- Email: [email protected]
Optimal product strategies in the presence of network externalities
Information Economics and Policy 10 (1998) 489–499
Optimal product strategies in the presence of network externalities Ernan Haruvy a , *, Ashutosh Prasad b a
Department of Economics, University of Texas, Austin, TX 78712 -1173, USA Department of Marketing, University of Texas, Austin, TX 78712 -1176, USA
b
Received 30 March 1998; accepted 12 June 1998
Abstract A network externality exists when a user’s benefit from a product increases with the number of other users in the same network. We examine the possibility that a software firm may exploit network externalities by introducing a limited feature version of its commercially available software into the market. The two versions need not be perfectly compatible and network externalities are allowed to decline as the difference between the versions increases. We obtain conditions under which introducing a limited feature version is optimal. 1998 Elsevier Science B.V. All rights reserved. Keywords: Network externalities; Shareware JEL Classification: L1
1. Introduction A network externality, also known as demand externality, exists when the benefit to a consumer from a product increases with the number of other users of identical, highly similar, or compatible products. Several reasons for this additional utility have been offered. Consider the example of software. From the consumers’ perspective, a larger software network size means more and better services, a larger base of compatible software, file compatibility, the availability of newsgroups, an increased likelihood of future upgrades, and reduced search costs and uncertainty about the product (Herbig and Kramer, 1993; Shurmer, 1993). * Corresponding author. [email protected].
Tel.:
11-512-4789396;
fax:
11-512-4713510;
0167-6245 / 98 / $19.00 1998 Elsevier Science B.V. All rights reserved. PII S0167-6245( 98 )00014-6
e-mail:
490
E. Haruvy, A. Prasad / Information Economics and Policy 10 (1998) 489 – 499
Internet newsgroups allow consumers to help each other in learning the software and in getting relevant information about its applications and extensions. Network externalities have been exploited in high-technology product markets for a long time. The literature on network externalities in these markets includes, but is not limited to, the use of penetration pricing (Katz and Shapiro, 1986), tolerance of piracy (Conner and Rumelt, 1991; Takeyama, 1994), compatibility with existing products (Conner, 1995), and product pre-announcements (Farrell and Saloner, 1986). Another avenue for software firms to capitalize on demand network externalities in the software market is the introduction of ‘limited versions’ of commercially available software products. Product strategies falling under the ‘limited version’ category include free limited period trials, stripped down versions of the software, shareware, freeware, and limited feature products at lower prices; for example, non-commercial and student versions. This essay concerns the optimization of these latter methods by seeking to provide guidelines for product strategies falling in the ‘limited version’ category. Note that distribution of the limited version may cannibalize sales from the commercial version and result in lower profits for the firm. We analyze the trade-off faced by a software firm deciding to produce a limited version of its existing software and provide conditions where undertaking such action is optimal. In taking the decision to introduce a limited version, the firm must examine the associated trade-off. On one hand, sales of the commercial version may be cannibalized by the limited version, or, in trying to reduce cannibalization, the firm may have to lower prices on its high quality commercial version. On the other hand, a larger user base increases the software’s value and results in higher prices. The limited version also encourages trial of the software and allows consumers to learn their valuations for it, though these benefits are not modeled in this paper. The present essay deals with multiple versions of software, which raises the issue of compatibility between versions (Choi, 1994; Katz and Shapiro, 1985; Katz and Shapiro, 1992). In contrast to the literature that assumes that versions are either totally compatible or totally incompatible, the approach taken here is to allow for intermediate levels of compatibility. Unlike papers on piracy where the firm has no control over the quality of the pirated version, in the present situation the quality of the different versions is endogenous to the firm, which complicates the analysis somewhat. We model the quality of the limited version product as an endogenous variable, and make the network externality derived between products contingent upon the relative quality levels of the two versions. A mechanism design approach is taken. The intuition is that firms may be able to exploit network externalities by introducing a limited feature version with quality high enough for consumers who have low valuation for quality to acquire it, but low enough that high-valuation consumers are still willing to purchase the higher priced commercial version.
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2. Real world examples of the ‘limited version’ product strategy Limited feature software is time limited if the program or service is available for a limited time, or trial period, after which it is terminated. An example is America Online’s offer of free limited duration access to its online services on trial diskettes. Other examples include trial subscriptions to Internet magazines, newspapers, and chat rooms. Software may also be content limited, also known as ‘‘demo’’ versions. These programs are not perfect substitutes to the ones offered commercially for lack of graphics, sound, or other neat but not essential, features of the sold version. The limited version can be either time limited, content limited, or both. For example, in the America Online trial offer, certain services were restricted to members only. Freeware and shareware products, which are widely available on the Internet, can often be viewed as limited versions. Freeware, or free copyrighted software, can be thought of as a content limited offer. The Satan security network, the Linux operating system, and the Mosaic browser are all examples of commercial programs that started as freeware. Satan was released as a commercial version in January 1996, after having been released as a freeware in April 1995. Its commercial version was much more comprehensive than the freeware version (Wingfield, 1996). A commercial version of Linux also followed its freeware version in order to meet the needs of IS managers for support and maintenance (Corcoran and Schlack, 1995). Mosaic’s freeware version was the first graphical interface to the Internet. It was developed as one of the projects of the NCSA, which also developed the freeware Telnet. A commercial version of Mosaic was released by Mosaic Communications Corp. in October 1994. Currently both the commercial version and the older freeware versions are available. Netscape 1.ON by Netscape Communication and Sparkle for viewing quicktime movies by Maynard Handley are other examples of programs that were initially distributed as freeware. Shareware is defined as ‘‘try before you buy’’ software, and is a market estimated at $300 million (Foley, 1995). The ‘‘try’’ and the ‘‘buy’’ versions correspond to the two versions in our model. Unlike cheapware which is free public domain software, and freeware which is also free but copyrighted, shareware is offered for the purpose of making profit (Morin, 1993a). Shareware is typically distributed over electronic bulletin boards along with instructions to mail a check to the developer if one uses the software. Because shareware publishers do not have marketing costs, the price is quite low, and includes charges for consultation, documentation and upgrades 1 . Some shareware programs have sold millions of copies. Two prominent examples are the 1 Customers pay the shareware fee to obtain the additional quality. To an extent though, paying for shareware is based on a honor system which is somewhat difficult to capture in a model of fully rational economic agents.
