the conditions under which software protection yields higher or lower industry profit than nonprotection. Section 6 analyzes arket configurations where firs follow different protection policies. Section 7 investigates the conditions under which protection or nonprotection constitutes an equilibriu in a noncooperative software industry and whether the software industry benefits fro the iposition of an industry-wide protection policy. Section 8 concludes.. Model of the Software Industry Consider an industry with two firs producing two differentiated software packages denoted by and located at the endpoints of the interval w0, 1 x. Let p denote the price of software package and p the price of software package. We assue that production is costless..1. Software Users Consuers are heterogeneous in two respects. First, soe consuers gain extra utility fro the services and support provided by the software firs to those custoers who pay for the software, whereas

6 168 Journal of Econoics & Manageent Strategy other consuers are support-independent and do not. 3 Second, consuers rank the two software packages differently. Forally, consuers are classified as: v Support-oriented consuers ( type 1 ), who gain an extra utility s ) 0 fro services and support provided by software firs to their legal custoers. The ideal software packages of the support-oriented consuers are uniforly distributed over the interval w0, 1 x. Thus, a consuer indexed by a high x is software--oriented, whereas a consuer indexed by a low x is software--oriented. v Support-independent consuers ( type ), who do not derive utility fro the services and support provided by the software firs to their legal custoers. The support-independent consuers are also uniforly distributed over the interval w0, 1 x. Whenever it is convenient, we will index these consuers by y ( rather than x ) to distinguish between the two types. The total population in the econoy has a easure of. Hence we suppose that the populations of support-oriented and support-independent consuers have the sae size; though restrictive, this assuption allows us to concentrate on the pure effect of copetition on the strategic choices ade by firs regarding software protection. This assuption is relaxed in the concluding section. Each consuer in the econoy has five options: the consuer can buy software, buy software, pirate software, pirate software, or not use any software. In case of pirating, the consuer does not pay for the software and does not receive any support fro software firs. ssuption 1: Software firs bundle the support with purchase. Illegal software users cannot obtain support fro an independent supplier. Let n ( siilarly, n ) denote the nuber of consuers who legally and illegally use software ( software ). We assue that consuers utility is enhanced with an increase in the nuber of other consuers using ( legally or illegally) the sae software package. The assuption of a network externality here eans that consuers benefit fro exchanging files generated by the sae software 3. This distinction is siilar to the distinction in the copying literature between the relative value of copies and originals to different consuers. For exaple, support-oriented consuers could also be those who are strongly risk-averse with respect to being prosecuted for using software illegally.

7 í Strategic pproach to Software Protection 169 packages and that files generated by different software are incopatible. 4 Thus, the utility of a consuer of type i s 1, and indexed by x g w0, 1 x is given by I i y x q n y p q s if buys software, y x q n if pirates software, U( x, i ) y ( 1 y x ) q n y p q s if buys software, i y ( 1 y x ) q n if pirates software, J 0 if does not use software, s, i s 1, where s ( 1) i x 0 i s, where G 0 is the coefficient easuring the iportance of the network size to a software user. The utility function ( 1) iplies that a support-oriented consuer will prefer buying software instead of pirating software if and only if s G p, that is, if the utility fro the custoer support provided by fir is larger than the package s price. Siilarly, a support-oriented consuer would prefer buying software over pirating software if and only if s G p. We will use the following notation. For a given price pair ( p, p ), let x be the support-oriented consuer who is indifferent between buying software and not buying any software. Forally, x is the solution to U( x, 1) s y x q n y p q s s 0. x is siilarly defined. Let y be the support-independent consuer who is indifferent between pirating software and not using any software. Forally, y is the solution to U( y, ) s y y q n s 0. y is siilarly defined. Finally, let x be the support-oriented consuer indifferent between software and. Forally x solves y x q n y p q s s y ( 1 y x ) q n y p q s, or 1 q ( n y n ) q p y p x s. ( ).. Software Industry Equilibriu Since consuers value of a particular software package increases with the nuber of people using it, we odel the arket as a two-stage gae in which both firs and consuers are players. The 4. Whereas the introduction of variable copatibility would ake the odel ore realistic, Chou and Shy ( 1993) show that partial copatibility generates severe discontinuity odeling probles.

