Software Piracy: A Strategic Analysis and Policy Instruments

Transcription

1 Software Piray: A Strategi Anaysis and Poiy Instruents Dyuti S. BANERJEE a Otober 00 Abstrat We eaine te governent s roe in restriting oeria iray in a software arket. Wefare aiization ay or ay not resut in onitoring as te soiay otia outoe. Corresondingy eiter onooy situation or arket saring between an origina fir and a irate are subgae erfet euiibria. If it is rofitabe for a onooist to revent iray by instaing a rotetive devie ten not onitoring is te euiibriu. We aso disuss te effets of network eternaities in addition to deriving te effets of anges in te reiabiity of te irated software and network benefits on te oiy variabes te etent of iray and te onooist s inentive to revent iray. Keywords: Network eternaities riing strategy reiabiity fator JEL Cassifiation: K4 L0 a Te autor woud ike to aknowedge Cey Fook Heng for is resear assistane. Te suggestions and oents of Noe aston are seiay aknowedged. Te autor woud aso ike to tank Sugata Marjit Steen Martin Ivan Png Sougata Podder and an anonyous referee for vauabe oents. Naturay te usua disaiers ay. Corresonding autor: Dyuti S. Banerjee Soo of Business Bond University od Coast Queensand 49 Austraia. e-ai: dyuti_banerjee@bond.edu.au.

2 . INTRODUCTION Te eisting iterature on software iray addresses te issue fro te viewoint of iray by end-users and te iortane of network effets in roteting te software industry against iray. Cen and Png 999 sow tat it is better for a fir to dea wit iray by end-users troug riing rater tan onitoring. Ceng Sis and Teegen 997 and Noyee 990 ention tat te ig rie of software is te doinant reason for iray. Sy and Tisse 999 sow tat for strong network effets no rotetion against iray is an euiibriu for a nonooerative software industry. Earier resear by Takeyaa 994 Conner and Ruet 99 and Nasiento and Vanonaker 988 aso disusses te roe of network effets on te arketing of software. However te issue of governent oiy towards iray as iterto not been addressed. Tere is great variation in te iray rates defined as te ratio of te nuber of irated oies to tota instaed oies aross ountries. For eae in 997 te iray rates range fro 7 erent in te United States to 98 erent in Vietna. Tese figures inude oying by end-users and te sae of irated software. An iortant iiation is tat te software arket in soe ountries is very ose to a onooy wie in oters tere is a varying degree of arket saring between an origina fir and irates wo offer unautorized rerodutions of iensed software oeriay to oete wit te origina software. Te eistene of su a setru of arket strutures ay be due to differenes in te governents stane towards iray and te resoures reuired in ieenting teir oiies. In tis aer we eaine te governent s roe in ontroing iray troug

3 its oie of oiy instruents. We onsider a arket in wi tere is an origina software fir ereafter referred to as te onooist and tere is aso software ounterfeiting by a irate wo offers unautorized rerodutions of iensed software oeriay to oete wit te onooist s software. In su a arket te onooist wo ay not be oay eaduartered ay even be ereived wit soe ostiity and te governent ay ignore te onooist s inentive to innovate and ae greater vaue on te sort run benefits assoiated wit iray. Te doesti soia-wefare aiizing oiy instruents wi onsist of onitoring and enaizing te irate s iega oerations endogenousy deterine weter or not tere wi be arket saring between te onooist and te irate. Te otia oies of oiy variabes refet te governent s attitude towards iray. We aso study te onooist s roe in reventing iray troug instaing a tenia rotetive devie tat revents oying. We ten disuss te effets of network eternaities on te otia oiy instruents te etent of iray and te onooist s inentive to revent iray. A network eternaity eans tat a onsuer s utiity fro using software inreases wit an inrease in te nuber of oter onsuers using te sae software. Tey benefit troug te eange of fies using te sae software. In our ode tere is a eterogeneous grou of onsuers wit different vauations of te software. Te reiabiity of te irated software is te ony differene between te origina software and te forer. We anayze tree riing gaes Bertrand eader-foower and onooy riing. In te onooy riing See IPR 998

4 gae te onooist arges te re-entry onooy rie ignoring te treat of entry by te irate. We inude tis gae to study te oiy variabes tat ay restore te onooy outoe. Assuing tat onitoring is osty te governent ooses te oiy variabes tat aiize doesti soia-wefare subjet to baaned budget onstraints. Te atter is assued to avoid issues of redistribution. In te ase of net revenue aiization te surus is distributed aong te ouation troug soe transfer eanis. Wefare aiization ay or ay not resut in onitoring as te soiay otia outoe. Corresondingy te onooy situation and te eader-foower outoe are te two subgae erfet euiibria. Te resut deends on te onitoring tenoogy refeted in te onitoring ost wi is a deadweigt oss and oter araeters su as te size of te arket and te reiabiity fator. So te soia-wefare aiizing objetive deterines te governent s aggressiveness or assiveness towards iray wi in turn deterines te otia arket struture. Te onooist an aso revent iray by instaing a rotetive devie as ong as te net onooy rofits fro doing so eeed rofits wen te arket is sared. In tis ase not onitoring is te euiibriu. Intuitivey if te onooist an revent iray te governent does not need to onitor. Te otia onitoring rate tat resuts in te onooy outoe is iger wen tere are network eternaities. It aso resuts in an inrease in te etent of iray and te onooist s inentive to revent iray. Coarative stati resuts sow tat anges in te reiabiity of te irated software and network benefits ave ositive effets on iray te onooist s inentive to rotet is software and te otia onitoring rate tat resuts in te onooy outoe. 4

