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Product compatibility as a signal of quality in a market with network externalities
International Journal of Industrial Organization 20 (2002) 949–964 www.elsevier.com / locate / econbase
Product compatibility as a signal of quality in a market with network externalities Jeong-Yoo Kim* Department of Economics, Dongguk University, 3 -26 Pildong, Chungku, Seoul 100 -715, South Korea Received 5 August 1998; received in revised form 20 July 1999; accepted 22 December 2000
Abstract In this paper, I consider the compatibility decision as a signaling device of the quality of a newly introduced technology of which users are not informed. Provided that firms are located sufficiently far apart in Hotelling’s [0,1] interval, I find separating equilibria where low compatibility signals high quality. This possible separation is due to the fact that low compatibility is more advantageous to the high-quality entrant than to the low-quality entrant, since it can prevent users of the established technology from enjoying network benefits from the new technology very much. 2002 Elsevier Science B.V. All rights reserved. JEL classification: L15 Keywords: Product compatibility; Experience goods; Network externalities; Signaling
1. Introduction Many industries are characterized by the existence of network externalities; the value of consuming a particular product or service increases in the number of consumers (the installed base) who use compatible products or services. Prominent examples include the computer industry, the broadcasting industry, the tele* Tel.: 182-2-2260-3716; fax: 182-2-2260-3716. E-mail address: [email protected] (J.-Y. Kim). 0167-7187 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0167-7187( 01 )00058-3
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communications industry, and many consumer electronics industries such as video cassette recorders, compact disc players, etc. Meanwhile, the degree of compatibility between products is not a mere consequence of technological constraint, but is often a result of a firm’s strategic consideration.1 For instance, a firm that wants to maintain its dominant position in the market sometimes prevents rivals from achieving compatibility through judicial means by asserting intellectual property rights.2 At other times, a firm attempts to make its product compatible with its competitor’s to attract the consumers locked in to the competing product.3 Then, why do firms choose such different degrees of compatibility? There have been many formal and informal discussions on how asymmetric positions between firms, depending on their installed bases, their reputations and their product offerings, lead to different degrees of compatibility. In this paper, I will investigate the relationship between quality and the choice of compatibility and explore a new role of product compatibility, the quality-signaling effect. To this purpose, I consider an oligopoly situation in which a firm has generated a product of some unknown quality and introduced it into the market where there is another firm supplying established products of quality that is known to all consumers. If both products generate network externalities, the entrant must decide how compatible its product will be made with the established one. Its compatibility decision, however, will depend on the private information regarding the quality of the product it sponsors, and thus some useful information on the product quality may be reflected in the compatibility decision. In this article, I will demonstrate that high quality can be signaled through low compatibility. This possibility comes from the fact that the cost of a change in compatibility is different between a high-quality firm and a low-quality firm. High compatibility is disadvantageous to the entrant who introduces a new high-quality technology, since it gives users of the established technology large network benefits from the new technology.4 Moreover, this disadvantage becomes more
1 By compatibility, I mean that each firm continues to produce according to its own technology, but the products of the two firms can use the same software or communicate directly with one another. 2 A well-known example is the proprietary Macintosh operating system. Apple used its copyright on its operating system software to prevent competitors from producing an Apple-compatible clone so as to deny them access to applications software written for its computers. 3 Many later entrants have taken this strategy; Microsoft Word against WordPerfect in word processors, Quattro Pro, Excel against Lotus 1-2-3 in spreadsheets for personal computers, Compaq against IBM in personal computers, etc. 4 In fact, high compatibility may be advantageous to the entrant, since the quality becomes important relative to the network benefit in determining the demand for a technology as the degree of compatibility is increased. Due to this effect, I may obtain the opposite result that high compatibility signals high quality in a model of purely vertical differentiation. For a detailed discussion, see Kim (1998).