8 170 Journal of Econoics & Manageent Strategy solution concept used is the subgae-perfect Nash equilibriu. In the first stage, firs select their software prices p g w 0, ` ) i. In the second stage, given any pair of prices, p and p, potential software users ake adoption decisions. software adoption equilibriu of a second-stage subgae is a partition of consuers between those who buy software ( ), those who pirate software ( ), and nonusers, such that no individual whose utility is specified in ( 1) would be strictly better by changing his adoption or nonadoption behavior. The proof of the following lea is given in ppendix. Lea 1: Let p and p be any pair of prices satisfying p, p F s. If 1 -, then there is an adoption equilibriu such that all support-oriented consuers buy software. However, when both p and p are large enough, there exists a second adoption equilibriu, which turns out to be unstable. This equilibriu involves soe support-oriented consuers who do not buy and do not pirate any software. We analyze this equilibriu for software only. It is described by the following conditions: y x y p q n q s s 0, y y q n s 0, and n s x q y, which are solved for 1 y x s ( s y p ), 1 y 1 which is saller than as long as p is close enough to s. This equilibriu is unstable because slightly increasing ( decreasing) the nuber of users leads to an increase ( decrease) in s network size, thereby increasing ( decreasing) both the nuber of support-oriented consuers buying software and the nuber of support-independent users pirating this software. Note that this instability is generated by arginal deviation of support-oriented and r or supportindependent consuers. Hence, there exists a unique stable equilibriu such that the entire support-oriented population is served, whereas the second equilibriu is unlikely to be realized. In what follows we focus only on the stable adoption equilibriu. Then, firs profits are defined as the nuber of consuers buying their software ties their price ( recall that the nuber of buyers can be saller than the nuber of users, since soe users ay pirate the software ). In the first stage, we solve for a Nash

9 Strategic pproach to Software Protection 171 equilibriu where both firs siultaneously choose their prices so as to axiize their profit. We ake the following assuptions. 1 ssuption : The network-effect paraeter is bounded: -. If ssuption is reversed, then there does not exist a purestrategy Nash equilibriu in software prices in which both firs sell strictly positive aounts and earn strictly positive profits. In fact, when network effects are very strong, each fir wants to undercut its rival s price by subsidizing the transportation cost of the consuer ost oriented toward its rival, thereby gaining a larger network of consuers. ssuption 3: The support-oriented consuers place a high value 3 on the support they can receive fro software firs. Forally, s ). This assuption allows us to restrict the nuber of arket configurations to be investigated in that only the support-independent consuers ay find it optial to opt out. In the next two sections we first describe consuers behavior and then solve for equilibriu prices when neither fir protects its software and when both firs protect their software. 3. Equilibriu Prices When Firs Do Not Protect Their Software Suppose that neither fir protects its software; hence each consuer can either buy the software ( and obtain support, if needed ), or can costlessly pirate and use the software ( without obtaining support ). It follows fro the utility functions given in ( 1) that no consuer will purchase software i if p i ) s, since the software s price exceeds the support-oriented consuers utility fro the service provided by the software firs to legal users. In this case all users will prefer pirating software over buying it. Hence, in equilibriu it ust be that software firs set p F s, i s,. Therefore, ( 1) i iplies that support-oriented consuers never pirate software. ong the support-oriented consuers, we know that the consuer who is indifferent between buying software and buying software is given by x s 1 q ( n y n ) q p y p

10 17 Journal of Econoics & Manageent Strategy whose location is depicted in the upper part of Figure 1. Notice that the location of the arginal consuer is affected not only by the relative software prices, p y p, but also by the difference in network sizes, n y n. s shown in the following lea, the utility function ( 1) and ssuption iply, with a zero reservation utility, that soe support-independent consuers will not use any software even if they can obtain it illegally for free ( the proof is given in ppendix ). Lea : When neither fir protects its software, ( a) soe support-independent users pirate software and soe pirate software, and ( b) soe support-independent consuers do not use any software. The consequences of Lea are illustrated in the botto part of Figure 1, where soe ( but not all) of the support-independent consuers pirate software. Recall that y ( y ) denotes the supportindependent consuer who is indifferent between pirating software ( software ) and not using any software. Therefore, y s n and y s 1 y n. ( 3) For the consuer partition depicted in Figure 1 to constitute an adoption equilibriu, the nubers of and ( legal and illegal) users are iplicitly given by 1 y n y p q p n s x q y q, y 3 1 y n y p q p n s ( 1 y x ) q ( 1 y y ) s. y 3 FIGURE 1. TOP: THE SUPPORT-ORIENTED CONSUMER, x, WHO IS INDIFFERENT ETWEEN UYING -SOFTWRE ND - SOFTWRE; OTTOM: THE SUPPORT-INDEPENDENT CON- SUMER, y ( y ), WHO IS INDIFFERENT ETWEEN PIRTING SOFTWRE ( SOFTWRE ) ND NOT USING NY SOFTWRE.

