Strategic Choice of Network Externality and its Impact on Digital Piracy

Transcription

1 From the SeletedWorks of Sougata Poddar Summer 06 Strategi Choie of Network Externality and its Impat on Digital Piray Sougata Poddar, University of Redlands Yuanzhu u, Central University of Finane and Eonomis Available at:

2 Strategi Choie of Network Externality and its Impat on Digital Piray Yuanzhu u Sougata Poddar China Eonomis and Management Aademy Shool of Business Central University of Finane and Eonomis University of Redlands Beijing, China California, USA yuanzhulu@ufe.edu.n sougata_poddar@redlands.edu June 06 Abstrat Network externality plays a major role in the digital produts market. The strength or the degree of the network externality has serious impliations on the overall value or uality of the digital produt. We fous on a situation where the degree of network externality of the produt is a strategi hoie of a digital firm faing a ommerial pirate produing a lower uality of that produt. We haraterize the strategi response of the original firm for the pirate. We find the optimal degree of network externality hosen by the original firm under any ost environment and relative uality differene between the original and pirated good. Market struture and market overage are endogenously determined in the model whih has impliations on piray. Interestingly we show that the relationship between optimal degree of network externality and relative uality differene between the produts an be monotoni or non-monotoni. Keywords: Vertial produt differentiation, Network externality, Market struture, Market overage, Investment ost JE Classifiations: D3, D43, 3, 86 We are extremely grateful for the detailed omments and thoughtful suggestions of the editor of the journal and two anonymous referees on an earlier version that helped us to signifiantly improve the paper. We also thank the seminar and onferene partiipants at Nanyang University of Tehnology, Singapore, the 03 APJAE Symposium on Industrial Organization and Global Value Chains in ong Kong and Jadavpur University, India (04), and 49 th Annual Conferene of the CEA, Toronto, Canada (05) for helpful omments. Yuanzhu u thanks National Natural Siene Foundation of China (No. 707) for finanial support. Address for orrespondene.

3 . Introdution In the modern environment of digital produts market with strong features of network externalities, a leading firm in this industry is not only just interested to inrease the size of its users-base i.e. the network size of its produts, it is also interested to enhane the strength of the network effet by making appropriate investments, whih onseuently inreases the overall value of its produts. Adding new apps, features and supporting devies or aessories to its ore produt enhanes the usage and overall uality of the produt. This is an alternative way to enhane the effetive uality of an existing produt without investing to improve the intrinsi uality of the produt whih may not also be feasible in many irumstanes. This way of inreasing network strength to enhane the overall uality of the produt has another major impliation in the digital world. It also helps the original produer of the digital good to fight piray or at least take a greater ontrol of its market to limit the impat of piray. In this paper, we will fous on this partiular problem and analyse a situation with an original firm and a ommerial pirate operating in the same market. The ommerial pirate makes digital opies of the original produt that is also ompatible (fully or partially) with the digital platform or the network of the original produt. owever, sine it is a opy of the original good, its uality is typially lower than the original item. The following example explains why that would be the ase. Think of a pirated version of any original software produt, for example, let s take pirated (or unliensed) version of the Mirosoft s Windows operating system that is installed in a omputer. Various appliations that are ompatible with original Windows system would most likely run in the pirated Window version as well, and the network benefits will be translated unless Mirosoft deliberately wants to stop that. Mirosoft may also limit to a ertain extent (but not fully) for the appliations to run on its unliensed or pirated operating system. Depending on Mirosoft s poliy, the pirated version may lose some of its usefulness to the user that is oming from the network. Moreover, the pirated version may also have problem in upgrading in future when Mirosoft upgrades its operating system. Thus, overall the pirated version will provide a lower benefit and network