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severe as the quality of the new technology increases. This is the main force that enables low compatibility to signal high quality. There are some examples found in practice that support this argument. In 1982, Satellite Software International introduced WordPerfect 2.0, run on personal computers, that was made incompatible with WordStar by designing it specifically for the new standard MS-DOS. Satellite Software International did not design WordPerfect for the obsolete standard CP/ M that WordStar is designed for, nor did it go to pains to introduce another version that was redesigned for CP/ M so as to attract consumers loyal to WordStar. Similarly, in the early 1980s, Apple introduced the Macintosh computer using GUI (Graphical User Interface)-based Mac OS without any concern about compatibility with the IBM-PC using MSDOS which was popular at that time. In these examples, neither WordPerfect nor Mac OS was in a superior position in terms of its installed base or its reputation, so it is hard to say that their compatibility choices were a consequence of strategic motives other than quality consideration. Several authors have addressed the issue of firms’ incentives to make their products compatible when introducing a new product in a market with network externalities. Katz and Shapiro (1992) show that the firm introducing a new technology with cost advantage prefers incompatibility if the market grows rapidly, since incompatibility enables the firm to enjoy an installed base advantage that will come soon. Regibeau and Rockett (1996) show that the firm contemplating entering the market prefers incompatibility and this preference for incompatibility increases over time for a similar reason as shown by Katz and Shapiro (1992). They also point out the possibility of time inconsistencies that, before the precursor introduces its technology, the potential entrant may prefer compatibility since it may affect the time when the precursor introduces the technology in a way that increases its profits. Other than those works, Katz and Shapiro (1986) assert that the sponsor of a superior technology, whose costs are falling relative to those of its rival, may choose incompatibility to gain control of the market by taking advantage of the nature of increasing returns to scale, and Farrell et al. (1998) discuss how firms’ asymmetric strategic positions with respect to cost can lead them to different preferences about compatibility. Also, some works (e.g. Economides, 1991, 1996) have pointed out that a stronger firm in terms of demand prefers incompatibility. In particular, Economides (1991) asserts that the private network with a large demand prefers incompatibility while the smaller private network prefers compatibility. However, no author has explored the role of product compatibility as a signal of the quality of the new product. By incorporating asymmetric information, this paper shows that, under asymmetric information, the firm with a superior technology may attempt to signal its high quality by choosing low compatibility. There has been much literature on signaling the quality of experience goods. Judd and Riordan (1994) and Daughety and Reinganum (1995) present a model of prices as signals of quality. Nelson (1974); Schmalensee (1978) and Kihlstrom
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and Riordan (1984) argue that advertising can signal quality. Milgrom and Roberts (1986) and Hertzendorf (1993) consider two potential signaling instruments, price and advertising, simultaneously. Also, Grossman (1980) offers an interesting model of warranty as a signal of quality. This paper suggests the possibility of another signaling device that has not been paid attention to. The article is organized as follows. In Section 2, I describe the model. In Section 3, I analyze the model under full information as a benchmark case. The main theorem is derived in Section 4. Section 5 discusses the robustness of the results, and concluding remarks follow in Section 6.
2. Model Users are located uniformly on an interval [0,1]. The established firm A sponsoring technology A is located at one extreme of the interval, x 5 0. Another firm B, which has just developed a new technology B, is located at the other extreme x 5 1. Both technologies generate network externalities but they are not compatible with each other. Users know that the quality of technology A is r, but they are not sure of the quality of technology B, rB , which is private information of firm B. I assume that rB is either r H or r L where r H . r L . r and that Prob(rB 5 r H ) 5 l.5 Here, the quality of a technology reflects how well it performs the designated job.6 I define the type of firm B, v, as its quality. If its quality is r H (r L ), firm B will be called to be of type H (L).7 Each firm is assumed to have identical, constant marginal cost. In fact, this assumption implies that the unit production cost of firm B is the same whether the type of firm B is either L or H.8 Without loss of generality, I will normalize it to 0. A user’s valuation of a technology consists of a stand-alone component and a compatibility component. First, a user gets utility directly from the quality of the technology he adopts. Also, a user incurs a transportation cost t per unit of length, which represents the user’s preference over the technology. Then, the stand-alone component for a technology is the sum of direct utility from the quality and disutility from the transportation cost. Additionally, a user derives benefits from compatibility with other users. For simplicity, I will assume that benefits from
5
I am assuming that a new technology is always superior to an old technology. It is plausible that the later a technology is developed, the higher quality it has, since technological progress is ongoing. 6 Some authors (Milgrom and Roberts, 1986; Hertzendorf, 1993) measure quality as the probability that the product in question will turn out to be satisfactory. Daughety and Reinganum (1995) refer to various dimensions of product quality. 7 On this account, I will use H, L interchangeably with r H , r L if there is no possibility of confusion. 8 Low quality with the same production cost may be due to poor architecture design or inefficient software programming.
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network is linear in the network size. Therefore, if the network size of technology i is z i , a user’s benefit from the network when he adopts technology i is a z i , where a . 0. Also, if a technology is partially compatible with another technology, a user adopting one technology can derive some benefits from the network of the other technology. If b denotes the degree of compatibility, where b [ [0,1], I assume that he derives a fraction b of the full compatibility benefits from the network of the other technology. These are compatibility components of a user’s valuation for a technology. Then, the overall valuation of a user located at x on technology A is r 2 pA 2 tx 1 a zA 1 ab zB and the valuation on technology B is rB 2 pB 2 t(1 2 x) 1 a zB 1 ab zA . I consider the following two-period price competition model. In the first period, firm B decides how compatible it will make its technology with technology A by choosing b. It incurs extra costs c( b ) to achieve compatibility.9 The cost of achieving compatibility c( b ) is assumed to be continuous with respect to b with c9( b ) . 0, c0( b ) . 0, c(0) 5 0, c9(0) 5 0.10 After the compatibility decision by firm B, firm A modifies its belief that v 5 H by lˆ and then two firms choose their prices simultaneously based on the updated posterior belief. After observing the compatibility decision and the prices, users decide which technology to adopt based on the posterior belief.11 In the second period, firms compete again in a Bertrand fashion.12 In this period, all users are replaced by new users who are again uniformly distributed on the unit interval, but they are all informed of the quality of technology B.13 I assume that, at each period, a user adopts at most a single unit of the technology. For the analysis of the two-period model, I will use the following notation:
pi 5per-period profit of firm i given the compatibility cost is sunk.