11 Strategic pproach to Software Protection 173 Solving for n and n yields ( p y p y ) y p q p q 1 n s and ( y 3 q 1) ( p y p y ) q p y p q 1 n s. ( y 3 q 1) ( ) 4 ( ) ( ) Substituting 4 into, we have ( p y p y ) y p q p q 1 x ( p, p ) s. ( 5) ( 1 y ) We now look for a Nash equilibriu in software prices in which fir chooses p to axiize p s p x( p, p ) and fir chooses p to axiize p s p w 1 y x( p, p )x, where x( p, p ) is given in ( 5 ). The best-response functions are given by 1 y p p s R ( p ) s q if p - s, ( 1 y ) 1 y p p s R ( p ) s q if p - s. ( 6) ( 1 y ) The equilibriu prices and profit levels when both firs do not protect are given by 1 y 1 y u u u u ( ) 1 y ( 1 y ) p s p s ) 0 and p s p s ) 0. 7 Using ssuption 3, it can be checked that the equilibriu prices are saller than s, thereby satisfying the two best-response functions ( 6 ). Substituting ( 7) into ( 4) yields 1 1 u u n s n s ), ( 8) ( 1 y ) iplying that soe support-independent consuers pirate software. To find the nuber of consuers pirating software and, we

12 174 Journal of Econoics & Manageent Strategy ( ) subtract the nuber of legal users fro 8. Therefore, u u y s 1 y y s y s -. ( 1 y ) ( 1 y ) Consequently, we have shown: Proposition 1: When software is unprotected, a unique equilibriu exists for any adissible value of. 4. Equilibriu Prices When Firs Protect Their Software We now suppose that each software fir possesses the eans of protecting their software packages, thereby aking software piracy not beneficial to any consuer. For exaple, each software fir ay set the software so that a special plug or a chip is necessary to launch the application. Then consuers ust choose between buying the software and not using any software. In order to highlight the strategic iportance of protection, we assue that software protection is costless for the software firs ( see also Conner and Ruelt, 1991 ). Lea shows that not all support-independent consuers pirate software when software is unprotected. Therefore, when software is protected, it ust be that soe support-independent consuers do not purchase any software. Consequently, we need to derive equilibriu prices for the two cases where ( i) soe ( but not all) support-independent consuers buy software, and ( ii) none of the support-independent consuers buy software Soe Support-Independent Consuers Purchase Software The arginal support-oriented consuer is still given by ( ). The support-independent consuer y who is indifferent between buying Software and not using any software is found by solving U( y, ) s y y q n y p s 0. Siilarly, the support-independent consuer y who is indifferent between purchasing software and not using any software is found by solving U( y, ) s y ( 1 y y ) q n y p s 0. Hence, y s n y p and y s 1 y n q p. ( 9) 5. Recall that we have seen in Section. that, for any price pair, there exists a unique stable adoption equilibriu, so that the first-stage profit functions are uniquely defined.

13 Strategic pproach to Software Protection 175 The nuber of -software users ( which equals the nuber of -buyers, since software is protected) is n s x q y. The nuber of -software users ( buyers) is equal n s ( 1 y x ) q ( 1 y y ). Substituting ( ) and ( 9) into these equations and then solving siultaneously for n and n yields ( p y 1) y 3 p q p q 1 n s and ( y 3 q 1) ( p y 1) y 3 p q p q 1 n s. ( 10) ( y 3 q 1) Since both software firs protect their software, the nuber of buyers equals the nuber of users of each software package. Therefore, fir chooses p to axiize p s pn, and fir chooses p to axiize p n, where n and n are given in ( 10 ). The best-response functions are given by s s 1 y q p p s R ( p ) s if p - ( 3 y 4 ), 1 y q p p s R ( p ) s if p - ( 3 y 4 ). ( ) 11 Therefore, if a Nash equilibriu exists, it ust be that prices, nubers of buyers, and profit levels are given by 1 y 3 y 4 p p p p p s p s, n s n s, 5 y 8 ( 1 y )( 5 y 8 ) ( 1 y )( 3 y 4 ) p p p s p s. ( 1 y )( 5 y 8 ) ( ) 1 The nubers of support-independent consuers buying software and software are given by 8 y 9 q y s n y p s s 1 y y ( 1 y )( 8 y 5) p p p Ö 9 y 17 G 0 if and only if ). 16