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file-compression utility PKZIP, and the computer game DOOM (Gutman, 1996). DOOM by ID software is an action game that is available in several versions. The shareware version has only 8 game levels whereas the commercial version called ‘‘DOOM II: Hell on Earth’’ has 30 levels as well as additional features. The variety of shareware products currently on the market is very large and includes screen savers, file compression and decompression software, word processors, anti-virus software, specific program enhancers, games, graphics, file managers, scientific libraries, and more. Two of the largest shareware sites – Jumbo and C / net – distribute hundreds of thousands of freeware and shareware titles. Shareware and commercial versions of a program may be released simultaneously, as in our model; an example of which is PROCOMM PLUS by Datastorm Technologies, Inc. Some freeware and shareware programs are of very high quality comparable with commercially available programs. More commonly, however, shareware and freeware of commercially available programs are of lower quality, where the limitations include lack of documentation and technical support, lower reliability due to lack of extensive debugging (Morin, 1993b) and a higher possibility of virus infection. Consultation services may be quite poor which is one reason why large companies prefer more expensive commercially marketed software. The low-quality version serves the purpose of allowing users to familiarize themselves with the software and generates network externalities for adopters of the commercial version.
3. The model We present a static model of a software firm’s decision making process on whether or not to make a second version of a commercial product available given the presence of network externalities. In a static two-stage game setting, the firm moves first, making a decision on the number of versions to be introduced, their qualities, and their prices. Next, the potential consumers decide whether or not to adopt either version of the product. For simplification purposes, it is assumed that there is no sequential introduction of products. This is reasonable if consumers have perfect foresight and little or no discounting of the future. The model is limited to two types of consumers and hence, to two versions of the product. It could, however, be more realistically extended to include more than two consumer types. A general representation is discussed first and then suggestions are made for parametric forms of the consumers’ utility functions. We assume the firm is a monopolistic supplier of the software it produces, meaning that the product in question is highly differentiated from all other products of its type. The firm has an existing software version of quality Q H . It also has the option of marketing a second version with a lower quality Q L 5 g Q H , where 0 # g , 1. The firm seeks to maximize its profits by deciding on
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appropriate prices for its products as well as on an appropriate quality, Q L , for its limited feature version. A decision to not introduce the limited version is equivalent to g 5 0. The term ‘‘quality’’ is used in the most general sense. Quality 2 may refer to the number of features available in a product version, time limit on the use of the product, availability of customer service, availability of product upgrades, packaging, or any other consistent quantifiable measure of quality such that higher quality would imply higher utility. There are two homogenous consumer types that differ in the amount of value they assign to quality. The high valuation type will henceforth be referred to by the letter H, and the low valuation type by the letter L. There are Ni consumers of type i, where i [ hL, Hj. Consumers of both types H and L face the same set of prices for purchasing the high-quality and low-quality software. Marginal costs are assumed constant and equal to zero.3 Depending on the functional form of the utility function and on NH and NL , there may be multiple equilibria. We will focus on separating and pooling equilibria in which all agents of the same type select the version intended for them. The strategic decisions that the firm needs to make are shown in Table 1. The expected profits, P, associated with each decision are calculated by adding up the price of each version times the quantity sold of that version. The prices Pi , i 5 1,...,5, are subscripted to identify their location in Table 1 during further analysis. Specifically, P1 is the price of the commercial version if the low valuation type does not participate. P2 is the price of the commercial version if both consumer types participate. P3 is the commercial version price when the limited version is free. And P4 is the price of the commercial version when the limited version is sold at price, P5 . Cells 1 and 2 represent the alternatives open to the firm under the single version
Table 1 Strategic choices for the firm Sell to high types only
Sell to both types
No limited version
Cell 1 P1 5NH P1
Cell 2 P2 5(NH 1NL )P2
Introduce limited version
Cell 3 P3 5NH P3
Cell 4 P4 5NH P4 1NL P5
2
We consider quality to be a continuous measure readily observable by all players. This is a simplification of the actual market in which one of the purposes of a limited version is to allow an assessment of the quality of the commercial version. 3 The main reason behind this assumption is to make the marginal costs independent of the quality level in order to prevent several additional equilibria. The assumption is valid in the situation, such as we assume, where the commercial version already exists, and providing a limited version merely involves disabling some of the features of the commercial version. Moreover, the major portion of costs in the software industry is fixed costs.