9 These include costs of developing a compatible product and the costs of inventing converters that allow one product to utilize software designed for another product. Here, I assume implicitly that the cost of achieving compatibility is the same regardless of the quality of technology B. However, it is possible in practice that it is more costly for a highly developed technology to be made compatible with the other technology using a different standard. This assumption disregards the possibility. 10 For instance, c( b ) 5 Kb 2 , where K . 0, satisfies all these conditions. 11 In fact, users update their posterior belief from pB as well as b. However, I do not need to distinguish users’ posterior belief from firm A’s posterior belief, because, in equilibrium, the price charged by firm B does not convey any informative message, so that users’ posterior belief does not differ from firm A’s posterior belief. See Section 4 for detailed discussion. 12 The established firm may increase the degree of compatibility with the new technology in the second period if the new technology turns out to be so strong as to threaten the market dominance of the established firm. However, considering the established firm’s possible reactions would make the analysis extremely complicated. Therefore, throughout the article, the established firm is assumed to be passive in determining the degree of compatibility. 13 This may be the result of learning by word of mouth from the first-period users or by reading Consumer Reports.
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P i 5present discounted value of two-period profits of firm i net of the compatibility cost. p ti 5price charged by firm i at period t. s 5type that firm B is perceived to be in the first period.14 d 5discount factor; d,1. In order to solve the model explicitly, I need a behavioral assumption on how users’ expectations on the network size of each technology are formed. Throughout the paper, I will assume that users have rational expectations, i.e. users’ expectations on the network size of each technology are actually fulfilled.15
3. Analysis under full information: benchmark case Suppose all users are informed of the quality of technology B. Given that b is chosen, two firms make their pricing decisions simultaneously. As a result of price competition, either both technologies survive (nonstandardization equilibrium) or only one technology survives, i.e. the market may be standardized by one technology (standardization equilibrium). A standardization equilibrium will occur if all users believe that others will adopt the same technology, whereas a nonstandardization equilibrium will occur otherwise. Throughout the paper, I will focus only on the nonstandardization equilibrium,16 assuming that the market is covered.17 In a non-standardizatio in equilibrium, some users adopt technology A, while
s is determined directly from lˆ ; s 5 H corresponds to lˆ 5 1, while s 5 L corresponds to lˆ 5 0. Katz and Shapiro (1985) calls the solution concept with this property the Fulfilled Expectations Equilibrium in the context of full information. 16 There may be standardization equilibria as well. For example, an equilibrium in which the market is standardized by the new technology B is viable if the user located at x 5 0 prefers adopting technology B, i.e. rB 2 pB 2 t 1 a > maxhr 2 pA 1 ab,0j. In this equilibrium, firm B does not benefit at all from achieving compatibility, so as to choose b 5 0. Therefore, if I assume that pA 5 0, firm B will charge pB 5 rB 2 r 2 t 1 a, the maximum price at which all users will adopt its technology, so long as pB > 0. 17 The Editor suggested that it would be worthwhile to discuss the case in which firms are located strictly inside [0,1] so that the market is possibly not covered at the edges while firms compete for consumers between them. If firms become closer to each other, the positive effect of an increase in b on the entrant is strengthened since the quality advantage becomes more important, whereas its negative effect on the entrant with the larger user size is weakened because demands for two firms could be both increased in the presence of backyard consumers. Thus, in the extreme case that both firms are located at the center of the interval, which corresponds to the case of no horizontal differentiation, high-quality firm B will prefer high compatibility as I put in Footnote 4. This implies that the main result of this paper could be reversed when the market does not have full coverage. Yet, if firms are located far enough, my result still holds. 14 15
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others adopt technology B. Let the cutoff user, given b, be x b* . Then, x b* must satisfy: r 2 pA 2 tx *b 1 a x *b 1 ab (1 2 x *b ) 5 rB 2 pB 2 t(1 2 x *b ) 1 a (1 2 x *b ) 1 ab x *b .