4 effet to its users ompared to somebody using the original liensed version. In this sense, the pirated version is almost always a lower uality produt. Thus, the digital produt market we are looking here is vertially differentiated where the original good is of higher uality and the pirated good is of lower uality. The original firm strategially invests to improve the strength of network externality by enhaning the network features (e.g. introduing new apps, features and servies) of the produt in order to inrease the overall value for its users. owever, in the proess, the ommerial pirate also benefits (by free riding) from the effetive inrease of the network strength for its pirated good whih in turn attrats buyers for the pirated version as well. But as we said, sine it is not a liensed produt from the original produer, it may have limited aess in absorbing all the network benefits in some or all areas. Thus, the original produt almost always generates more value to its users ompared to the value generated by the pirated produt for its users. Beause of this, it also gives adeuate inentive for the original firm to invest in inreasing the strength of network effet so that it an better ontrol its market where there is a pirate. In this setup, we study the strategi interation between the two firms, the impat of the investment by the original firm on its network to ontrol piray, and the resulting euilibrium market struture and market overage of the two firms. To apture the situation, we onsider a simple two-stage game where in the first stage, the original firm makes ostly investment to improve the impat of network externality. In the seond stage it ompetes in prie with the pirate in the vertially differentiated produt market. We solve the two-stage game and find out the impat of investment by the original firm on the network strength and market struture for any given level of relative uality differene between the produts of the two firms. We first find out what would be the optimal levels of the network strength for the original firm under different investment ost environments. Then under any given ost environment, we find out what would be the ensuing euilibrium market struture (i.e. whether market outome is monopoly or duopoly i.e. whether the piray is stopped or not) and whether the market will be partially or fully overed in the euilibrium. We an provide a similar example with Mirosoft s very popular Offie software. Both the original and the pirated version are available in the market, pirated version mostly in the poor and developing ountries. Mirosoft s poliy towards piray ontrol effetively determines the uality of the pirated produt.

5 Our main findings are as follows. We find when the ost of investment on the network is low and the uality differene between the two produts is high, the market is always monopolized and fully overed by the high uality firm (hene piray is eliminated), while it remains duopoly when the uality differene is low. On the other hand, when the ost of investment on the network is relatively high, the market always remains duopoly (i.e. piray remains), however, it may be partially or fully overed. Two major kinds of omparative statis analysis are done: ow does the optimum network strength vary (i) when there is an inrease in the ost of strengthening the network, (ii) when there is a derease in the uality differene of the produts? An inrease in the ost of strengthening the network leads to a redution in the optimum network strength. This is an expeted outome. owever, the more interesting result is, a derease in the uality differene between the two produts an hange the optimum network strength non-monotonially. Under very low or high ost environments, the optimal level of network externality is always inreasing in uality differene of the produts, and the relationship is monotoni (though it may move disontinuously). But for any other intermediate ost environments even if the optimal level of network externality is inreasing in uality differene pieewise, the overall relationship between the two is non-monotoni. There are two other important aspets we also address in this paper. Typially, in the models of produt differentiation with network externality, the degree or the strength of the network effet is mostly assumed as a parameter. We depart from this and endogenize the degree of network externality and see its impat on the market struture. Seondly, in the models of vertial produt differentiation, more often the extent of the market overage whether full or partial is assumed to be exogenous. ere we show that overing or not overing the market is a part of the endogenous outome of the strategi game between the firms and is at the heart of strategi problem. Piray of digital goods beame ommon due to the easy availability of opying tehnology. It is understood that rampant piray of digital goods is not desirable from the innovators as well as soiety s point of view in the long run. In this ontext, we onsider a model with an original produer and a ommerial pirate sharing the same platform and the network. We show how the In another rare instane, Wauthy (996) onsidered a two-stage duopoly game of uality-prie ompetition and emphasized the endogenous aspet of market overage. 3