14 176 Journal of Econoics & Manageent Strategy def Let s. The following proposition is proved in ppendix C. 5 Proposition : When software is protected, an equilibriu where soe support-independent consuers buy software exists if and only if G. If -, the network effect is sufficiently weak to induce each fir to raise its price, thereby specializing upon support-oriented consuers only. In contrast, when G protection leads to an increase in the nuber of buyers fro both firs. This follows fro the fact that no support-independent consuers buy software in the absence of protection. However, in spite of the increase in sales, coparing ( 7) and ( 1) reveals that firs ake lower profits under protection. This is due to the fact that protection results here in a sharp drop in equilibriu prices, as shown by coparing ( 7) and ( 1 ). 4.. Support-Independent Consuers Do Not uy Software We now solve for an equilibriu where software firs set high prices, so all support-independent consuers refrain fro buying ( and hence fro using) any software. In this case, n s x and n s 1 y x, where x is given in ( ). Solving these two equations for n and n yields 1 y y p q p 1 y y p q p n s and n s. ( 1 y ) ( 1 y ) Fir chooses p to axiize p s pn, and fir chooses p to axiize p s p n, yielding best-response functions p s R ( p ) s ( 1 y q p ) r and p s R ( p ) s ( 1 y q p ) r. Hence, the candidate equilibriu prices, nuber of buyers, and profit levels are 1 1 y p p p p p p p s p s 1 y, n s n s, p s p s. ( 13) We need to confir that at these prices, none of the support-independent consuers buys any software. To see this, observe that the utility of the consuer indexed by y s 0 when buying software is 1 1 U( 0, ) s y 0 q = y ( 1 y ) - 0, since -. Finally, in order for the prices ( 13) to constitute an equilibriu, no fir should be able to increase its profit by sharply reducing its price, thus attracting soe of the support-independent consuers to

15 Ö Strategic pproach to Software Protection 177 buy its software. ppendix D provides the proof for the following proposition. Let def 5 y 17 s. ( 14) M Proposition 3: When software is protected, an equilibriu where no support-independent consuers buy software exists if and only if F. 6 M If the condition of the proposition is reversed, the network effect becoes so strong that each fir can increase its profit by unilaterally lowering its price, thereby aking soe support-independent consuers buying its software. Coparing ( 7) and ( 13) reveals that firs now ake higher profits under protection, because price copetition is softened due to the weaker effect of saller network sizes Suary of Equilibria When oth Firs Protect We have shown that, depending on the value of, when both firs protect their software so that piracy is not an option for consuers, two equilibria ay exist: a low-price equilibriu where soe service-independent consuers buy software, and a high-price equilibriu where service-independent consuers do not buy ( and therefore do not use) any software. Figure illustrates how the two equilibria are related to the network paraeter. FIGURE. SUMMRY OF EQUILIRI WHEN OTH FIRMS PRO- TECT THEIR SOFTWRE. SI s support-independent consuers. 6. For s there exist two equilibra. M

16 178 Journal of Econoics & Manageent Strategy 5. Software Industry s Protection Policy In this section, we analyze how software protection affects industry profit and software prices by coparing the two policies analyzed in Sections 3 and 4. First, for F, coparing ( 7) and ( 8) with ( 13) yields M u p u p p y p s - 0, n y n s ) 0, y 1 ( 1 y ) u p p y p s - 0. ( y 1) ( ) 15 ( ) ( ) ( ) Second, for G, coparing 7 and 8 with 1 yields ( 1 y )( 4 y 7 ) u p p y p s ) 0, ( 1 y )( 5 y 8 ) 1 y u p n y n s ) 0, ( 16) ( 1 y )( 5 y 8 ) ( 1 y ) ( 11 y 16 ) u p p y p s ) 0. ( 1 y )( 5 y 8 ) ( ) ( ) Last, prices and profits are higher in 13 than in 1. These results lead to the following proposition. Proposition 4: ( ) 1. There are ore buying plus pirating software users when firs do not protect than when firs protect their software.. Let 0 - F. Then firs prices and profit levels are higher when both firs protect their software. 3. Let - F M. Then profits are higher under protection at the high-price equilibriu, and lower at the low-price equilibriu, than profits under nonprotection Let M - -. Then firs prices and profit levels are higher when firs do not protect their software. The intuition behind Proposition 4 is as follows. For sall values of ( F ), the network effect is weak and the sole buyers are the support-oriented consuers. Hence, the price-copetition effect doinates the network effect and both firs are better off by protecting, since this allows the to relax price copetition in a