5 Te aer is arranged as foows. In setion we disuss te ode te different riing gaes and te euiibriu governent oiies. In setion we eaine te effet of network eternaities. In setion 4 we rovide soe onuding rearks.. THE MODEL WITHOUT NETWORK EXTERNALITIES We onsider four tyes of agents: te onsuers te deveoer of an origina akaged software referred to as te onooist a irate wo iegay rerodues and ses iensed software and te governent wi is resonsibe for onitoring and enaizing te irate. We begin our anaysis by desribing te onooy situation in te absene of iray. Tere is a ontinuu of onsuers indeed by [ ]. is assued to foow a unifor distribution. We assue tere is no resae arket for used software. Ea onsuer is assued to urase ony one unit of te software. Foowing Tiroe 988 te utiity of a tye onsuer fro urasing a unit of te software is if te onsuer buys te software U 0 if te onsuer does not buy. is te vauation of te onsuer and is te rie of one unit of te software arged by te onooist. Tus in te ode onsuers differ fro one anoter on te basis of teir vauation of te software. Te eterogeneity of te onsuers reresented by te different agnitudes of an be interreted as a funtion of fators ike software usage freueny degree of utiization user rofiieny and so on. Higer agnitudes of ea of tese fators are indeed by iger vaues of. is te argina onsuer wo is indifferent between buying and not 5

6 buying: U 0. In te absene of iray te onooist faes te deand funtion D d. We treat te ost inurred by te onooist to deveo te software as a sunk ost. Te ost of reiating te software after it as been deveoed is assued to be zero. Hene te eeted rofit of te onooist is te tota revenue wi is D. Te onsuer surus is CS d. Te euiibriu onooy resuts are 4 and CS 8. 4 Now assue tat a irate eists in te arket. We furter assue tat wit te advent of digita tenoogy and in-buit douentation and software suort identia oies an be ade fro te origina software wit a negigibe oss in uaity. Te ost of duiating is assued to be zero. Te differene between te origina and te irated software ies urey in te risk of defet for a irated oy. Sine te irate oerates in te arket using a akesift arrangeent if te irated software turns out to be defetive tere is no ane of getting te defetive software reaed. Te irated software is oerationa wit a robabiity 0 were is given eogenousy. Wit robabiity any artiuar unit turns out to be defetive in wi ase te buyer oses te We set tis bound to ensure tat te rofits are not indeterinate. 6

7 rie beause te irated oy is not under warranty. is a easure of te reiabiity of te irated version of te software and is assued to be oon knowedge. We assue tat te origina rodut reeives fu warranty. Te utiity of a tye onsuer is U 0 if te onsuer buys te origina software if te onsuer buys te irated software if te onsuer does not buy. 5 and is te rie and effetive vauation of te irated oy. Tere are two argina onsuers. Te argina buyer is indifferent between buying te origina and te irated software:. 6 Te argina buyer is indifferent between buying fro te irate and not buying at a: 0. 7 Te deand faed by te onooist and te irate is given by 8 and 9. D d. 8 D d. 9 We assue tat te arket for software is uite arge and is not fuy overed i.e. D + D < D > 0 D > 0 Wauty 996. Te onsuer surus is Te utiity fro buying te irated software is U. 7

8 CS d + d. 0 Let us now disuss te oiy variabes. Te governent ony works troug te suy side in ontroing iray. Users do not fae te risk of roseution fro te use of irated software. Te governent is resonsibe for onitoring and enaizing te irate. Let and be te onitoring rate and te enaty. Let be te ost of onitoring. We assue 0 0 > > 0. Te governent ooses and to aiize doesti soia-wefare subjet to a baaned budget onstraint. We assue tis to avoid issues of redistribution tat are assoiated wit aiization of net revenue. We assue tat a fir reains in te arket ony if it is aking nonzero rofit. If te irate s iega oerations are deteted wi ours wit robabiity e as to ay te enaty. Te eeted rofits of te origina fir and te irate are D D. Let R be te net eeted revenue of te governent. R. Te baaned budget onstraint eans R 0. Tis iies tat te enaty euas te average ost of onitoring: for > 0. 4 In te absene of onitoring te enaty is irreevant. So we assue 0 if 0. 8