6 original produer by optimally hoosing the strength of the network an strategially eliminate the pirate from the market or limit the ompetition from the pirate. Thus, in the markets where ommerial piray is a serious threat, piray an be fought by influening the demand network externality as an effetive instrument apart from other regular instruments; like monitoring, enrypting the software or drawing attention to the IPR authority to take punitive ation against the pirate. All these regular options to limit piray have already been disussed in great detail in the literature, but using the strength of the network effet as a strategi tool to address the problem is yet to be explored. We undertake that analysis in this paper. The rest of the paper is organized as follows. In Setion, we do a brief literature review. In Setion 3, we present the basi model followed by Setions 4 and 5 where we analyze the prie ompetition between the two firms when the market is partially and fully overed respetively, assuming the degree of network externality as a parameter. In Setion 6, we endogenize the degree of network externality. We allow the original firm to strategially hoose the optimal degree of network externality under any ost environment. First we haraterize the possible market strutures and overage that are endogenously determined in the euilibrium followed by the omparative statis analysis. Setion 7 onludes.. Related iterature The impat of network externality or network effets on various eonomi situations is studied in the literature in several ontexts. There is a sizeable researh disussing the effets of network externality in eonomi ontexts whih originated from the studies by Rohlfs (974), Katz and Shapiro (985), followed by Chou and Shy (990), Churh and Gandal (993) among many others. Grilo et. al (00) modelled soial pressures suh as onformity or vanity in terms of onsumption externalities in a model of spatial duopoly and haraterized various possible euilibrium outomes and market strutures. ambertini and Orsini (005) onsidered a model of vertial produt differentiation with the feature of positive network externality and foused on the existene of uality-prie euilibrium. In another area, where the impat of network externality got a renewed interest is opyright violations or piray of the digital produts market (see the work done by Conner and Rumelt 99, Takeyama 994, Shy and Thisse 999, Banerjee 003, 03 among others). owever, the researh dealing with the impat of network externality on onsumer and produer behavior in all the above studies assumes the degree or strength of the 4

7 network effet as an exogenous parameter in the analysis. But in the urrent stage of rapid tehnologial progress and digital environment, it is apparent that from a firm s point of view, improving the network strength of its produt has to be a part of strategi deision making proess apart from the priing deisions. 3. The Model A two-stage game is onsidered in a vertially differentiated produt market with the original firm and the ommerial pirate. The original produt is of high uality and denoted by while the pirated produt is of low uality and denoted by. We will interhangeably all the original produt as the high uality produt and the pirated produt as the low uality produt. There is a ontinuum of onsumers distributed uniformly over a unit interval with heterogeneous preferenes towards produt uality. The produts exhibit the feature of positive network externality. 3 owever, as explained before, the impat of the network effet or externality is asymmetri between the users of the original produt and the pirated produt. The users of original produt enjoy a higher level of network externality ompared to the users of pirated produt as the absorption apaity of the network effet of the original produt is more than that of the pirated produt. 4 In terms of utility, the onsumer who buys original produt, first of all, gets all the intrinsi benefit from the produt due to its high uality; seondly she also enjoys the full extent of the network externality generated by those users who also buy the original produt, plus the (limited) network externality generated by the pirated produt users. The buyers of the pirated produt an enjoy all the value of the produt (intrinsi as well as network) subjet to limitation that the lower uality an permit. We normalize the uality of the original firm s produt to one. The uality of the pirated produt is indexed by, 0, depreiation. where aptures the uality Formally, the utility of a typial onsumer X ( X 0, ) is given as follows: 5 3 We rule out the ase of any negative network externality in this model. 4 The original produt has all latest features funtional to absorb all the network effet, while the pirated produt whih is not liensed from the original produer may have limited funtionality and absorption apaity of the network effet. 5 Also see Banerjee (003) for similar utility representation. 5

8 where D, X D D p if buys high uality produt, U X D D p if buys low uality produt, 0 if buys none, p and D, p are the demand and pries for the high uality and low uality produts respetively. 0, is the oeffiient whih measures the level or strength of network externalities. For example, higher implies stronger effet of network externality, whereas when is lose to zero, it implies almost no effet of network externality. In our model only the original firm an influene. The interpretation is hoosing a higher level of is same as hoosing more network features and funtionality. Think of various apps or supporting devies for the ore produt to enhane the overall strength of the network externality and onnetivity among the users. In Stage, the original firm hooses how muh to invest to improve the strength of network effet, i.e. hooses a level of. In Stage, the original firm and the ommerial pirate ompete in pries in the produt market for a given level of. The original firm an hoose the level of network externality by inurring a ost of k, where k 0 measures how ostly it is to invest in enhaning the level of network externality. For simpliity, we assume the osts of prodution for the firms are zero. The size of the market is normalized to. We look for the subgame perfet Nash euilibrium of this game and work bakward. Consider the prie ompetition stage. We will first deal with ases when the market is partially overed and when it is fully overed separately. The market overage aspet gets endogenized later when is hosen. 4. Partial Market Coverage The marginal onsumer uality produt, is given by This gives us X X m, who is indifferent between buying the high uality and low X D D p X D D p. m m m p p D buying the low uality produt and buying none, is given by. The marginal onsumer Y m, who is indifferent between 6