(1)
This yields: pB 2 pA 1 t 2 a 1 ab 2 rB 1 r x *b 5 ]]]]]]]]] 2(t 2 a 1 ab ) Then, firm A’s profit function is: pB 2 pA 1 t 2 a 1 ab 2 rB 1 r pA 5 pA qA 5 pA x *b 5 pA ]]]]]]]]] 2(t 2 a 1 ab )
(2)
Differentiating it with respect to pA , I obtain pA 5 ]21 ( pB 1 t 2 a 1 ab 2 rB 1 r).18 Similarly, I have pB 5 ]21 ( pA 1 t 2 a 1 ab 1 rB 2 r) by differentiating pB with rB 2 r rB 2 r respect to pB . Thus, I get p A* 5 t 2 a 1 ab 2 ]], p *B 5 t 2 a 1 ab 1 ]], 3 3 and thus q *A 5 x b* 5 p *B 2 p *A 1 t 2 a 1 ab 2 rB 1 r / 2(t 2 a 1 ab ) 5 ]12 2 rB 2 r / 6(t 2 a 1 ab ), q *B 5 1 2 x *b 5 ]21 1 rB 2 r / 6(t 2 a 1 ab ), provided that t 2 a 1 ab . rB 2 r / 3.19 In turn, I have r 2r t 2 a 1 ab 2 ]]D S 3 p * 5 p * q * 5 ]]]]]]] and 2
B
A
A
A
2(t 2 a 1 ab ) rB 2 r 2 t 2 a 1 ab 1 ]] 3 p B* 5 p *B q B* 5 ]]]]]]]. 2(t 2 a 1 ab )
S
D
Notice that p B* . p A* and that q B* . q A* . The firm with higher quality charges the higher price and gets the higher market share.20 Also, as the technologies become more compatible, the price for the new technology increases, whereas the demand for it decreases. It is also worth noticing that prices become lower in the presence of network externalities. This is because it makes the competition for market shares more severe. If b 5 1, the network size no longer becomes important to firms, so that they charge the same prices as in the absence of network externalities.
18
The second order condition is satisfied if t . a (1 2 b ). Of course, this is the case only if the net valuation of the cutoff user is nonnegative, i.e. r 2 rB 2 r / 3 1 ab > 0, so that the market is covered. 20 In this model, even in the presence of network externalities, a late-comer like firm B can be a dominant firm as soon as it enters the market, insofar as the technology it sponsors is superior to the rival’s. Under the assumption of rational expectation, the installed base does not matter at all in determining the market share in the current period. 19
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Now, I will consider the compatibility decision by firm B. The following proposition will be useful to characterize the compatibility decision. Proposition 1. ≠p B* ≠ 2 p *B ≠p B* ( b,H ) ≠p B* ( b,L) (i) ]] . 0. (ii) ]] (iii) ]]] , ]]] 2 . 0. ≠b ≠b ≠b ≠b Proof. See Appendix A. This proposition says that the profit of the entrant increases as its technology becomes more compatible with the established one, but increases less when its quality is higher. Firm B of type v will choose b 5 b * (v ) to maximize PB ( pA , pB , b,v ) 5 (1 1 d )pB ( pA , pB , b,v ) 2 c( b ). Assuming that the second order condition is satisfied, i.e. ≠ 2 P B* ( b,v ) / ≠b 2 , 0 where P B* ; PB ( p *A ( b,v ), p *B ( b,v ), b,v ), I have the following proposition: Proposition 2. Under full information, either b * (H ) , b * (L) or b * (H ) 5 b * (L) 5 1. Proof. Direct from Proposition 1 and assumptions on c( b ) (See Fig. 1.) This proposition implies that either firm B prefers lower compatibility when the quality is higher or it chooses full compatibility regardless of the quality. The former case occurs when the optimization problem for firm B of type H has the interior solution and the latter case does when it has the corner solution. The intuition for the former case is as follows. As mentioned above, increasing compatibility has both the price effect and the market share effect on firm B. As b becomes larger, firm B can charge a higher price, but at the same time it loses its market share, since compatibility gives users of technology A larger network benefits than users of technology B which becomes dominant in the market.21 On this ground, if the quality of technology B is higher, an increase in b gives users of technology A much larger network benefits, so that the negative effect of an increase in b on the market share is larger, while the effect on its price is the same. This makes it in the interest for firm B with higher quality to keep a lower degree of compatibility than for firm B with lower quality. 21
In fact, compatibility does not bring the benefits of superior quality of technology B to users of technology A. Rather, it allows them to benefit from the network externalities enjoyed by the users of technology B. Therefore, it is not because a user can enjoy virtually all the benefits of superior quality of technology B with cheaper technology A that firm B loses its market share as b is increased.
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Fig. 1. Optimal compatibility levels under full information.