9 is an inreasing funtion of. By assution te argina ost of onitoring inreases wit onitoring. So te average ost of onitoring aso inreases wit onitoring. Te soia wefare is te su of te rofits of te origina deveoer and te irate and onsuer surus. Using 4 te soia wefare an be written as SW + CS CS. 5 Fro 5 it is evident tat te onitoring ost is a deadweigt oss. Te gae ayed between te governent te onooist and te irate is seified in etensive for as foows. Stage : overnent announes and tat aiizes soia-wefare subjet to baaned budget onstraint. Stage : Te onooist observes te oiy variabes. He ten deides weter to oose is rie siutaneousy wit te irate Bertrand gae or to ove first and oose a rie. In te atter ase e an arge te onooy rie wi we a te onooy riing gae tus ignoring te fat tat a irate ay enter te arket or to set a rie taking into onsideration tat a irate ay enter te arket wi we a te eader-foower gae. Te onooist an oose to ove first being te origina deveoer of te software. Te irate ats aordingy. In te net subsetion we ony disuss te onooy riing and te eaderfoower subgaes. 4 We ten deterine te euiibriu oiy variabes and te subgae erfet euiibriu riing gae in subsetion.. 4 We reegate te disussion of te Bertrand gae to Aendi A. Later we sow tat te onooist wi aways oose to ove first as e earns a iger rofit by oving first rater tan siutaneousy. 9

10 .. PRICIN SUBAMES In tis setion we anayze te eader-foower f and te onooy riing subgaes. We derive te euiibriu ries te euiibriu arket sare of bot ayers euiibriu rofits and te onsuer surus in ea gae. LEADER-FOLLOWER AME In te f gae te onooist takes into onsideration tat a irate wi enter te arket and terefore inororates te reation funtion 5 of te irate into its rofit funtion and ten ooses te rofit-aiizing rie. Te resuts of tis gae are suarized in Proosition. Te roof is rovided in Aendi A. Before disussing te resuts of te f gae et us ention an iortant roerty onerning te onitoring rate wi is used in Proosition. Lea is an inreasing funtion of 0 <. d Te roof of Lea foows fro te fat tat > 0. d Proosition i Te no iray ondition is were. 4 Te euiibriu resuts are f f f and f 0. ii A neessary ondition for iray is <. Te euiibriu ries and te argina onsuers are f f f and 0

11 f 4. Te arket is unovered at te euiibriu if >. Te rofits of te onooist and te irate are: f f Te irate s rofit is f 4. and are te oiy variabes tat satisfy f 0 in wi ase te irate annot enter te arket. Tese an be interreted as te iniaist oiy variabes tat deter te irate s entry. Using f 0 we get. 8 4 Fro te baaned budget onstraint we know tat. Te irate annot enter if. Fro Lea we know tat is an inreasing funtion of. So te irate annot enter if. Te irate enters if < and f f tere is iray in euiibriu beause > 0. Using 0 te onsuer surus is CS f if < oterwise. 9 5 See euation A in te Aendi.

12 Te irate annot enter if and ony te onooist serves te arket. Tis eains te onsuer surus desribed in 9. MONOPOLY PRICIN AME Let us anayze te ase were te origina fir arges te re-entry onooy rie ignoring te ossibiity of a irate s entry. We disuss tis ase in order to eaine te oiy variabes tat deter te irate s entry and aintain te onooy outoe desribed in 4. Te irate observes tis rie and inororates it into its reation funtion. We introdue te onets of artia rowding-out and oete rowding-out. Partia rowding-out eans tat te irate artiay atures te arket of te onooist. Soe of te onsuers swit fro buying te origina rodut to buying te irated rodut. Coete rowding-out eans tat te irate atures te entire arket. Te resuts of tis gae are suarized in Proosition. Te roof is ontained in Aendi A. Proosition i If < a neessary ondition for artia rowding-out is < satisfies 6. Te arket is unovered at te euiibriu wen > 4. Te euiibriu is araterized by > >

13 ii If a neessary ondition for oete rowding-out is < satisfies. Te arket is unovered at te 6 euiibriu wen > 4. Te euiibriu is araterized by iii Te onooy resuts od if < and or if and. and and or are te iniaist oiy variabes tat deter te irate s entry and ead to te onooy outoe if < or. Te neessary onditions in Proosition i and ii are obtained using te roerties of in Lea. Fro 0 we see tat te onooist earns ositive rofit if onooy rofits ony if oterwise te arket is sared. Fro te <. He earns euiibriu vaues of te argina onsuers in Proosition i we see tat soe of te onsuers swit fro buying te origina software to buying te irated software >. Tere is iray beause >. Fro 0 we furter see tat te onooist does not eist in te arket if and <. Te irate atures te entire arket. Te onsuer surus in tis gae is

14 CS if < and if < and < if and if and <. In Proosition we sow tat te Bertrand gae is never a subgae erfet euiibriu. To do tis we need to oare and wi is rovided in Lea. Te roofs of Lea and Proosition are given in Aendi A. Lea > > > 0. > > > >. Tis eans tat it is reativey osty to ieent te onooy situation oared to te f situation wit or witout te irate s entry. Sine is an inreasing funtion of. > > > > Proosition Te onooist aways oves first and ooses is rie for any vaues of te oiy variabes. Eiter te onooy situation or te f euiibriu wit or witout te irate s entry wi resut. Te first art of Proosition resuts fro te fat tat te onooist earns a iger rofit by oving first rater tan siutaneousy. Te seond art of Proosition iies tat oete rowding-out or artia rowding-out wi not our. If for or for < te onooist arges te onooy rie and te onooy outoe resuts beause te irate annot enter. 4