17 Strategic pproach to Software Protection 179 arket of a given size. In contrast, for large values of ( ) ) M, the network effect is stronger than the copetition effect, so that both firs gain by expanding the network of users. lthough firs could expand the nuber of legal users by protecting the software, they earn higher profits by not protecting, because they are able to charge a uch higher price to the support-oriented consuers. Finally, for the interediate values of ( belonging to a doain of size saller than 0.04 ), it is hard to predict what is the optial industry policy, since it depends on the particular equilibriu that will arise under protection. However, since for - F M the high-price equilibriu under protection doinates both the equilibriu without protection and the low-price equilibriu under protection fro the firs viewpoint, it is reasonable to suppose that inial coordination will take place within the industry, leading firs to select the high-price equilibriu together with the protection policy. ltogether, we ay conclude that it is in the interest of the software industry to ipleent nonprotection when network effects are strong, while protection is preferable otherwise. Though epirical evidence is issing, the first scenario ight well be the ore likely one for the software industry. 6. Equilibriu Prices When Fir Protects and Fir Does Not Protect In order to study a noncooperative software industry where firs are free to choose their own protection policy, we need to derive equilibriu prices when firs use different protection policies. With no loss of generality, suppose that fir protects its software whereas fir does not. In this case, siilarly to the analysis of Section 4, there can be two equilibria: one in which soe service-independent consuers purchase software ( the protected software) and a second one where the price of -software is high, so that service-independent consuers do not purchase software Soe Support-Independent Consuers Purchase Software Let y ) 0. Then the nuber of support-independent consuers buying software is given by ( 9 ), so that n s x q y. Siilarly, the nuber of support-independent consuers pirating software can be obtained fro ( 3 ), so that n s 1 y x q 1 y y. Substituting for x

18 Ö 180 Journal of Econoics & Manageent Strategy into these equations and solving siultaneously for n and n yields 1 y q ( 4 y 3) p q ( 1 y ) p n s x q y s, ( y 3 q 1) 1 y q p q ( y 1) p n s 1 y x q 1 y y s. ( y 3 q 1) Fir chooses p to axiize p s pn, and fir chooses p to axiize p s p ( 1 y x ). Solving the first-order conditions yields the prices ( ) 3 y 1 16 y q 7 p u p s and p s. ( 17) 16 y 11 ( y 1)( 16 y 11) Hence, the nubers of users of each software package are 3( 4 y 3) 8 y 7 p u n s and n s. ( 1 y )( 16 y 11) ( 1 y )( 16 y 11) It is readily verified that the corresponding value of y is positive if and only if ) ( 9 y 17 ) r 16. Finally, the profit levels are given by 9( y 1)( 4 y 3) p p s and ( 1 y )( 16 y 11) ( )( 8 y 7 16 y q 7) u p s. ( 1 y )( 16 y 11) ( ) 18 It reains to check under which conditions fir does not find it profitable to raise its price and to serve only the support-oriented consuers. The following proposition is proven in ppendix E. Proposition 5: If G, then ( 17) constitutes a unique asyetric price equilibriu. 6.. Support-Independent Consuers Do Not Purchase Software When y s 0, the nuber of software- buyers ( which equals the nuber of users) is n s x, where x is given in ( ). The nuber of support-independent consuers who pirate software is found fro

19 Strategic pproach to Software Protection 181 y ( 1 y x ) q n s 0, where x is given in ( ). Substituting ( ) into these equations, and solving siultaneously for n and n yields n s x s 1 y y ( 1 y )( p y p ) p and y 4 q 1 y q p y p u n s 1 y x q 1 y y s. y 4 q Fir chooses p to axiize p s p x, and fir chooses p to axiize p s p ( 1 y x ), yielding the prices y 6 q 3 y 6 q 3 p u p s and p s. ( 19) 3( 1 y ) 3( 1 y ) Hence, the nubers of users are y 6 q 3 y 6 q 3 p u n s and n s. ( ) ( )( 3 y 4 q 3 1 y y 4 q ) It can now be easily verified that n p y p p - 0; hence service-independent consuers do not purchase software. lso, it can be u 1 1 shown that n ) and that x ), which iplies that soe support-independent consuers pirate software. Finally, the profit levels are ( ) y 6 q 3 p p p s p x s, ( )( 9 1 y y 4 q ) ( ) y 6 q 3 u p s p u ( 1 y x ) s. 9( 1 y )( y 4 q ) ( ) 0 We now check under which conditions fir will find it unprofitable to lower its price and to serve soe support-independent consuers. ppendix F provides the proof for the following proposition. Proposition 6: If F, then ( 19) constitutes a unique asyetric price equilibriu.