9 p. We thus have Y D D m 0 Y D D p. m The demand for the high uality produt is given by D X D = p p The demand for the low uality produt is given by: D X m Ym = m ; we then obtain. () p p. 6 () The firms ompete by hoosing pries strategially. The Nash euilibrium pries and demands are p 4, p 4 The profits of the firms are respetively 4 4, D 4, Under this ase, the market struture is always duopoly. Next we deal with the ase of full market overage. 4, D Full Market Coverage Note that we have normalized the size of the market to be. There will be an upper bound of the level of network effet for whih D D. Denote that upper bound by ˆ. From the previous analysis, we find ˆ. So when ˆ, the market is always fully overed. 4 Now, when the market is fully overed, we have the following analysis. First, in the ase of full market overage, we an distinguish two ases: (i) both the firms are ative (i.e. duopoly); and (ii) only the original firm serves the whole market (i.e. monopoly) Case (ii) arises when is p p 6 To be preise, this demand system is orret only when. owever, it an be shown that in euilibrium we do have p p. For the sake of simpliity, here we omit the demand system when p p. 7

10 above a threshold value denoted by ~ (whih will be defined later), and ase (i) realizes when ˆ ~. When ase (ii) arises the market atually gets bak to monopoly from duopoly as we will see that the pirate annot sell its produt even if it sets its prie at marginal ost. Thus, market monopolization happens endogenously here as the strength of the network effet rosses a ertain threshold. Now we will analyze ase (i) in Setion 5. and ase (ii) in Setion 5. under the full market overage in detail. 5. ˆ ~ (Moderate level of network externality) ere, the demand for the original firm remains same as in the previous ase, i.e. euation (), while the demand for the pirate is D p p D. (3) Note that in this ase, full overage of the market implies the onsumer with X=0 also obtains nonnegative surplus, whih an be expressed as p 0. It turns out we need to distinguish two subases (a) and (b). In subase (a) the onsumer with X=0 has no surplus while the onsumer gets positive surplus in subase (b). The Nash euilibrium pries, demands and eah firm s profit are given below. The detailed analysis is presented in Appendix A. Subase (a) When p, ˆ ˆ 4 p, ; D, D, 4, Subase (b) When ˆ ~ 8

11 p, p 3, 3 D, 3, 3 9 D, ~ (igh level of network externality) When ~, from the expression of the prie and demand of the pirate (in the previous Setion 5., subase (b)), we find that they go to zero (hene the profit as well). This means when reahes that threshold or beyond, the pirate is unable to ompete profitably, market beomes monopoly and all onsumers buy the high uality produt even if the low uality produt is free (stritly speaking, sold at marginal ost). To ensure the onsumer with the lowest X(=0) buys the high uality produt, the following ondition has to be satisfied: D p D D p p (sine D, D 0, p 0 ). It is not hard to see that the original harges a prie to maximize its profit and its total profit is also (reall that the size of the market is normalized to ). This is true irrespetive of the uality of the low uality produt. The following figure summarizes the market struture and market overage as a funtion of network externality. Figure Market Struture as a Funtion of Network Externality 9