15 Oterwise te onooist wi aways arge te euiibriu rie in te f gae beause is rofit in te f gae eeeds tat in te Bertrand gae. If e arges te onooy rie te irate enters and tere wi be oete or artia rowding-out. Te onooist s rofit in te f gae eeeds tat in te gae wit artia or oete rowding-out. In te situation were te onooist arges te euiibriu rie in te f gae te irate s entry deends uon te otia onitoring rate. Tis we disuss in te net subsetion. Te governent ooses. OPTIMAL CHOICE OF POLICY INSTRUMENTS and in stage of te etensive for gae to aiize 4 soia-wefare subjet to te baaned budget onstraint. We assue > to guarantee tat te arket is unovered for a te riing gaes disussed earier. Fro 5 we know tat te soia wefare funtion is SW + Lea + CS. SW is a dereasing funtion of. Intuitivey as onitoring inreases te irate s rofit dereases and te ost of onitoring inreases tus inreasing te deadweigt oss. So soia wefare dereases. Let be te governent s euiibriu onitoring rate. Fro Proosition we see tat eiter te onooy situation or te f euiibriu wit or witout te irate s entry is te ossibe outoe. Fro Lea we know tat te soia wefare dereases as onitoring inreases. So to aiize soia-wefare te governent wi oose fro aong te iniaist onitoring 5

16 rates tat ead to te above outoes. or are te iniaist onitoring rates tat ead to te onooy outoe for or <. is te iniaist onitoring rate tat resuts in te f euiibriu witout te irate s entry. Te f euiibriu wit te irate s entry resuts if <. So 0 is te iniaist onitoring rate tat eads to tis resut. Tis anaysis gives us te euiibriu set of airs of onitoring rates and enaty { } wi is disussed in Lea 4. Lea 4 { { 00} if 00} if <. i i i. i Using 5 we deterine te soia-wefare funtions for ea of te above vaues of. We ten oare te different soia-wefare funtions to deterine te euiibriu onitoring rate and te enaty. SW SW SW SW Te seond ter in te RHS of 8 is te irate s rofit in te f gae wit 0. 6

17 Fro 5 and 6 it is ear tat SW 0 > SW. Tis is beause in te f gae wit te irate s entry soia wefare inudes te irate s rofit wi is not inuded in 5 and te onsuer surus is iger beause soe of te onsuers swit fro not buying to buying fro te irate. Te onooist s rofit is te sae in 5 and 6. So 0 strongy doinates. Hene te governent wi oose between 0 and or for < or. 5 SW 0 SW SW 0 SW Using 7 and 8 we suarize te otia oiy variabes in Proosition 4. Proosition 4 i For < 0 0 if SW 0 SW 0 if 0 < 0. SW SW If 0 ten te f gae wit te irate s entry is te subgae erfet euiibriu. If ten te onooy situation is te subgae erfet euiibriu. ii For 00 if SW 0 SW 0 if 0 < 0. SW SW If á 0 ten te f gae wit te irate s entry is te subgae erfet euiibriu. If ten te onooy situation is te subgae erfet euiibriu. Te roof of Proosition 4 foows fro 7 and 8. Intuitivey if te onitoring ost wi refets te onitoring tenoogy is very ow ten te 7

18 onooy situation ay be te subgae erfet euiibriu. Te resut aso deends on te arket size and te reiabiity fator. Te f gae is te uniue subgae erfet euiibriu outoe if. Tis aso foows fro 5 7 and 8. Ea of te eressions are ositive if è è 5 è è. 5 It is interesting to note tat tere are soe araeter vaues for wi onitoring is te otia outoe. Let us onsider a nueria eae tat suorts tis finding. Sine anedota evidene suggests tat is generay very ig we take 0. 9 in our nueria eae. We assue 0. and. 00. Tese 4 suort vaues satisfies te ondition for unovered arket 00 >. Suose. Assue. Now. Substituting te 6 vaues of te araeters and using te above for of te onitoring ost funtion we get Substituting tis and te araeter vaues in 8 we get 5 SW 0 SW < 8 0. If 0. ten SW 0 SW < 0. Tis nueria eae sows tat for soe vaues of te araeters onitoring is te otia oiy. Furter a derease in te vaue of inreases te ossibiity of onitoring to be te otia oiy. Te doesti governent s soia-wefare aiizing objetive deterines its aggressiveness or assiveness towards iray wi in turn endogenousy deterines weter tere wi be arket saring between te onooist and te 8