Before I finish this section, let me identify the set of parameters for which the above results hold. For this purpose, I will use a specific functional form of c( b ) 5 Kb 2 . As already seen, the condition for concavity of pi is that t 2 a 1 ab . 0, and the condition for the existence of the nonstandardization equilibrium in which the market is covered is that t 2 a 1 ab . rB 2 r / 3 and r 2 rB 2 r / 3 1 ab > 0. Also, a sufficient condition for concavity of P B* in b is that K . 3a 2 (1 1 d ) /(rL 2 r)3 .22
4. Analysis under incomplete information In this section, I will analyze the model under incomplete information set up in Section 2 by focusing mainly on separating equilibria. In separating equilibria, each type of firm B makes a different choice, so that the type is revealed by its decision. Since all uncertainty is resolved at the beginning of the second period, the analysis for the second period is trivial. My interest thus will focus only on the
22
This is immediate, since ≠ 2 P *B / ≠b 2 5 (1 1 d ) 2a 2 / 9(t 2 a 1 ab )3 2 2K , 6a 2 (1 1 d ) /(rB 2 r) 2 2K , 0 for all b [ (0,1). 3
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first-period compatibility decision and price decisions by firms and on the concomitant beliefs of firm A and users, which enables me to suppress the superscript t. Therefore, hereafter, I will write the first-period price of technology i simply as pi . Suppose firm B of type H chooses bH and firm B of type L chooses bL with bH ± bL in equilibrium. Once firm B reveals its type through its compatibility decision, it does not need to engage in costly signaling by prices. As a result, prices must be equilibrium ones under full information given the compatibility decision. To avoid the trivial case, I will assume that there is no separating equilibrium in which each type of firm B behaves as under full information, i.e. assume that the low-quality type of firm B would wish to pool if bH were equal to b * (H ). Put ˆ B ( b * (H ),H,L) . P ˆ B ( b * (L),L,L), where formally, it is assumed that P ˆ * * * PB ( b,s,v ) 5 pB ( p A ( b,s ), p B ( b,s ), s ) 1 dpB ( p A ( b,v ), p *B ( b,v ),v ) 2 c( b ) and p *i ( b,s ) is the equilibrium price of technology i given the compatibility level b and firm B’s first-period perceived type s.23 Since the low type does not have to worry about being mimicked, it will choose bL 5 b * (L), its full-information compatibility level. Then, bH must be chosen so as to satisfy the incentive compatibility conditions of both types. Let b *I (s,v ) be the optimal compatibility level when firm B’s perceived type is s and its true type is v.24 Then, the incentive compatibility conditions are ˆ B ( bH ,H,H ) > P ˆ B ( b *I (L,H ),L,H ) P
(3)
ˆ B ( bL ,L,L) > P ˆ B ( bH ,H,L) P
(4)
The incentive compatibility condition for H-type firm B, given by inequality (3), requires that H-type firm B should not deviate from bH by choosing the compatibility degree, b I* (L,H ), that is most favorable to it if users in the first period believe that it is of type L. The inequality (4) is the incentive compatibility condition for L-type firm B, implying that L-type firm B should have no incentive to mimic the type H by choosing bH instead of bL . L-type firm B may charge a deviant price after it chooses bH . Such a price, however, cannot be a best response to the price of firm A, p A* ( bH ,H ). The intuition behind these conditions are as follows. First, H-type firm B can enjoy high demand by choosing bH that is distorted from b * (H ) so as to persuade users that it is of type H. If it chooses a different b, it may make users believe that it is producing a low-quality technology, which yields lower profits. The first condition requires that, when the high-quality type gives up revealing its type, the
23 24
It is obvious that firm B of type H has no incentive to mimic one of type L. Notice that b I* (H,H ) 5 b * (H ), b I* (L,L) 5 b * (L).
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loss from the decreased demand exceed the gain from picking up the optimal b. On the other hand, the low-quality type of firm B may increase its first-period net profit by mimicking the compatibility of the high-quality type and thereby increasing the demand for its technology. However, mimicking it may be costly to the type L with regard to its profit realized in the second period. The second condition requires that the second-period loss of mimicking the type H exceed the first-period gain. To characterize the set of bH satisfying inequalities (3) and (4), it is sufficient to note that the high-quality type must make its technology sufficiently less compatible with the established technology than under full information. This is because it is more costly for the low-quality type to make compatibility low in the light of Proposition 1 (iii). Therefore, I have a continuum of separating equilibria ] ] if there is a nonempty interval [bH ,bH ] , [0,1],25 where bH satisfies inequality (4) ] with equality and bH satisfies inequality (3) with equality (Fig. 2 and Table 1). ] Theorem 1. The following strategies and beliefs constitute separating equilibria: ] ] (i) H-type firm B chooses bH [ [bH ,bH ] where bH , b *(H ) and L-type firm B chooses bL 5 b * (L). (ii) Firm A]and users update their belief lˆ ( b ) 5 1, or
Fig. 2. Set of separating equilibria.