12 6. Choie of Optimal evel of Network Externality Now aording to the analysis in Setions 4 and 5, the high uality firm s profit in the seond stage an be summarized as 4 4 if 0, 4 if, 4 4 if, 9 if. k. N In Stage, the high uality firm hooses to maximize its net profit N Note that is ontinuous in. Denote of ), g h f 4 4 k for (denote this as first region or domain 4 k 4 for k for 9 4 (seond region of ), j k for (third region of ), (fourth region of ). To find the optimal level of network externality for the high uality firm, we need to find the maximum of regions of and then ompare these maximums. f, g, h and j in the relevant To get an idea on the optimal level of, first we fous on two simple ost environments (low and high) for the high uality firm. We will use numerial examples for that purpose. In our framework we notie that a lower value of k i.e. k= will suffie a low ost environment and a higher value k= will suffie high ost environment. ater the parameter k will be treated as a ontinuous variable to see the impat. 0

13 The seond thing we fous on following the optimal level of is the resulting market struture and market overage that ome out endogenously in euilibrium. 6. ow and igh Cost Environment Numerial Example (k = ): emma : Under low ost environment, the optimal level of network externality hosen by the high uality firm is if k 0.6, if k 0.6. The market is always fully overed and the market struture an be monopoly or duopoly. Proof: See Appendix B. When is relatively small (as defined above), the high uality firm is a monopolist and hooses a higher level of network externality (i.e. high level of ); whereas when is relatively big (as defined above) both the high uality and the low uality firm share the market (duopoly), and the high uality firm hooses a lower level of network externality. The intuition of the result is as follows. First note that a small means the pirate s produt is not reliable (a very low uality), hene not a very big threat (or less ompetition) to the original firm in the produt market, as a result easier to deter the pirate and stay as monopoly; whereas a relatively large means the pirate s produt is lose to the original produt, hene diffiult to keep the pirate away from the market. Now when is small and the market is fully overed and monopoly, from the orresponding seond stage profit expression ( ), it is not diffiult to see that the high uality would like to hoose a relatively high value of that maximizes its profit. On the other hand, when is large, it has to share the market and the low uality firm gets the benefit from the network (free riding effet), the high uality firm wants to hoose a lower value of to redue this negative impat of free riding and keep its ompetitive advantage. Under the low ost environment, sine the market is always fully overed and no sope of growth, keeping the respetive market shares is the driving fore.

14 Comparative Statis Figure plots the optimal level of network externality as a funtion of the uality index of the low uality produt. We find that the optimal level of network externality is dereasing in as it should be as the high uality firm wants to limit the free riding effet. owever, there is downward jump in the optimal level of as rosses a partiular threshold. Figure The optimal level of network externality as a funtion of when k= Numerial Example (k = ): emma : Under high ost environment, the optimal level of network externality hosen by the high uality firm is if k 0.644, if k 0.644, where 0, 4 is the optimum of f defined above. The market struture is always duopoly and it an be partially or fully overed. Proof: See Appendix B. First note here that the market struture is always duopoly. When is small, the high uality firm hooses a low level of network externality and the market is partially overed; when

15 beomes bigger, the high uality firm hooses a higher level of network externality and the market is fully overed. The intuition of the result is as follows. In this senario when is uite small, (i.e. the market is not very ompetitive), it is profitable for the high uality firm to hoose a lower level of i.e.. Whereas, when gets bigger and the market beomes more ompetitive, the high uality firm would like to hoose a higher level of, beause of the opportunity of growth in the market (as the market overage moves from partial to full) ignoring some of the negative impat of free riding of the low uality firm. In other words, the positive impat of revenue growth dominates the negative impat of free riding for the high uality firm here. Comparative Statis In Figure 3, we find that the optimal level of network externality is still dereasing in pieewise, however, we see a big upward jump in the optimal level of, when rosses the low threshold. Thus, the overall relationship between the two beomes non-monotoni. Figure 3 The optimal level of network externality as a funtion of when k= 6. Optimal evel of Network Externality Generalization One way to find the optimal level of for any ost environment is by omparing the marginal benefit and the marginal ost of inreasing. The marginal ost funtion of inreasing is simple: MC k. 3