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scenario. Cell 3 is a separating equilibrium in the two version scenario, where the limited version is offered free to the low type consumers. This is a special case of Cell 4 in which both the high and low types pay positive prices. We shall now proceed to calculate the profit-maximizing prices and compare the profits in the different cells.
3.1. The one version scenario The valuation of a given product for a type i consumer, i [ hL, Hj, is given by the general form Vi (Q, X), where Q denotes the product’s quality and X denotes the size of the product’s network. In the following derivations, a convenient and realistic assumption is that NH and NL are sufficiently large to make the network externality effect of one user switching from one version to another insignificant. Otherwise, numerous unstable and inconsequential equilibria are possible. Vi is increasing in both Q and X. We assume that X is a function of the number of adopters of the commercial version and the number of adopters of the limited version. We further assume that the marginal utility of the high type from an additional unit of quality is higher than that of the low type for a given quality and installed base; that is: dVH (Q, X) / dQu Q 5Q * . dVL (Q, X) / dQu Q 5Q * . In other words, the high valuation type appreciates quality more than the low valuation type. This is the usual assumption of the single crossing property. In Cell 1 of Table 1, the firm can charge the high valuation consumers their valuation for the product: P1 5VH (Q H , NH ),
(1)
and reap the profits:
P1 5 NHVH (Q H , NH ).
(2)
Cell 2 is a pooling equilibrium where both high and low valuation types purchase the single version offered. The low type’s participation constraint must be satisfied, and given that it is satisfied, the participation constraint holds for the high valuation type as well. The maximum price that the firm can charge and its profits are given by: P2 5VL (Q H , NH 1 NL ),
(3)
P2 5 (NH 1 NL ) VL (Q H , NH 1 NL ).
(4)
and,
Comparing Eqs. (2) and (4), it is clear that P2 is more likely to be preferred to P1 the larger NL is relative to NH and the closer VL (?) is to VH (?). P2 will be worse off in comparison to P1 if the reverse conditions hold. In order to quantify these
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comparisons, further assumptions are required. These are made in Section 4 where functional forms are introduced.
3.2. The two version scenario With two versions, the quality of the second version can be represented as a fraction g of the quality of the existing version. Hence, the second version and the existing version are imperfect substitutes. This implies that though the two versions may be compatible and belong to the same installed base, the network externality derived by users from an additional user of the same version is greater than that derived from an additional user of a different version. That means that in a separating outcome the network size for consumer type i5L, H will have the form: X 5 Ni 1 g(N2i , g ),
i 5 L, H
(5)
where g is increasing in g and Ni , but where g(N2i , g ),N2i for all 0#g # 1. A possible choice for g(N2i , g ) is g N2i . The intuition is that if the two versions have similar qualities, a higher network externality will result. Consider Cell 4 in Table 1. We have a separating strategy for the firm in which the original version is intended for the high-valuation type and the limited version is intended for the low valuation type. For a separating strategy, the firm has to make sure each consumer picks the contract intended for her type. Four constraints result: VL (Q H , NH 1 g (NL , g )) 2 P4 #VL (g Q H , NL 1 g (NH , g )) 2 P5 ,
(6a)
VH (Q H , NH 1 g (NL , g )) 2 P4 $ VH (g Q H , NL 1 g (NH , g )) 2 P5 ,
(6b)
VL (g Q H , NL 1 g (NH , g )) 2 P5 $ 0,
(6c)
VH (Q H , NH 1 g (NL , g )) 2 P4 $ 0.
(6d)
The above four constraints ensure incentive compatibility for the low valuation type, incentive compatibility for the high valuation type, participation of the low types, and participation of the high types, respectively. Noting that constraint (6d) is redundant since it is implied by restrictions (6b) and (6c), we identify the firm’s problem as having to choose the three variables g, P4 , and P5 which maximize its objective function P4 5NH P4 1NL P5 , subject to the three constraints (6a), (6b), and (6c). It is a general result in mechanism design models that the incentive compatibility constraint for the high-valuation type and the participation constraint for the low-valuation type will be binding. From this we obtain the values for P4 and P5 .
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P4 5VH (Q H , NH 1 g (NL ,g )) 2VH (g Q H , NL 1 g (NH ,g )) 1VL (g Q H , NL 1 g (NH ,g )), P5 5VL (g Q H , NL 1 g (NH ,g )).
(7) (8)
The prices in the profit calculation for Cell 4 of Table 1 are obtained from (7) and (8). The profit is then:
P4 5 NH [ VH (Q H , NH 1 g (NL ,g )) 2 VH (g Q H , NL 1 g (NH ,g )) 1 VL (g Q H , NL 1 g (NH ,g ))] 1 NL [VL (g Q H , NL 1 g (NH ,g ))].