25
The Editor and an anonymous referee raised a question of whether this condition could be compatible with other conditions derived in the analysis. Table 1 provides the result of a numerical ] simulation showing when the interval [bH ,bH ] exists and how it is changed with varying values of ] parameters (a and t). It indicates that H-type firm B chooses a lower level of compatibility than the optimal level under full information, b * (H ), or the equilibrium compatibility level for L-type firm B under incomplete information, b * (L).
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Table 1 Range of equilibrium bH (calculated on the basis of d 5 .61, K 5 3.28, r 5 4.2525, r L 5 8.01 and r H 5 9.01) ] a t b * (L) b * (H ) bH bH ] 5.01 7.595834 0.582007 0.560791 0.171798 0.186329 5.01 8.595834 0.591365 0.577020 0.210563 0.218673 5.01 9.595834 0.597047 0.586555 0.210563 0.218673 6.01 7.595834 0.701303 0.677847 0.276621 0.296051 6.01 8.595834 0.711073 0.695162 0.324706 0.334578 6.01 9.595834 0.717088 0.705388 0.347792 0.354237
equivalently, s ( b ) 5 H if b < bH and lˆ ( b ) 5 0, i.e. s ( b ) 5 L if b . bH . (iii) At each period, firm i charges p i* ( b,s ), s 5 L,H, i 5 A,B. Proof. See Appendix A. This theorem implies that a low degree of compatibility signals high quality and that the compatibility degree chosen by high-quality firm B is downward distorted from its optimal degree under full information because the high-quality type wants to reveal its good quality by making its technology too incompatible for the low-quality type to mimic.26 However, it is not difficult to see that not all separating equilibria are reasonable. In Appendix A, I will prove that only the least-cost separating ] equilibrium involving b 5bH passes the intuitive criterion proposed by Cho and Kreps (1987). One may wonder if there exists a separating equilibrium in which only prices convey an informative message, while the compatibility decision does not. However, it can be easily shown that there is no such equilibrium, since the type L could be always better off by mimicking the price of the type H. In fact, this is a direct consequence of the assumption that production costs are the same regardless of the quality. As a consequence of this assumption, the per-period profit is not affected directly by the true type but only through the price charged. Thus, both types of firm B, either L or H, must prefer one price to another and, consequently, the type L can always increase its first-period profits by mimicking the price of the type H; otherwise, the price would not be the best for the type H, either. Thus far I have considered separating equilibria in which users become fully informed of the quality of a new technology through the behavior of its sponsor, but there can also exist pooling equilibria in which they learn nothing at all from observing the compatibility choice and prices. In a pooling equilibrium, both types
26
The analytic methodology employed in this section is a standard one in the signaling literature. See Fudenberg and Tirole (1986) for a typical treatment of a signaling game with two types.
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of firm B select the same degree of compatibility and the same price, and users base their adoption decision on the average quality of technology B, (1 2 l)r H 1 lrL ; rl . In this equilibrium, L-type firm B wants to mimic the type H by choosing a lower degree of compatibility than the optimal degree of compatibility when it would be perceived to be the type L, and he actually succeeds in pretending the type H by doing so. This equilibrium can occur when it is too costly for the type H to separate itself from the type L type by choosing a very low level of compatibility. However, all the pooling equilibria can be eliminated by universal divinity 27 which is a more refined concept than the intuitive criterion.28 This can be easily seen from the observation that a deviation to a slightly lower level of compatibility than a pooling equilibrium one is more profitable to type H, implying that such a deviation must be believed to come from type H.
5. Discussion In this section, I briefly discuss the robustness of the results derived in this article by considering alternative models. First, I have assumed that two technologies are both horizontally and vertically differentiated. If, instead, I consider a model of purely vertical differentiation, the result is turned over. The difference is essentially due to the fact that quality is relatively more important than market share in determining the demand for a technology in the case of purely vertical differentiation. For this reason, a high-quality firm prefers higher compatibility and signals its good quality by making its technology excessively compatible with the existing one. Second, I asserted in Section 4 that the price would have no signaling effect and that this was due to the assumption of cost parity for different-quality technologies. Suppose I modify this assumption and, instead, assume that the unit production cost of a high-quality firm is higher than that of a low-quality firm. Then, it can be shown that even without repeat purchases this asymmetric cost condition can generate an equilibrium in which quality is signaled through price alone. The intuition is simple. Generally, in a two-period setup, there are two effects involved in signaling through prices. On the one hand, from a dynamic perspective, the high-quality firm may have more incentive to offer a low price to encourage users to experiment and thereby induce more repeat purchases. This is the so-called Nelson effect. On the other hand, from a static point of view, the low-quality firm may have more incentive to charge a low price because, given a price, low quality yields high profits due to lower production cost. This is the
27 Roughly, universal divinity proposed by Banks and Sobel (1987) requires off-the-equilibrium beliefs to place positive probability only on those types that are most likely to deviate. 28 I am grateful to an anonymous referee for pointing this out.