16 MB Using the expressions for given at the beginning of Setion 6, we an straightforwardly derive the marginal benefit to firm of inreasing given below: MB It an be shown that 4 4 if 0, 4 if, 4 4 if, 9 if. MB is inreasing and stritly onvex in the first three regions and independent of in the last region. owever, on the whole, it is not well behaved: neither ontinuous nor monotoni. When rosses the boundary between the first region and the seond region, the third region, and the last region, MB jumps up; when rosses the boundary between the seond region and MB jumps down; when rosses the boundary between the third region MB jumps up again; and it remains onstant thereafter. Figure 4 shows the typial marginal benefit urve where we set =/ gamma Figure 4 The typial marginal benefit urve of inreasing the level of network externality (=/) 4

17 We an now say something about how is determined. Sine MB is not well behaved, is not neessarily determined by the intersetion point of marginal benefit urve and marginal ost urve as usual. For example, even if MB and MC interset at a point in the first region, sine MB jumps up when rosses the boundary between the first region and the seond region, a higher level of network externality may be even better for the high-uality firm. Given this ompliay, we turn to simulation. Figure 5 presents the main result from the simulation, in whih three olour-shaded (blue, green, brown) areas represent the first region, the boundary between the seond region and the third region (i.e. ), and the fourth region respetively.7 From Figure 5, we an see that there are three ritial values of k, k, k and k 3, whih separate k into four regions, eah orresponding to one pattern of the region distribution of When k k, as inreases from lose to 0 to lose to, moves from the fourth region to the boundary separating the seond region and the third region, i.e.,. When k k k, as inreases from lose to 0 to lose to,. moves from the fourth region to the first region and then to. When k k k3, as inreases from lose to 0 to lose to, moves from the first region to. When k k3, for any 0,, always lies in the first region. More simulation analysis refines the results and shows that the three ritial values of k are around.784,.805 and Refer to the beginning of Setion 6 (page 0), to reall the defined regions of. 5

18 Figure 5 Region distribution of the optimal level of network externality (k 7 and 0 ) The interval between k=.784 and k=.805 is very narrow, whih makes it diffiult to distinguish the seond pattern and the third pattern. owever, if we look at Figure 5 more losely, we an distinguish these two patterns: The brown-shaded area intersets the k-axis at a point above the point at whih the brown-, green-, and blue-shaded areas interset. Alternatively, we an draw another figure to show this differene more learly. Figure 6 presents the region distribution of for.6 k and

19 Figure 6 Region distribution of the optimal level of network externality (.6 k and 0 0.) From the above analysis, we find that three possible optimal values of will atually be hosen by the high uality firm in euilibrium: (medium level of ), and (low level of ), 4 (high level of ), where k k.805. k M Now orresponding to eah optimal value of an euilibrium market struture (monopoly or duopoly) is emerged and the market overage (full or partial) is also determined endogenously. 7

20 When the optimal value of is whih orresponds to a low degree of network externality, the market struture is duopoly i.e. shared by the high uality and the low uality firm and the market is partially overed. When the optimal value of is M whih orresponds to a medium degree of network externality, the market struture is duopoly i.e. shared by the high uality and the low uality firm and the market is fully overed. When the optimal value of is whih orresponds to a high degree of network externality, the market is monopolized by the high uality firm and the market is fully overed. In the table below, we list all possible euilibrium outomes, where k are ritial values of in eah relevant ase. k, Table Euilibrium outomes for different investment osts and relative uality differenes 8 Investment ost ow uality Euilibrium Outome (k) ow (k<.784) ow-medium (.784<k<.805) Medium (.805<k<5.05) Index () k Optimal degree of network externality Market Struture Market overage igh ( ) Monopoly Full k Medium ( ) Duopoly Full M k igh ( ) Monopoly Full k k ow ( ) Duopoly Partial k Medium ( ) Duopoly Full k M ow ( ) Duopoly Partial k igh (k>5.05) 0 ow ( Medium ( ) Duopoly Full M ) Duopoly Partial k and 8 The relative uality differene is defined to be -. 8