(9)
The choice of g can be determined by the maximization of P4 with respect to g to obtain the optimal value g *. The profits in Cell 3 are a special case of this where P5 50. Since the strategy space for Cell 3 is a subset of that for Cell 4, we would expect strategy of Cell 3 to be weakly dominated by strategy of Cell 4. Consider now a comparison of the profits in the pooling equilibrium, P2 , and the profits in the separating equilibrium, P4 . The separating equilibrium is preferred if the following condition holds: NH [VH (Q H , NH 1 g(NL , g *)) 2VH (g Q H , NL 1 g(NH ,g *)) 1VL (g Q H , NL 1 g (NH ,g *)) 2VL (Q H , NH 1 NL )] $ NL [ VL (Q H , NH 1 NL ) 2VL (g Q H , NL 1 g(NH ,g *))].
(10)
This condition is more likely to be met the larger the size of the high valuation group relative to the size of the low valuation group and the larger the value of g *; that is, the closer the quality levels of the two versions.
4. Introducing functional forms Recall that the utility that a consumer derives from the product he selects is increasing in the quality of the product, Q, and the network size for the product in that period, X. Also, recall the essential single crossing property condition. There are infinitely many functional forms for consumer utility that would satisfy these simple requirements. Consider the functional form introduced by Padmanabhan et al. (1997): Vi (Q, X) 5 (ui 1 b X a ) Q, where ui , b, a . 0 and uH . uL .
(11)
This general form leads to intractable first and second order conditions. Upon setting b51 and a 51 as suggested by Padmanabhan et al. (1997), with some loss of generality, second order conditions rule out maximization of Eq. (9) with respect to g. Furthermore, this form does not allow for estimation of the
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parameters u, b, and a by traditional linear regression methods, and rather requires more complicated non-linear methods. Therefore, we suggest the alternative form: Vi (Q, X) 5 ui X a Q, where ui , a . 0 and uH . uL .
(12)
This functional form corresponds to the traditional Cobb-Douglas utility in economic theory, satisfies the single crossing property, allows for linear estimation procedures on the parameters (by taking the affine log transformation of the utility function), and no loss of generality for preliminary analysis occurs when a 51 (under certain restrictions). Maximizing P4 in Eq. (9) with respect to g using the functional form of Eq. (12), we get the optimal quality parameter g to be NL uL (NH 1 NL ) g * 5 ]]]]]]]. 2NH [(uH 2 uL )NH 2 NLuL ]
(13)
Note that g * is more likely to be positive when uH is large relative to uL , and NH is large relative to NL . Furthermore, the larger NH is relative to NL , the more likely g * is to be less than 1. To demonstrate, let NH 5 f NL . Then as f →`, g *→0. Note that if g *[ ⁄ (0,1), no equilibrium involving a limited version product strategy will survive. Hence, a limited version strategy will be optimal only when NH is large relative to NL (as well as more likely to be optimal the larger uH is relative to uL ). This claim is confirmed by the second order condition to the maximization problem: d 2 P4 ]] 5 2 2NH Q H [(uH 2 uL )NH 2 NLuL ] , 0. dg2
(14)
Moreover, the larger size of NH relative to NL is crucial for a separating outcome to be preferred by the firm to a pooling outcome, as is evident from Eq. (10). Hence, after estimating (or calibrating) parameters uH and uL and assessing the network base, NL and NH , if Eq. (13) yields g * such that 0,g * ,1, this will generally indicate that NL
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to include more general functional forms using the non-form specific equations of Section 3.
5. Conclusions and future extensions We introduced a mechanism design procedure to allow software firms (as well as firms in other markets with demand externalities) to exploit the presence of network externalities. We have shown that there are conditions under which a separating equilibrium exists, with two versions of a software product sold to two different consumer classes. Our mechanism explains to a great degree the recent trend toward increasing prominence of shareware and freeware versions of many software products. We believe that our characterization of the limited version mechanism may help in optimizing the design of these versions for the firms’ benefit. The results of this paper should be interpreted with caution. While the basic intuition is robust to relaxation of assumptions, some of the results such as the weak domination of freeware versions by positive priced limited versions may change. The reason for this is the assumption that the quality of the products is identifiable by all the consumers. When this is not possible, freeware becomes important as a device for encouraging trial. We have also not accounted for competition. It is difficult to say what the results would be if competitive brands were available. A dynamic model of sequential introduction warrants serious pursuit. Such a model would have the capability to account for asymmetric information, where in the initial period the firm may obtain information on the network base by releasing the limited version as well as provide the consumer with information on the quality of the commercial version.
References Choi, J.P., 1994. Network externality, compatibility choice, and planned obsolescence, Journal of Industrial Economics 42, 167–182. Conner, K.R., Rumelt, R.P., 1991. Software piracy: An analysis of protection strategies, Management Science 37, 125–139. Conner, K.R., 1995. Obtaining strategic advantage from being imitated: When can encouraging ‘‘clones’’ pay?, Management Science 41, 209–225. Corcoran, C.T., Schlack, M., 1995. Internet servers for under $100? Here’s one!, Datamation 41 (12), 41–43. Farrell, J., Saloner, G., 1986. Installed base and compatibility: Innovation, product preannouncements, and predation, American Economic Review 76, 940–955. Foley, J., 1995. The shareware alternative, Information Week 540 (August 14), 32. Gutman, D., 1996. Software deals, Success 43 (9), 64.