19 irate or te onooy outoe wi resut. In Proosition 5 we disuss te effets of an inrease in te reiabiity of te irated software. Te roof is in Aendi A. Proosition 5 i An inrease in inreases iray. ii An inrease in inreases te otia onitoring rate tat resuts in te onooy outoe. A ange in te reiabiity fator does not affet te arket in te ase of te onooy outoe. However it affets te arket wen te f gae is te subgae erfet euiibriu. Any ange in does not affet te onooist s arket f beause does not deend on. Intuitivey as te reiabiity of te irated software inreases te onooist aintains te sae arket as in te f d onooy ase by owering its rie < 0. Te rofit of te d onooist aso goes down in resonse to an inrease in. Sine f d d 4 < 0 it eans tat te irate s arket sare and iray inreases wit an inrease in. Part ii of Proosition iies tat sine iray in te onooy riing gae inreases wit an inrease in te otia onitoring rate tat restores te onooy outoe aso inreases. Let us disuss te iiations of te baaned budget assution. To do tis we need to study te effets on governent oiies if te governent s net revenue is not binding and ositive. Suose te governent eoys a onitoring agent wi is a governent ageny and rovides it wit a budget B to onitor oeria iray. So te 9

20 governent s net revenue is now R B and te agent s net revenue is B. In tis foruation one an eet te onitoring agent s budget onstraint to be binding so tat B. Hene te governent s net revenue beoes R. Suose te governent s net revenue does not bind and is ositive tat is R > 0. Te soia wefare funtion is te sae as in 5 and is a dereasing funtion of. Let us now eaine te effets of ositive governent net revenue on and wi are te iniaist onitoring rates in te f and subgaes. Te irate s rofit is D. So te iniaist onitoring rates ust satisfy D 0 D. Sine R > 0 we ave >. Fro Lea we know tat is an inreasing funtion of. Hene te resut > > ontinues to od. Cobining tis wit te fat tat te soia wefare is a dereasing funtion of te euiibriu onitoring rates reains te sae as disussed in Proosition 4. However sine R > 0 we annot deterine te enaty endogenousy fro te ode. In tis ase beoes an eogenousy given araeter. In genera te ain iiation of te baaned budget onstraint is tat te enaty is derived endogenousy. If we assue tat te governent s net revenue is ositive ten te euiibriu onitoring rates are te sae as suarised in Proosition 4. However we annot deterine te enaty endogenousy fro te ode. Te enaty orresonding to te different euiibriu onitoring rates as suarised in Proosition 4 ust be su tat te governent s net revenue fro 0

21 onitoring is ositive. 6 Let us now disuss te onooist s roe in deterring iray.. MONOPOLIST S ROLE IN PREVENTIN PIRACY Te origina fir aways favors te onooy outoe. However if te otia onitoring rate is 0 ten te irate enters and te onooist s rofit goes down by f 4. Te uestion terefore is weter te onooist an do anyting to revent iray. Let us suose tat te onooist an insta a tenia rotetion devie in te software to revent oying. For siiity we assue tat tis rotetive devie does not ause any inonveniene to te user. So te users of te origina software ontinue buying te origina software. 7 Let F be te fied ost of instaing te tenia rotetion devie. Tis is oon knowedge. Proosition 6 i If F < 4 ten te onooist instas te rotetive tenia devie and 0. Oterwise te resuts are te sae as in Proosition 4. ii An inrease in te reiabiity fator inreases te onooist s inentive to rotet is software against iray. 6 Introduing a araeter tat easures te argina soia vaue of revenue an erit te study of te oiy issues in a ore genera for. Let λ be a easure of te argina soia vaue of an additiona doar of revenue to te governent. So te soia wefare funtion beoes: SW D + D D + D + CS + λ + CS + λ. Soia wefare an now be an inreasing or a dereasing funtion of. If it is a dereasing funtion ten te resuts for te euiibriu onitoring rates are te sae as tose in Proosition 4. However if te soia wefare is an inreasing funtion of ten te resuts are different. 7 urnsey 995 ites tat software wit rotetion toug it revents oying tends to be user-

22 Te onooist instas te rotetive devie for a onitoring rates if te net onooy rofit fro te instaation eeeds is rofit in te eader-foower ase. So if te onooist revents te irate s entry te governent does not need to onitor. However if F 4 ten te onooist as no inentive to insta te rotetive devie and te resuts are te sae as desribed in Proosition 4. Te onooist s inentive to revent iray deends on te ost of doing so. For ig osts te onooist is better off aowing iray if te otia onitoring rate is zero. So for ig osts of instaing a rotetive devie iray deends on te otia oiy variabes and te onooist ays no roe in it. As seen earier an inrease in owers te euiibriu rie of te onooist in te eader-foower gae wi redues is rofit. Tus te differene between te onooy rofit witout te rotetive devie and te eader s rofit inreases wit an inrease in. 8 Intuitivey te greater te differene between te onooy rofit witout te rotetive devie and te eader s rofit te iger wi be te onooist s inentive to rotet is software. It aows te onooist to send ore in instaing te rotetive devie.. EFFECTS OF NETWORK EXTERNALITIES NE In tis setion we eore te network effets on te oiy variabes and on te onooist s inentive to revent iray troug instaing a osty tenia rotetive devie. We oare te resuts wit tose in te absene of NE. Te unfriendy. Tis redues te onsuers vauation of te software and soe of te buyers ay not buy. So te origina fir s rofit ay fa and sef-rotetion beoes uestionabe.