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Schmalensee effect. If the model is of one period, only the Schmalensee effect exists and high quality is signaled through a high price. Even with considering the two-period model, as long as I retain the assumption that all users are informed of the quality of both technologies in the second period, the Nelson effect does not exist, since the first period pricing decision cannot affect the behavior of users in the second period.29 Moreover, if I relax the assumption that the second-period users all are informed of the quality, the price-signaling result could be obtained even without the assumption of cost asymmetry. Third, if increasing compatibility is more costly to the high type than to the low type, i.e. c( b ;H ) . c( b ;L), the high-quality firm will make its technology even less compatible with the established technology. This will make it more difficult for the low-quality firm to mimic the compatibility level the high-quality firm chooses and thus separating equilibria will more likely exist. Finally, this paper avoids technological complexities arising from intertemporal interaction by assuming that there is no market inertia and, obviously, a more realistic model would be one in which there is market inertia due to the presence of switching costs or some users who have myopic expectations. If there are switching costs involved, for instance, a firm can milk away some customers loyal to the rival by making its technology more compatible with the established one so as to lower the costs of switching from the rival’s technology to its own. Also, by choosing high compatibility or equivalently low switching costs, a firm can credibly commit not to extract rents from the consumers in the second period and increase the demand for its technology.30 Thus, the incentive of a new entrant to achieve higher compatibility will become stronger regardless of its type. Such a consideration, however, would not affect the qualitative nature of the results.
6. Conclusion In the real world, we observe an infinite variety of compatibility levels among substitutable technologies. This may be a natural consequence of technological constraint, but, in many cases, a consequence of strategic decisions by firms. This paper shows that a newly introduced technology can signal its quality by how compatible it is with the existing technology. Most papers consider a firm’s compatibility decision as a means of increasing its market share directly by allowing its users to enjoy the network benefits of the competitor’s technology, but this paper suggests that it can be also used as a way of conveying its private information that it is of good quality.
29
See Kim (1998) for the detailed analysis. A similar issue can be found in Choi and Thum (1998). Also, see Kim (1996) for price competition after a firm’s strategic decision to reduce switching costs. 30
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Real market situations are much more complex than the one assumed in this paper. In particular, technologies that were initially incompatible may be made compatible ex post either by the new firm or by the established firm. Incorporating the reaction of the established firm to the entrant’s compatibility choice remains an interesting extension for future research.
Acknowledgements I would like to thank Jay Pil Choi and the audiences at the conference of Korean Industrial Organization Association and at the Economic Theory Workshop at Yonsei University, and Jong Hee Chung for her superb research assistance. I am especially grateful to Nicholas Economides and two anonymous referees for their extensive comments on earlier drafts. Research support from Dongguk University is gratefully acknowledged.
Appendix A Proof of Proposition 1. Let s ; rB 2 r and n 5 a (1 2 b ) . 0. Then, I have s p B* 5 (t 2 n 1 ] )2 / 2(t 2 n ). Differentiating it yields 3 2 ≠p *B a (t 2 n 2 ]3s )(t 2 n 1 ]3s ) ≠ 2 p B* 2a ]] ]] ]]] 5 ]]]]]]] . 0, 5 . 0, and ≠b 2(t 2 n )2 ≠b 2 9(t 2 n )3
≠p B* ( b,H ) a a s 2H a s 2L ≠p *B ( b,L) a ]]] 5 ] 2 ]]]2 , ] 2 ]]]2 5 ]]] , ≠b 2 18(t 2 n ) 2 18(t 2 n ) ≠b where s H 5 r H 2 r, s L 5 r L 2 r. Proof of Theorem 1. Given lˆ specified in (ii), if H-type firm B chooses b . bH , ˆ B ( bH ,H,H ) > then lˆ ( b ) 5 0, which would be unprofitable, since P ˆ ˆ PB ( b *I (L,H ),L,H ) > PB ( b,L,H ) for any b from (3). If it chooses b , bH , then ˆ B ( b,H,H ) / ≠b . 0 so long lˆ ( b ) 5 1, but it would not be profitable, either, since ≠P as bH , b * (H ). On the other hand, the most profitable deviation for L-type firm B would be to bH . But, it is direct to see from (4) that it would not be profitable. This completes the proof. ] Claim. bH 5bH and bL 5 b *I (L,L) are the only separating equilibrium compatibility level satisfying the intuitive criterion.
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] ] ˆ B (] Proof of Claim. For any bH [ [bH ,bH ), choose b 5bH . Then, (i) P bH ,L,H ) . ] ] ˆ B ( bH ,H,H ) ; P ˆ B* (H ), (ii) P ˆ B (b ˆ ˆ * P ,L,L) < P ( b ,L,L) ; P (L) by the definition H B L B ] of bH . This completes the proof.