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Herbig, P., Kramer, H., 1993. Innovation inertia: The power of the installed base, Journal of Business and Industrial Marketing 8, 44–57. Katz, M., Shapiro, C., 1985. Network externalities, competition, and compatibility, American Economic Review 75, 424–440. Katz, M., Shapiro, C., 1986. Technology adoption in the presence of network externalities, Journal of Political Economy 94, 822–841. Katz, M., Shapiro, C., 1992. Product introduction with network externalities, Journal of Industrial Economics 40, 55–84. Morin, R., 1993a. The meaning of freeware, Unix Review 11 (12), 101–102. Morin, R., 1993b. Distributed quality assurance, Unix Review 11 (9), 107–108. Padmanabhan, V., Surendra, R., Srinivasan, K., 1997. New products, upgrades, and new releases: A rationale for sequential product introduction, Journal of Marketing Research 34, 456–472. Shurmer, M., 1993. An investigation into sources of network externalities in a packaged PS software market, Information Economics and Policy 5, 231–251. Takeyama, L.N., 1994. The welfare implications of unauthorized reproduction of intellectual property in the presence of demand network externalities, Journal of Industrial Economics 42, 155–166. Wingfield, N., 1996. Internet securities releases commercial version of Satan, Infoworld 18 (3), 18.
Optimal product strategies in the presence of network externalities Ernan Haruvy a , *, Ashutosh Prasad b a
Department of Economics, University of Texas, Austin, TX 78712 -1173, USA Department of Marketing, University of Texas, Austin, TX 78712 -1176, USA
b
Received 30 March 1998; accepted 12 June 1998
Abstract A network externality exists when a user’s benefit from a product increases with the number of other users in the same network. We examine the possibility that a software firm may exploit network externalities by introducing a limited feature version of its commercially available software into the market. The two versions need not be perfectly compatible and network externalities are allowed to decline as the difference between the versions increases. We obtain conditions under which introducing a limited feature version is optimal. 1998 Elsevier Science B.V. All rights reserved. Keywords: Network externalities; Shareware JEL Classification: L1
1. Introduction A network externality, also known as demand externality, exists when the benefit to a consumer from a product increases with the number of other users of identical, highly similar, or compatible products. Several reasons for this additional utility have been offered. Consider the example of software. From the consumers’ perspective, a larger software network size means more and better services, a larger base of compatible software, file compatibility, the availability of newsgroups, an increased likelihood of future upgrades, and reduced search costs and uncertainty about the product (Herbig and Kramer, 1993; Shurmer, 1993). * Corresponding author. [email protected].
Tel.:
11-512-4789396;
fax:
11-512-4713510;
0167-6245 / 98 / $19.00 1998 Elsevier Science B.V. All rights reserved. PII S0167-6245( 98 )00014-6
e-mail:
490
E. Haruvy, A. Prasad / Information Economics and Policy 10 (1998) 489 – 499
Internet newsgroups allow consumers to help each other in learning the software and in getting relevant information about its applications and extensions. Network externalities have been exploited in high-technology product markets for a long time. The literature on network externalities in these markets includes, but is not limited to, the use of penetration pricing (Katz and Shapiro, 1986), tolerance of piracy (Conner and Rumelt, 1991; Takeyama, 1994), compatibility with existing products (Conner, 1995), and product pre-announcements (Farrell and Saloner, 1986). Another avenue for software firms to capitalize on demand network externalities in the software market is the introduction of ‘limited versions’ of commercially available software products. Product strategies falling under the ‘limited version’ category include free limited period trials, stripped down versions of the software, shareware, freeware, and limited feature products at lower prices; for example, non-commercial and student versions. This essay concerns the optimization of these latter methods by seeking to provide guidelines for product strategies falling in the ‘limited version’ category. Note that distribution of the limited version may cannibalize sales from the commercial version and result in lower profits for the firm. We analyze the trade-off faced by a software firm deciding to produce a limited version of its existing software and provide conditions where undertaking such action is optimal. In taking the decision to introduce a limited version, the firm must examine the associated trade-off. On one hand, sales of the commercial version may be cannibalized by the limited version, or, in trying to reduce cannibalization, the firm may have to lower prices on its high quality commercial version. On the other hand, a larger user base increases the software’s value and results in higher prices. The limited version also encourages trial of the software and allows consumers to learn their valuations for it, though these benefits are not modeled in this paper. The present essay deals with multiple versions of software, which raises the issue of compatibility between versions (Choi, 1994; Katz and Shapiro, 1985; Katz and Shapiro, 1992). In contrast to the literature that assumes that versions are either totally compatible or totally incompatible, the approach taken here is to allow for intermediate levels of compatibility. Unlike papers on piracy where the firm has no control over the quality of the pirated version, in the present situation the quality of the different versions is endogenous to the firm, which complicates the analysis somewhat. We model the quality of the limited version product as an endogenous variable, and make the network externality derived between products contingent upon the relative quality levels of the two versions. A mechanism design approach is taken. The intuition is that firms may be able to exploit network externalities by introducing a limited feature version with quality high enough for consumers who have low valuation for quality to acquire it, but low enough that high-valuation consumers are still willing to purchase the higher priced commercial version.