23 agebrai anaysis and te roofs are given in Aendi B. A network eternaity eans tat a onsuer s utiity inreases wit an inrease in te nuber of oter onsuers using te sae software egay or iegay. Consuers benefit troug eange of fies using te sae software. Tis feature is atured in te utiity funtion. We begin our disussion wit te no iray ase. Te utiity of a tye onsuer fro buying one unit of te software is + D if te onsuer buys te software U 9 0 if te onsuer does not buy. is te oeffiient easuring te degree of network eternaities. We assue tat 0 to avoid indeterinate resuts. D is te deand for te origina software and is te rie arged by te onooist. Coarison of te onooy resuts in te resene and in te absene of NE sows tat te euiibriu rie is te sae in bot te situations. However te onooist s arket sare inreases in te resene of NE. Conseuenty wit network effets te onooist s rofit is iger. Let us introdue te irate in te ode. is te robabiity tat te irated software is oerationa. Te onsuer buying te origina software enjoys te benefit and te network eternaity generated by tose wo buy te origina and te irated software ony if te atter is oerationa. Te onsuer buying te irated software enjoys te benefit and te network ony if te irated software is oerationa. So te utiity funtion is 8 d f d > 0.

24 + D + D if te onsuer buys te origina software U + D + D if te onsuer buys te irated software 0 0 if te onsuer does not buy. and are te rie arged by te irate and te deand of te irated D software. and are te oiy variabes in tis ode wit NE. Te governent in euiibriu ay or ay not onitor. In te first ase te onooy outoe is te subgae erfet euiibriu. In te seond ase te f outoe wit te arket being sared by te onooist and te irate is te subgae erfet euiibriu. To avoid reetition we just rovide a disussion of te oarative anaysis of te resuts in te resene and absene of NE. Te iortant asets of te oarative anaysis are suarized in Proositions 7 and 8. Proosition 7 i Piray in te f gae wit NE is iger tan tat in te gae witout NE. Piray inreases as network benefits inrease. ii Te otia onitoring rates tat resut in te onooy outoe in te resene of NE eeed tose in te absene of NE. iii Te otia onitoring rates tat resut in te onooy outoe inreases wit an inrease in network benefits. Due to network effets te irate s arket is arger in te f gae wit NE oared to tat witout it. Sine te rie is te sae in bot te situations but te arket size of ea ayer is greater in te f gae wit NE te rofit of ea ayer is aso iger in te atter ase. Te irate s arket sare inreases as te benefit fro network effets wi is atured by te oeffiient easuring NE inreases. Te irate s eeted rofit in te gae wit NE is iger tan tat witout NE. In te artia and te oete rowding-out ases wit NE te 4

25 irate s arket is arger tan te sae witout NE. Terefore it reuires a iger onitoring rate to detet te irate. For te sae reason an inrease in te oeffiient easuring network benefits auses an inrease in te onitoring rates tat restore te onooy outoe. Tus our ode sows tat te iger is te eve of iray greater is te onitoring rate and te iger is te ost of ieenting te onooy outoe. Corresondingy te enaty is aso iger. Tis foows fro te fat tat te enaty is an inreasing funtion of onitoring rate as disussed in setion. Let us now anayze te onooist s roe in reventing iray and oare it wit te resuts in te absene of NE. Suose te onooist inurs a fied ost F in instaing a tenia rotetive devie to revent oying. He wi insta te devie ony if te net onooy rofit fro doing so eeeds is rofit in te f gae. So te onooist wi insta te rotetive devie for any onitoring rate if F < f 4. 9 Terefore te governent wi not onitor and 0. Oterwise te onooist wi not insta te rotetive devie and te revention or eistene of iray deends on te governent s otia oiy. Witout NE te ondition for instaing te rotetive devie is F < 4. Now 4 > Proosition 8 4. i In te resene of NE te onooist as greater inentive to revent iray. ii Wit NE te onooist s inentive to revent iray inreases wit an inrease in or an inrease in. In resene of NE te origina fir s rofit in te onooy and in te f 5

26 ases are iger tan te sae witout NE. However due to network effets te differene between te onooy rofits and te origina fir s rofit in te f gae is iger tan tat in te absene of NE. Tis aows te onooist in te ase of NE to send ore in instaing te rotetive devie. Aso sine te onooist s rofit is iger in te resene of NE e as a te ore inentive to revent iray. Te resut stated in Proosition 8 ii foows fro te fat tat d d f > 0 and d d f 4 4 > 0. Intuitivey wit an inrease in or an inrease in te differene between te onooy rofit witout rotetion and te eader s rofit inreases. Tis inrease in te differene between te two aows te onooist to send ore in instaing te rotetive devie and te onooist as ore inentive to rotet te software. We see tat iray in te resene of NE is arger tan tat in its absene. Canges in network benefits ave a ositive effet on iray. 0 Wit network effets te otia onitoring rate tat resuts in te onooy outoe is iger oared to tat witout it. Te onooist as ore inentive to revent iray due to iger rofits in te resene of NE. Canges in te reiabiity fator and te network benefits ave ositive effets on te onooist s inentive to revent iray. 4. CONCLUSION Te fous of te revious resear on software iray as been on iray by end- 9 Refer to euations B and B8 in Aendi B. 0 Unfortunatey te oarative stati anaysis wit reset to te reiabiity fator beoes agebraiay intratabe. 6