20 18 Journal of Econoics & Manageent Strategy Equations ( 19) and ( 0) as well as ( 17) and ( 18) reveal that p u ) p p and p u ) p p regardless of the value of. In words, for any degree of network effect, the unprotecting fir charges the higher price and earns a larger profit. The intuition is that, due to the network effects, the fir that does not follow a protection policy can charge a higher price because its software is used by ore consuers, and hence is ore valuable to soe support-oriented consuers. Despite the fact that this fir has a saller nuber of buyers 1 than its rival ( x ) ), it earns a higher profit. 7. Software Protection Strategies So far, we have investigated the effects of software protection assuing that firs follow the sae policy regarding protection. In this section, we investigate a noncooperative software industry where each fir is free to choose its own protection policy. To this end, we add a preliinary stage in which both firs siultaneously choose fro the two-action set v U, P 4, where U stands for not protecting and P for protecting. In the reainder of the paper, we ignore the sall paraeter range - - M in order to liit the nuber of cases to investi- gate and to focus upon low or high network effects only. It is our belief that not uch relevant inforation is lost by aking this assuption. We will use the following terinology. Definition 1: We say that network effects are weak if - and strong if ). M 7.1. Equilibriu Protection Policies under Weak Network Effects Suppose that -. Table I provides the profit levels of software firs and for the four possible outcoes, given in ( 7 ), ( 13 ), and ( 0 ). Direct calculations fro Table I yield the following result. Proposition 7: When network effects are weak, 1. if , both firs protecting their software, ( P, P ), constitutes a unique Nash equilibriu;. If G 0.765, there are exactly two Nash equilibria, ( P, U) and ( U, P ), where one fir protects its software and the other does not. Thus, when the network effects are very weak, an industry-wide protection policy is supported as a Nash equilibriu. For stronger

21 Strategic pproach to Software Protection 183 table I. Equilibriu Profits under Weak Network Effects Fir P U 1 y 1 y ( y 6 q 3 ) ( y 6 q 3 ) Fir P 9 ( 1 y )( y 4 q ) 9 ( 1 y )( y 4 q ) ( y 6 q 3 ) ( y 6 q 3 ) 1 y 1 y U 9 ( 1 y )( y 4 q ) 9 ( 1 y )( y 4 q ) ( 1 y ) ( 1 y )

22 184 Journal of Econoics & Manageent Strategy but still oderate network effects, asyetric protection policies are the only equilibria and they do not support collusion. 7.. Equilibriu Protection Policies under Strong Network Effects Suppose that ) M. Table II provides the profit levels of software firs and for the four possible outcoes, given in ( 7 ), ( 1 ), and ( 18 ). Direct calculations fro Table II yield the following result. Proposition 8: When network effects are strong, there are exactly two equilibria, ( P, P) and ( U, U ), where both firs protect or both refrain fro protecting their software. n iportant conclusion that we draw fro this proposition is that a utual decision to protect or not to protect software can be enforced as a noncooperative outcoe. s shown by Proposition 4, ( U, U) yields strictly higher profits to both firs than ( P, P ), so that it is reasonable to assue that ( U, U) will prevail. Consequently, the foregoing result provides a rationale why software firs have coplied with consuers desires to reove protection fro software packages since the id-1980s. Our result also shows that not protecting can be sustained as a Nash equilibriu of the protection gae when network effects becoe sufficiently strong, soething that sees to have happened as coputers gradually entered our daily routine Sequential Choice of Protection Policies s suggested by a referee, it is worthwhile to investigate a decisionaking process in which one fir chooses its protection policy before its rival, while prices are siultaneously chosen only after both firs have selected their protection policies. Under sequential oves, Proposition 7 reains unchanged except for part, where ( U, P) is a unique equilibriu, since the fir that is first to choose its protection policy will choose not to protect, as that yields larger profits ( see discussion following Proposition 6 ). On the other hand, Proposition 8 is odified in that ( U, U) is the only equilibriu outcoe, since it yields a higher industry profit and therefore the first over will pick U. This additional result highlights the fact that, for strong network effects, nonprotection is the unique equilibriu outcoe.