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2. Real world examples of the ‘limited version’ product strategy Limited feature software is time limited if the program or service is available for a limited time, or trial period, after which it is terminated. An example is America Online’s offer of free limited duration access to its online services on trial diskettes. Other examples include trial subscriptions to Internet magazines, newspapers, and chat rooms. Software may also be content limited, also known as ‘‘demo’’ versions. These programs are not perfect substitutes to the ones offered commercially for lack of graphics, sound, or other neat but not essential, features of the sold version. The limited version can be either time limited, content limited, or both. For example, in the America Online trial offer, certain services were restricted to members only. Freeware and shareware products, which are widely available on the Internet, can often be viewed as limited versions. Freeware, or free copyrighted software, can be thought of as a content limited offer. The Satan security network, the Linux operating system, and the Mosaic browser are all examples of commercial programs that started as freeware. Satan was released as a commercial version in January 1996, after having been released as a freeware in April 1995. Its commercial version was much more comprehensive than the freeware version (Wingfield, 1996). A commercial version of Linux also followed its freeware version in order to meet the needs of IS managers for support and maintenance (Corcoran and Schlack, 1995). Mosaic’s freeware version was the first graphical interface to the Internet. It was developed as one of the projects of the NCSA, which also developed the freeware Telnet. A commercial version of Mosaic was released by Mosaic Communications Corp. in October 1994. Currently both the commercial version and the older freeware versions are available. Netscape 1.ON by Netscape Communication and Sparkle for viewing quicktime movies by Maynard Handley are other examples of programs that were initially distributed as freeware. Shareware is defined as ‘‘try before you buy’’ software, and is a market estimated at $300 million (Foley, 1995). The ‘‘try’’ and the ‘‘buy’’ versions correspond to the two versions in our model. Unlike cheapware which is free public domain software, and freeware which is also free but copyrighted, shareware is offered for the purpose of making profit (Morin, 1993a). Shareware is typically distributed over electronic bulletin boards along with instructions to mail a check to the developer if one uses the software. Because shareware publishers do not have marketing costs, the price is quite low, and includes charges for consultation, documentation and upgrades 1 . Some shareware programs have sold millions of copies. Two prominent examples are the 1 Customers pay the shareware fee to obtain the additional quality. To an extent though, paying for shareware is based on a honor system which is somewhat difficult to capture in a model of fully rational economic agents.
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file-compression utility PKZIP, and the computer game DOOM (Gutman, 1996). DOOM by ID software is an action game that is available in several versions. The shareware version has only 8 game levels whereas the commercial version called ‘‘DOOM II: Hell on Earth’’ has 30 levels as well as additional features. The variety of shareware products currently on the market is very large and includes screen savers, file compression and decompression software, word processors, anti-virus software, specific program enhancers, games, graphics, file managers, scientific libraries, and more. Two of the largest shareware sites – Jumbo and C / net – distribute hundreds of thousands of freeware and shareware titles. Shareware and commercial versions of a program may be released simultaneously, as in our model; an example of which is PROCOMM PLUS by Datastorm Technologies, Inc. Some freeware and shareware programs are of very high quality comparable with commercially available programs. More commonly, however, shareware and freeware of commercially available programs are of lower quality, where the limitations include lack of documentation and technical support, lower reliability due to lack of extensive debugging (Morin, 1993b) and a higher possibility of virus infection. Consultation services may be quite poor which is one reason why large companies prefer more expensive commercially marketed software. The low-quality version serves the purpose of allowing users to familiarize themselves with the software and generates network externalities for adopters of the commercial version.
3. The model We present a static model of a software firm’s decision making process on whether or not to make a second version of a commercial product available given the presence of network externalities. In a static two-stage game setting, the firm moves first, making a decision on the number of versions to be introduced, their qualities, and their prices. Next, the potential consumers decide whether or not to adopt either version of the product. For simplification purposes, it is assumed that there is no sequential introduction of products. This is reasonable if consumers have perfect foresight and little or no discounting of the future. The model is limited to two types of consumers and hence, to two versions of the product. It could, however, be more realistically extended to include more than two consumer types. A general representation is discussed first and then suggestions are made for parametric forms of the consumers’ utility functions. We assume the firm is a monopolistic supplier of the software it produces, meaning that the product in question is highly differentiated from all other products of its type. The firm has an existing software version of quality Q H . It also has the option of marketing a second version with a lower quality Q L 5 g Q H , where 0 # g , 1. The firm seeks to maximize its profits by deciding on
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appropriate prices for its products as well as on an appropriate quality, Q L , for its limited feature version. A decision to not introduce the limited version is equivalent to g 5 0. The term ‘‘quality’’ is used in the most general sense. Quality 2 may refer to the number of features available in a product version, time limit on the use of the product, availability of customer service, availability of product upgrades, packaging, or any other consistent quantifiable measure of quality such that higher quality would imply higher utility. There are two homogenous consumer types that differ in the amount of value they assign to quality. The high valuation type will henceforth be referred to by the letter H, and the low valuation type by the letter L. There are Ni consumers of type i, where i [ hL, Hj. Consumers of both types H and L face the same set of prices for purchasing the high-quality and low-quality software. Marginal costs are assumed constant and equal to zero.3 Depending on the functional form of the utility function and on NH and NL , there may be multiple equilibria. We will focus on separating and pooling equilibria in which all agents of the same type select the version intended for them. The strategic decisions that the firm needs to make are shown in Table 1. The expected profits, P, associated with each decision are calculated by adding up the price of each version times the quantity sold of that version. The prices Pi , i 5 1,...,5, are subscripted to identify their location in Table 1 during further analysis. Specifically, P1 is the price of the commercial version if the low valuation type does not participate. P2 is the price of the commercial version if both consumer types participate. P3 is the commercial version price when the limited version is free. And P4 is the price of the commercial version when the limited version is sold at price, P5 . Cells 1 and 2 represent the alternatives open to the firm under the single version
Table 1 Strategic choices for the firm Sell to high types only
Sell to both types
No limited version
Cell 1 P1 5NH P1
Cell 2 P2 5(NH 1NL )P2
Introduce limited version
Cell 3 P3 5NH P3
Cell 4 P4 5NH P4 1NL P5
2
We consider quality to be a continuous measure readily observable by all players. This is a simplification of the actual market in which one of the purposes of a limited version is to allow an assessment of the quality of the commercial version. 3 The main reason behind this assumption is to make the marginal costs independent of the quality level in order to prevent several additional equilibria. The assumption is valid in the situation, such as we assume, where the commercial version already exists, and providing a limited version merely involves disabling some of the features of the commercial version. Moreover, the major portion of costs in the software industry is fixed costs.