27 users and effets of network eternaities in roteting te software industry. In tis aer we anayzed te governent s roe troug onitoring and enaizing te iega oeration of a software irate in restriting iray in a software arket were te origina fir is not eaduartered. Te governent s soia-wefare aiizing oiy endogenousy deterined te arket outoe. We found tat due to a first-over advantage te onooist aways oves first to oose is rie and te Bertrand gae is never a subgae erfet euiibriu. If not onitoring is te otia oiy ten te onooist and te irate sared te arket. In tis ase te irate s arket was arger in te resene of network eternaities tan in its absene. If onitoring is te otia oiy ten te onooy outoe resuted. However te onitoring rate is iger wen network eternaities are resent. Due to network eternaities te onooist s and te irate s arket sare inreased. However te inrease in te irate s arket sare is u ore ronouned tan tat of te onooist. Tis eains te iger degree of iray in te eader-foower outoe and te iger onitoring rate tat resuts in te onooy outoe wen tere are network eternaities. We aso found tat te onooist as a greater inentive to revent iray troug instaing a rotetive devie wen network eternaities are resent. Te onooy rofits are iger wen tere are network effets and so te inentive to revent iray is aso iger. Te oarative stati anaysis sowed tat anges in te reiabiity of te irated software and te oeffiient easuring network benefits ave ositive effets on iray and on te otia onitoring rate tat resuts in te onooy outoe. Teir effet on te onooist s inentive to revent iray is aso ositive. Te 7

28 reiabiity fator and te oeffiient easuring network benefits are deand-sifting araeters. So te sae of origina and irated software inreases wit an inrease in tese two fators. As a resut te onooist s and te irate s rofit inreases. Te governent an aso ontro iray troug eduation and awareness aaigns inforing te buyers on te azards and idden osts of using irated software. Su easures if suessfu devaue te uaity of te irated software. We oud roy tis ange by a fa in te reiabiity fator wi srinks te irate s arket. However su aaigns reuire resoures. So te revention of iray troug aaigns ay or ay not enane soia wefare. REFERENCES Cen Y. and Png I. Software Priing and Coyrigt: Enforeent Against End- Users ieo 999. Ceng H.K. Sis R.R. and Teegen H. To Purase or Pirate Software: An Eiria Study Journa of Manageent Inforation Systes Vo. No. 4 Sring Conner K.R. and Ruet R.P. Software Piray: An Anaysis of Protetion Strategies Manageent Siene Vo. 7 No Correa C.M. Te Lega Protetion of Software in United Nations Industria Deveoent Organization UNIDO Software Industry: Current Trends and Iiations for Deveoing Countries UNIDOVienna 99. urnsey J. Coyrigt Teft Asib ower Engand 995. Internationa Panning and Resear Cororation IPR 998 for Business Software Aiane BSA and Software Pubisers Assoiation SPA 997 oba Software Piray Reort BSA Wasington D.C. June. 8

29 Nasiento F. and Vanonaker W.R. Otia Strategi Priing of Reroduibe Consuer Produts Manageent Siene Vo. 4 No. 8 August Noyee T. Couter Software and Couter Servies in Five Asian Countries in United Nations Conferene on Trade and Deveoent/ United Nations Deveoent Prograe UNCTAD/UNDP Servies in Asia and te Paifi: Seeted Paers Vo United Nations New York 990. Oz. S. and Tisse J.F. A Strategi Aroa to Software Protetion Journa of Eonois and Manageent Strategy vo. 8 no. Suer Takeyaa L. Te Wefare Iiations of Unautorized Rerodution of Inteetua Proerty in te Presene of Network Eternaities Journa of Industria Eonois Vo. 6 No. June Tiroe J. Te Teory of Industria Organization Te MIT Press 988. Wauty X. Quaity Coie in Modes of Vertia Differentiation Te Journa of Industria Eonois Vo XLIV No. Seteber 996. APPENDIX A BERTRAND AME In tis gae ea ayer oetes in rie siutaneousy. Fro te first order onditions we get te foowing reation funtions: b b + b A b b b. A Te Nas Euiibriu ries are b 4 and b. Te 4 9

30 b argina ustoers are < and b 4 4. Ceary >. Now b b 4 > b >. Te arket is unovered at te euiibriu if 4 >. Te onooist eands its arket oared to te onooy ase. Ea ayer s rofit in euiibriu is b 4 4 < A 4 b 4. A4 Te irate enters te arket ony if b > 0 i.e. >. 4 Proof of Proosition We substitute te reation funtion of te irate A into te rofit funtion of te onooist A. Fro te first-order onditions te euiibriu ries and te argina onsuers are as foows: f b > A5 4 f > b A6 4 f and f. A7 f In euiibriu te arket is unovered if > 4 >. In euiibriu te rofits of te firs are: 0