21 From the above analysis, below we summarize the main findings. Proposition In a model of vertial produt differentiation with demand network externalities, when the degree of the network externality is a strategi hoie of the high uality firm, the market an be monopolized and fully overed by the high uality firm when the investment ost on the network is low and the uality differene between the two produts is high, otherwise the market remains duopoly whih may be partially or fully overed. Comparative Statis Now we do the omparative statis analysis. We want to see for any ost environment, how the optimal network strength (i.e. ) varies when (i) there is a hange in the ost environment (i.e. hange in k), (ii) there is a hange in the uality differene of the produts (i.e. as hanges). First hange k. This hanges only the marginal ost funtion. As a result, down as k inreases. should go Next, hange. In this ase, obviously there will be no hange in the marginal ost funtion. owever, the marginal benefit funtion in eah region will hange. More interestingly, the boundary between the regions will hange beause there will be a hange in ˆ and ˆ (as defined early in Setion 5. and Figure ). The harater of the euilibrium an hange beause of the hange of the marginal benefit funtion in eah region and the hange in the boundaries. For example, we an see from Table that when k<.784, the market in euilibrium is a monopoly for, but it hanges to a duopoly for k k. One an find more examples from Table. When there is no hange in the harater of the euilibrium, then will hange monotonially with ; indeed, this is the ase for k>5.05. When the harater of the euilibrium itself hanges, then gives an example in whih does not hange smoothly or even monotonially. Figure is monotonially dereasing in even if the harater of the euilibrium hanges while Figure 3 gives an example in whih does not hange monotonially as hanges. 9

22 ene, the main result on omparative statis is summarized as follows. Proposition If the investment ost on the network is very low or very high, the optimal degree of network externality is always dereasing in (or inreasing in uality differene of the produts), but for any other levels of investment ost the relationship is non-monotoni. 7. Conlusion Piray of digital goods beame ommon due to the easy availability of opying tehnology. It is understood that rampant piray of digital goods is not desirable from the innovators as well as soiety s point of view in the long run. In this ontext, we onsider a model with an original digital good s produer and a ommerial pirate sharing the same platform and the network. We show how the original produer by optimally hoosing the strength of the network externality an strategially ontrol the market ompetition. Thus, in the markets where ommerial piray is a serious threat, piray an be fought by influening the demand network externality as an effetive instrument apart from other regular instruments; like monitoring, enrypting the software or drawing attention to the IPR authority to take punitive ation against the pirate. All these regular options to limit piray have already been disussed in great detail in the literature, but using the expliit strength of the network externality as tool to do the job has never been explored. This work is a ontribution in that diretion. In the analysis, first we set up the environment to solve for the optimal degrees of network strength for the original firm under any ost environment and haraterize endogenous euilibrium market strutures and market overages. In the omparative statis analysis, we show if the investment ost on the network is very low or high, the relationship between the optimal degree of network externality and relative uality differene of the produts is monotoni, but for other levels of investment osts, the relationship is non-monotoni. Typially, in the models of produt differentiation with network externality, the degree or the strength of the network effet is mostly assumed as a parameter. We depart from this and endogenize the level of network externality and see its impat on the market struture. To this end, we would also like to emphasize the fat that in models of vertial produt differentiation more often the extent of the market overage whether full or partial is also assumed to be 0

23 exogenous. We show that overing or not overing the market ould atually be a onseuene of the strategi game between the ompeting firms. In future we would like to extend the researh in the following diretion. In this analysis, we tried to apture the story of an original digital firm ombating ommerial piray by strategially hoosing the strength of network externality. The framework is of vertial produt differentiation. In a more general situation, the original firm also ompetes with other firms in the similar produt ategory. Think of ompetition in the market for Operating Systems (OS) between Mirosoft s Windows and Google s Android or Apple s ios. Eah of these firms is interested to provide more value and grow the number of its users using their platform of OS through various eletroni devies (smartphones, tablet et.), onneting those devies to eah other, and adding useful apps to the software that run those devies. All these naturally enhane the impat of network externality of its ore produt. In this set up, however, the ompeting ore produts (here the OSs) are not neessarily vertially differentiated but it is more of horizontal differentiation aross firms. Instead of addressing the piray issue, there we ould fous on the strategi ompetition between these digital good providers and see its impat on the resulting market struture and other important harateristis of the produt market ompetition. Referenes Banerjee, D. S. (003), Software Piray: A Strategi Analysis and Poliy Instruments, International Journal of Industrial Organization, Vol., Banerjee, D. S (03), Effet of Piray on Innovation in the Presene of Network Externalities Eonomi Modelling, Vol.33, Chou, C. and O. Shy (990), Network Effets without Network Externalities, International Journal of Industrial Organization, Vol. 8, Churh, J. and N. Gandal (993), Complementary Network Externalities and Tehnologial Adoption, International Journal of Industrial Organization, Vol., Conner, K. and R. Rumelt, (99), Software Piray: An Analysis of Protetion Strategies, Management Siene, Vol. 37, Katz, M.. and C. Shapiro, (985), Network Externalities, Competition, and Compatibility, Amerian Eonomi Review, Vol. 75,