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scenario. Cell 3 is a separating equilibrium in the two version scenario, where the limited version is offered free to the low type consumers. This is a special case of Cell 4 in which both the high and low types pay positive prices. We shall now proceed to calculate the profit-maximizing prices and compare the profits in the different cells.
3.1. The one version scenario The valuation of a given product for a type i consumer, i [ hL, Hj, is given by the general form Vi (Q, X), where Q denotes the product’s quality and X denotes the size of the product’s network. In the following derivations, a convenient and realistic assumption is that NH and NL are sufficiently large to make the network externality effect of one user switching from one version to another insignificant. Otherwise, numerous unstable and inconsequential equilibria are possible. Vi is increasing in both Q and X. We assume that X is a function of the number of adopters of the commercial version and the number of adopters of the limited version. We further assume that the marginal utility of the high type from an additional unit of quality is higher than that of the low type for a given quality and installed base; that is: dVH (Q, X) / dQu Q 5Q * . dVL (Q, X) / dQu Q 5Q * . In other words, the high valuation type appreciates quality more than the low valuation type. This is the usual assumption of the single crossing property. In Cell 1 of Table 1, the firm can charge the high valuation consumers their valuation for the product: P1 5VH (Q H , NH ),
(1)
and reap the profits:
P1 5 NHVH (Q H , NH ).
(2)
Cell 2 is a pooling equilibrium where both high and low valuation types purchase the single version offered. The low type’s participation constraint must be satisfied, and given that it is satisfied, the participation constraint holds for the high valuation type as well. The maximum price that the firm can charge and its profits are given by: P2 5VL (Q H , NH 1 NL ),
(3)
P2 5 (NH 1 NL ) VL (Q H , NH 1 NL ).
(4)
and,
Comparing Eqs. (2) and (4), it is clear that P2 is more likely to be preferred to P1 the larger NL is relative to NH and the closer VL (?) is to VH (?). P2 will be worse off in comparison to P1 if the reverse conditions hold. In order to quantify these
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comparisons, further assumptions are required. These are made in Section 4 where functional forms are introduced.
3.2. The two version scenario With two versions, the quality of the second version can be represented as a fraction g of the quality of the existing version. Hence, the second version and the existing version are imperfect substitutes. This implies that though the two versions may be compatible and belong to the same installed base, the network externality derived by users from an additional user of the same version is greater than that derived from an additional user of a different version. That means that in a separating outcome the network size for consumer type i5L, H will have the form: X 5 Ni 1 g(N2i , g ),
i 5 L, H
(5)
where g is increasing in g and Ni , but where g(N2i , g ),N2i for all 0#g # 1. A possible choice for g(N2i , g ) is g N2i . The intuition is that if the two versions have similar qualities, a higher network externality will result. Consider Cell 4 in Table 1. We have a separating strategy for the firm in which the original version is intended for the high-valuation type and the limited version is intended for the low valuation type. For a separating strategy, the firm has to make sure each consumer picks the contract intended for her type. Four constraints result: VL (Q H , NH 1 g (NL , g )) 2 P4 #VL (g Q H , NL 1 g (NH , g )) 2 P5 ,
(6a)
VH (Q H , NH 1 g (NL , g )) 2 P4 $ VH (g Q H , NL 1 g (NH , g )) 2 P5 ,
(6b)
VL (g Q H , NL 1 g (NH , g )) 2 P5 $ 0,
(6c)
VH (Q H , NH 1 g (NL , g )) 2 P4 $ 0.
(6d)
The above four constraints ensure incentive compatibility for the low valuation type, incentive compatibility for the high valuation type, participation of the low types, and participation of the high types, respectively. Noting that constraint (6d) is redundant since it is implied by restrictions (6b) and (6c), we identify the firm’s problem as having to choose the three variables g, P4 , and P5 which maximize its objective function P4 5NH P4 1NL P5 , subject to the three constraints (6a), (6b), and (6c). It is a general result in mechanism design models that the incentive compatibility constraint for the high-valuation type and the participation constraint for the low-valuation type will be binding. From this we obtain the values for P4 and P5 .