23 Strategic pproach to Software Protection 185 table II. Equilibriu under Strong Network Effects Fir P U ( 1 y )( 3 y 4 ) ( 1 y )( 3 y 4 ) 9 ( y 1 )( 4 y 3 ) ( 8 y 7 )( 16 y q 7 ) Fir P ( 1 y )( 5 y 8 ) ( 1 y )( 5 y 8 ) ( 1 y )( 16 y 11 ) ( 1 y )( 16 y 11 ) ( 8 y 7 )( 16 y q 7 ) 9 ( y 1 )( 4 y 3 ) 1 y 1 y U ( 1 y )( 16 y 11 ) ( 1 y )( 16 y 11 ) ( 1 y ) ( 1 y )

24 186 Journal of Econoics & Manageent Strategy 8. Concluding Rearks The paper analyzes a trade-off faced by copeting software firs. Each fir can increase the copetitive value of its software by not protecting it. lternatively, each fir can protect its software by reducing the nuber of users to the nuber of buyers, thus aking its software less attractive. Proposition 4 deonstrates that a coordinated software industry should choose not to protect the software when the network effects are strong. The reason is that a larger nuber of users increases the utility of software. Thus, the paper provides a strategic reason why the use of software protection has declined since the id-1980s. Our results were derived under the assuption that the nubers of support-oriented and support-independent consuers are the sae and equal to one. One ay wonder how our results would be affected when there are fewer support-independent than support-oriented consuers. In order to gain soe insight, we consider the extree case in which there are no support-independent consuers. In this case, it is readily verified that the equilibriu profits are p s p s ( 1 y ) r, which are exactly the equilibriu profits given in ( 13) when network effects are not strong and both firs protect. This is because under the high-price equilibriu support-independent consuer do not buy the software, thereby aking their arket iaterial. On the other hand, when network effects are strong, p s p s ( 1 y ) r can no longer be obtained in equilibriu, since price copetition is very intense due to the stronger network effects in the presence of support-independent consuers. This discussion leads to the following iportant conclusion: when network effects are not strong, protecting is equivalent to the nonexistence of support-independent consuers. When network effects are strong, that is no longer so. Indeed, in this case we have shown that firs prefer not to protect their software. ltogether, under strong network effects firs are hared by the existence of support-independent consuers, and we conjecture that they becoe worse off as the relative nuber of support-independent consuers rises. ppendix. Proof of Lea 1 The support-oriented consuer who is indifferent between software and is p y p q ( n y n ) q 1 x s. ( 1)

25 Strategic pproach to Software Protection 187 Since n s x q y and y s n, we obtain x n s. ( ) 1 y Siilarly, since n s ( 1 q x ) q ( 1 y y ) and 1 y y s n, we get 1 y x n s. ( 3) 1 y ( ) ( ) ( ) Substituting and 3 into 1 yields 1 y 1 x s ( p y p ) y. ( 4) ( 1 y ) To prove the lea, it reains to show that the utility of consuer x is strictly positive. Substituting ( 4) into ( ) and then into ( 1 ), soe anipulations lead to 1 p q p U( x, 1) s y q s y ) 0, ( 1 y ) 1 because p, p F s and -. ppendix. Proof of Lea ( a ): Lea 1 iplies that, in equilibriu, all support-oriented consuers are served, so that n q n G 1. With no loss of generality, 1 we can assue that n G. y way of contradiction, suppose that none of the support-independent consuers pirate any software. Hence, the utility of the support-independent consuer indexed by y s 0, when pirating software, is U( 0, ) s y 0 q n ) 0, a contradiction. ( b ): If all support-independent consuers pirate software, then it ust be that n q n s. Consider the nondegenerate interval ( n, n q 1 y ) of the support-independent consuers. For any y in this interval, we have y ) n, so that y y q n - 0, which iplies that consuer y does not pirate software. Siilarly, we have y - n q 1 y, or equivalently, y 1 q y q y n - ( ) 0, which in turn aounts to y 1 y y q n - 0, since n s y n, so that consuer y does not want to pirate software.