24 Rohlfs, J. (974), A Theory of Interdependent Demand for a Communiation Servie, Bell Journal of Eonomis, Vol. 5, Shy, O. and J. F. Thisse, (999). A Strategi Approah to Software Protetion, Journal of Eonomis & Management Strategy, Vol. 8, Takeyama,. N., (994), The Welfare Impliations of Unauthorized Reprodution of Intelletual Property in the Presene of Network Externalities, Journal of Industrial Eonomis, Vol. 4, Wauthy, X. (996), Quality Choie in Models of Vertial Differentiation, Journal of Industrial Eonomis, Vol. 65, Appendix A p p The high-uality produer maximizes p D p The low-uality produer maximizes p p. The first-order ondition is p p 0. (A) p D p p p p subjet to p 0. Define the agrangian onditions are and If p p p p p. The first-order and slakness p p 0, p 0, p 0, p 0., then we must have p p 0. Given p (A), it follows that p p / /, (A3) p p /. Thus, 0 ˆ If p 0, then we must have 0 and p p 0. (A4)

25 The solution to the system of euations (A.) and (A.4) is It follows that Thus, 3, p p p 3 3. p 0 ˆ. 3. (A5) Note that for (A5) to be the solution, must not exeed : ~ ; so that the prie of the low-uality produt is nonnegative: p 0. The demands and profits for both firms are then obtained straightforwardly. The expressions are given in Setion 5. and will not be repeated here. Appendix B ow Cost Environment: k= Consider relevant region Next we examine f first. We an easily show that Therefore, f is maximized at. 4 4 relevant region 4 We now examine relevant region Finally we examine g. It an be shown that and thus f 0 in the g 0 in the 4 g is maximized at h. We an easily show that. Therefore, h is maximized at j. Sine j, 0 0.5, and is maximized at if h 0 in the. j is maximized at if 3

26 Combining the above results, we an onlude that (i) the optimal level of network externality is if 0.5 and (ii) if 0 0.5, to find the optimal level of network externality, we need to ompare the high uality firm s net profits when and when. Straightforward alulation yields that when h j 0 when igh Cost Environment: k= Consider f first. By examining f and f, we an easily show that f is maximized at the interior of the region expression of annot be derived. Next we examine g. By examining help of simulation, 9 we an show that the interior of the region 0, 4, denoted by g and g g is maximized at. owever, a losed-form and tedious alulation with the when , at 4, 4 denoted by when , and at when 0.6. owever, a losed-form expression of annot be derived. We now examine relevant region h. We an easily show that. Therefore, h is maximized at 9 h 0. in the 9 In the relevant range, 4, the funtion g is monotonially dereasing when , inreasing when 0.69, while it is inreasing first, then dereasing and then inreasing again when Given the omplexity of the funtional form, we have to turn to simulation when to determine the optimal level of network externality in this relevant range. Simulation results are available upon reuest. 4

27 Finally we examine j. Sine j 0, j is maximized at. Combining the above results, we an onlude that (i) the optimal level of network externality is if , (ii) if , to find the optimal level of network externality, we need to ompare the high uality firm s net profits when and when, and (iii) if 0.6, to find the optimal level of network externality, we need to ompare the high uality firm s net profits when and when. Sine the losed-form expressions of and annot be derived, we have to turn to simulation to find the optimal level of network externality. Simulation yields () is always dominated by, i.e., g f, and () g f when , while g f when