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P4 5VH (Q H , NH 1 g (NL ,g )) 2VH (g Q H , NL 1 g (NH ,g )) 1VL (g Q H , NL 1 g (NH ,g )), P5 5VL (g Q H , NL 1 g (NH ,g )).
(7) (8)
The prices in the profit calculation for Cell 4 of Table 1 are obtained from (7) and (8). The profit is then:
P4 5 NH [ VH (Q H , NH 1 g (NL ,g )) 2 VH (g Q H , NL 1 g (NH ,g )) 1 VL (g Q H , NL 1 g (NH ,g ))] 1 NL [VL (g Q H , NL 1 g (NH ,g ))].
(9)
The choice of g can be determined by the maximization of P4 with respect to g to obtain the optimal value g *. The profits in Cell 3 are a special case of this where P5 50. Since the strategy space for Cell 3 is a subset of that for Cell 4, we would expect strategy of Cell 3 to be weakly dominated by strategy of Cell 4. Consider now a comparison of the profits in the pooling equilibrium, P2 , and the profits in the separating equilibrium, P4 . The separating equilibrium is preferred if the following condition holds: NH [VH (Q H , NH 1 g(NL , g *)) 2VH (g Q H , NL 1 g(NH ,g *)) 1VL (g Q H , NL 1 g (NH ,g *)) 2VL (Q H , NH 1 NL )] $ NL [ VL (Q H , NH 1 NL ) 2VL (g Q H , NL 1 g(NH ,g *))].
(10)
This condition is more likely to be met the larger the size of the high valuation group relative to the size of the low valuation group and the larger the value of g *; that is, the closer the quality levels of the two versions.
4. Introducing functional forms Recall that the utility that a consumer derives from the product he selects is increasing in the quality of the product, Q, and the network size for the product in that period, X. Also, recall the essential single crossing property condition. There are infinitely many functional forms for consumer utility that would satisfy these simple requirements. Consider the functional form introduced by Padmanabhan et al. (1997): Vi (Q, X) 5 (ui 1 b X a ) Q, where ui , b, a . 0 and uH . uL .
(11)
This general form leads to intractable first and second order conditions. Upon setting b51 and a 51 as suggested by Padmanabhan et al. (1997), with some loss of generality, second order conditions rule out maximization of Eq. (9) with respect to g. Furthermore, this form does not allow for estimation of the
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parameters u, b, and a by traditional linear regression methods, and rather requires more complicated non-linear methods. Therefore, we suggest the alternative form: Vi (Q, X) 5 ui X a Q, where ui , a . 0 and uH . uL .
(12)
This functional form corresponds to the traditional Cobb-Douglas utility in economic theory, satisfies the single crossing property, allows for linear estimation procedures on the parameters (by taking the affine log transformation of the utility function), and no loss of generality for preliminary analysis occurs when a 51 (under certain restrictions). Maximizing P4 in Eq. (9) with respect to g using the functional form of Eq. (12), we get the optimal quality parameter g to be NL uL (NH 1 NL ) g * 5 ]]]]]]]. 2NH [(uH 2 uL )NH 2 NLuL ]
(13)
Note that g * is more likely to be positive when uH is large relative to uL , and NH is large relative to NL . Furthermore, the larger NH is relative to NL , the more likely g * is to be less than 1. To demonstrate, let NH 5 f NL . Then as f →`, g *→0. Note that if g *[ ⁄ (0,1), no equilibrium involving a limited version product strategy will survive. Hence, a limited version strategy will be optimal only when NH is large relative to NL (as well as more likely to be optimal the larger uH is relative to uL ). This claim is confirmed by the second order condition to the maximization problem: d 2 P4 ]] 5 2 2NH Q H [(uH 2 uL )NH 2 NLuL ] , 0. dg2
(14)
Moreover, the larger size of NH relative to NL is crucial for a separating outcome to be preferred by the firm to a pooling outcome, as is evident from Eq. (10). Hence, after estimating (or calibrating) parameters uH and uL and assessing the network base, NL and NH , if Eq. (13) yields g * such that 0,g * ,1, this will generally indicate that NL
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to include more general functional forms using the non-form specific equations of Section 3.
5. Conclusions and future extensions We introduced a mechanism design procedure to allow software firms (as well as firms in other markets with demand externalities) to exploit the presence of network externalities. We have shown that there are conditions under which a separating equilibrium exists, with two versions of a software product sold to two different consumer classes. Our mechanism explains to a great degree the recent trend toward increasing prominence of shareware and freeware versions of many software products. We believe that our characterization of the limited version mechanism may help in optimizing the design of these versions for the firms’ benefit. The results of this paper should be interpreted with caution. While the basic intuition is robust to relaxation of assumptions, some of the results such as the weak domination of freeware versions by positive priced limited versions may change. The reason for this is the assumption that the quality of the products is identifiable by all the consumers. When this is not possible, freeware becomes important as a device for encouraging trial. We have also not accounted for competition. It is difficult to say what the results would be if competitive brands were available. A dynamic model of sequential introduction warrants serious pursuit. Such a model would have the capability to account for asymmetric information, where in the initial period the firm may obtain information on the network base by releasing the limited version as well as provide the consumer with information on the quality of the commercial version.
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