26 188 Journal of Econoics & Manageent Strategy ppendix C. Proof of Proposition Suppose that fir aintains its equilibriu price, p s ( 1 y ) r ( 5 y 8 ). We now check under what condition fir cannot increase its profit by raising its price p, thereby losing its support-independent consuers. Substituting p s ( 1 y ) r( 5 y 8 ) into ( ) yields x s w ( n y n ) y p q ( 1 y ) r ( 5 y 8 )x r. The nuber of -users ( -buyers) is now n s x. Substituting x into this equation and solving for n yields n ( ) ( y 8 y 10 q 3 q 8 y 13 q 5) p s. ( y 4 q )( 8 y 5) Fir chooses p to axiize p s p x, yielding 8 y 10 q 3 ( 8 y 10 q 3) p s, p s. ( )( ) y 1 8 y 5 ( 1 y )( y 4 q )( 8 y 5) ( ) 5 To find under which condition this deviation by fir is not profitable, we check that the profit given ( 5) is saller than or equal to the profit given in ( 1) if and only if G. ppendix D. Proof of Proposition 3 Suppose that fir aintains its equilibriu price, p s 1 y, given in ( 13 ). We now check under what condition fir cannot increase its profit by lowering its price, p, thereby attracting soe support-independent consuers to buy software. Substituting p s 1 y into ( ) yields x s w ( n y n ) y p q y x r. The support-independent consuer who is indifferent between buying software and not using any software is given by y s n y p. The nuber of -users ( -buyers) is n s x q y. The nuber of -users ( -buyers) is n s 1 y x ( support-independent consuers do not purchase -software at p s 1 y ). Substituting x and y into these equations and solving for n yields ( 1 y ) y ( 3 y ) p n s. y 4 q 5

27 Ö Strategic pproach to Software Protection 189 Fir chooses P to axiize p s p n, yielding 1 y 1 y p s, n s, 3 y y 4 q ( 1 y ) p s. ( 3 y )( y 4 q ) ( ) 6 To find under which condition this deviation by fir is not profitable, one can show that the profit given ( 6) is saller than or equal to the profit given in ( 13) if and only if F ( 5 y 17 ) r. ppendix E. Proof of Proposition 5 Consider a price deviation by fir such that this fir serves only support-oriented consuers, that is, y s 0. Substituting for p given in ( 17) into ( ), we obtain n y 6( 8 y 10 q 3) q ( 16 y 17 q 11) p s x s. ( y 4 q )( 16 y 11) The axiu profit under deviation is then given by ( ) 9 8 y 10 q 3 p s. ( 7) ( 1 y )( y 4 q )( 16 y 11) ( ) ( ) Coparing 18 and 7 shows that deviation is not profitable if and only if G. ppendix F. Proof of Proposition 6 Consider a price deviation by fir such that this fir serves soe support-independent consuers, that is, y ) 0. In this case, we have ( y 6 q 3) q 3( 4 y 3) p n s x q y s. ( 6 y 3 q 1)

28 190 Journal of Econoics & Manageent Strategy The axiu profit under deviation is then given by ( ) y 6 q 3 p s. ( 8) 18( 3 y 4 )( y 3 q 1) ( ) ( ) Coparing 0 and 8 shows that deviation is not profitable if and only if F. References esen, S. and S. Kirby, 1989, Private Copying, ppropriability, and Optial Copying Royalties, Journal of Law and Econoics, 3, 55] 80. rynjolfsson, E. and C. Keerer, 1996, Network Externalities in the Microcoputer Software: n Econoetric nalysis of the Spreadsheet Market, Manageent Science, 4, 167] Chou, C. and O. Shy, 1993, Partially Copatible rands and Supporting Services, Econoics Letters, 41, 193] 197. Conner, K. and R. Ruelt, 1991, Software Piracy: n nalysis of Protection Strategies, Manageent Science, 37, 15] 139. Gandal, N., 1994, Hedonic Price Indexes for Spreadsheets and an Epirical Test of the Network Externalities Hypothesis, RND Journal of Econoics, 5, 160] 170. Givon, M., V. Mahajan, and E. Muller, 1995, Software Piracy: Estiation of Lost Sales and the Ipact on Software Diffusion, Journal of Marketing, 59, 9] 37. Johnson, W., 1985, The Econoics of Copying, Journal of Political Econoy, 93, 158] 174. Liebowitz, S., 1985, Copying and Indirect ppropriability: Photocopying of Journals, Journal of Political Econoy, 93, 945] 957. Novos, I. and M. Waldan, 1984, The Effects of Increased Copyright Protection: n nalytical pproach, Journal of Political Econoy, 9, 36] 46.