31 b f > A8 f. A9 4 Te irate enters if f > 0. Let and be te oiy variabes su tat 0. Using f 0 we get f 4. Te irate enters and is rofit is given by A9 if < Fro Lea < <. Te irate annot enter te arket and is rofit is 0 if. Te overa arket overed in te f gae is ess tan in te Bertrand gae f b f f beause >. Te irate s arket if e enters is. However te size of te arket overed by te irate in te f gae is iger tan f f tat in te Bertrand gae sine b > b 4 Proof of Proosition Te arket is unovered in euiibriu if > > 4. Substituting te 4 onooy rie in te reation funtion of te irate A we get te euiibriu ries argina onsuers and te rofits.. A0 8. A 6

32 and satisfies 0. 6 If < and ten te irate annot enter and te onooy resuts od. However if < and < ten te arket is sared. Te rofits of te two ayers are given in A0 and A. Tere is iray in euiibriu beause > Tis eans tat soe of te onsuers swit fro buying te origina software to buying te irated version. Let us onsider te situation were. In tis ase fro A0 we see tat 0 wi iies tat te irate atures te entire arket if e enters. We a tis te oete rowding-out situation. In tis ase. Te irate s rofit is d 4 6. A and satisfies 6. If < < ten te irate atures te entire arket oete rowding-out situation. Te irate s rofit in tis ase is given by A. Te onooy resuts od if. Proof of Lea Fro Lea we know is inreasing in. Let i i i i >

33 6 6 + ε 6 6. Sine in 6 we write as + ε ε [ ε + Terefore > 0. So > > > >. 6 Proof of Proosition If and te onooist arges te onooy rie beause te irate annot enter. Furter te onooist earns te igest rofit by arging te onooy rie. If and < ten tere is oete rowding-out if te onooist arges te onooy rie. Te onooist arges te euiibriu rie in te f gae beause is rofit eeeds tat in te Bertrand gae. f b 4 - > Te irate annot enter. If and < ten aso te onooist arges te euiibriu rie in te f gae beause of te sae reason. However in tis ase te irate enters. If < and ten te onooist arges te onooy rie beause te irate annot enter. If < and < ten tere is artia rowding-out if te onooist arges te onooy rie. In tis ase te onooist arges te euiibriu rie in te f gae beause

34 f - > 0. Te 8 8 irate annot enter. If < and < ten aso te onooist arges te euiibriu rie in te f gae but in tis ase te irate enters. Proof of Lea SW < 0 beause > 0 by assution. Proof of Proosition 5 f d i < 0. d 4 ii and 6. 6 d d > 0 and d d + d d > 0. Terefore > 0. Siiary > 0. d d APPENDIX B In Aendi B we rovide te oete agebrai anaysis wit NE. MONOPOLY RESULTS Let be te argina onsuer wo is indifferent between te buying te origina software and not buying. Setting + D we get D. Te deand for te software is 0 D d. B 4

35 5 Te euiibriu rie arket sare and te rofit are 4. B In te resene of te irate tere are two argina onsuers. Te argina onsuers indifferent between buying te origina and te irated software and indifferent between buying te irated software and not buying at a are. B Te deand for te origina and te irated software are. D D B4 Te rofit funtions of te onooist and te irate are. D D B5 RESULTS OF THE LEADER-FOLLOWER AME f and f. B6 f and f. B7 f. B8 f < oterwise. 0 if 4 B9

36 are te iniu oiy variabes tat deter te irate s entry in te f gae. Terefore satisfies f 4 0. B0 Te irate enters ony if <. Oterwise e earns zero rofit. Let us oare te size of te arket served by te onooist and te irate in te two situations. Coaring te argina onsuers does tis. f f > 0. B So te onooist s arket is arger in te f gae wit NE. Te irate s arket is. We oare tis for te two situations and get f f f f + > 0 sine <. B f f f f Fro A0 we see tat is an inreasing funtion of. RESULTS OF THE MONOPOLY PRICIN AME In tis ase te onooist arges te onooy rie. Te euiibriu rie of te irated software is. 4 Te argina onsuers are; 4 and In euiibriu te rofits of te onooist and te irate are 8 B 6

37 7 6. B4 Tere is artia rowding-out if and < <. < iies tat soe of te buyers of te origina software buy te irated software. Te onooy resuts od if - - and <. Suose. In tis ase te irate s rofit is B5 Tere wi be oete rowding-out if and < were Te onooist s rofit is 0 and te irate serves te entire arket. Te onooy resuts od if and. and are te iniu enforeent variabe tat deters te irate s entry for < and. Proof of Proosition 7 i Te roof foows fro B. Piray in te network eternaity ase f f f f is an inreasing funtion of. ii 0 6 > and > +. Now is an inreasing funtion of. So. and > > > >

38 iii Let 6 and and are inreasing in and is an inreasing funtion of. So and are inreasing funtions of. 8