References Banks, J., Sobel, J., 1987. Equilibrium selection in signaling games. Econometrica 55, 647–662. Cho, I., Kreps, D., 1987. More signalling games and stable equilibrium. Quarterly Journal of Economics 102, 179–221. Choi, J., Thum, M., 1998. Market structure and the timing of technology adoption with network externalities. European Economic Review 42, 225–244. Daughety, A., Reinganum, J., 1995. Product safety: liability, R&D, and signaling. American Economic Review 85, 1187–1206. Economides, N., 1991. Compatibility and the creation of shared networks. In: Guerrin-Calvert, M., Wildman, S. (Eds.), Electronic Services Networks: A Business and Public Policy Challenge. Praeger, New York, pp. 39–55. Economides, N., 1996. The economics of networks. International Journal of Industrial Organization 14, 673–699. Farrell, J., Monroe, H., Saloner, G., 1998. The vertical organization of industry: systems competition versus component competition. Journal of Economics and Mnagement 7, 143–182. Fudenberg, D., Tirole, J., 1986. Noncooperative game theory. In: Schmalensee, R., Willig, R. (Eds.). Handbook of Industrial Organization, Vol. 1. North-Holland, Amsterdam, pp. 259–327. Grossman, S., 1980. The role of warranties and private disclosure about product quality. Journal of Law and Economics 24, 461–483. Hertzendorf, M.N., 1993. I’m not a high quality firm — but I play one on TV. RAND Journal of Economics 24, 236–247. Judd, K., Riordan, M., 1994. Price and quality in a new Product Monoply. Review of Economic Studies 61, 773–789. Katz, M., Shapiro, C., 1985. Network externalities, competition, and compatibility. American Economic Review 75, 424–440. Katz, M., Shapiro, C., 1986. Product compatibility choice in a market with technological progress. Oxford Economic Papers 38, 146–165. Katz, M., Shapiro, C., 1992. Product introduction with network externalities. Journal of Industrial Economics 40, 55–83. Kihlstrom, R.E., Riordan, M.H., 1984. Advertising as a signal. Journal of Political Economy 92, 427–450. Kim, J., 1998. Product Compatibility as a Signal of Quality in a Market with Network Externalities. Korea Association for Telecommunications Policies, Working Paper No. 2. Kim, J., 1996. Attracting the rival’s customers in a model with switching costs. Japanese Economic Review 2001 (in press). Milgrom, P., Roberts, J., 1986. Price and advertising signals of product quality. Journal of Political Economy 94, 796–821. Nelson, P., 1974. Advertising as information. Journal of Political Economy 81, 729–754. Regibeau, P., Rockett, K., 1996. The timing of product introduction and the credibility of compatibility decisions. International Journal of Industrial Organization 14, 801–823. Schmalensee, R., 1978. A model of advertising and product quality. Journal of Political Economy 86, 485–503.
Product compatibility as a signal of quality in a market with network externalities Jeong-Yoo Kim* Department of Economics, Dongguk University, 3 -26 Pildong, Chungku, Seoul 100 -715, South Korea Received 5 August 1998; received in revised form 20 July 1999; accepted 22 December 2000
Abstract In this paper, I consider the compatibility decision as a signaling device of the quality of a newly introduced technology of which users are not informed. Provided that firms are located sufficiently far apart in Hotelling’s [0,1] interval, I find separating equilibria where low compatibility signals high quality. This possible separation is due to the fact that low compatibility is more advantageous to the high-quality entrant than to the low-quality entrant, since it can prevent users of the established technology from enjoying network benefits from the new technology very much. 2002 Elsevier Science B.V. All rights reserved. JEL classification: L15 Keywords: Product compatibility; Experience goods; Network externalities; Signaling
1. Introduction Many industries are characterized by the existence of network externalities; the value of consuming a particular product or service increases in the number of consumers (the installed base) who use compatible products or services. Prominent examples include the computer industry, the broadcasting industry, the tele* Tel.: 182-2-2260-3716; fax: 182-2-2260-3716. E-mail address: [email protected] (J.-Y. Kim). 0167-7187 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0167-7187( 01 )00058-3
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communications industry, and many consumer electronics industries such as video cassette recorders, compact disc players, etc. Meanwhile, the degree of compatibility between products is not a mere consequence of technological constraint, but is often a result of a firm’s strategic consideration.1 For instance, a firm that wants to maintain its dominant position in the market sometimes prevents rivals from achieving compatibility through judicial means by asserting intellectual property rights.2 At other times, a firm attempts to make its product compatible with its competitor’s to attract the consumers locked in to the competing product.3 Then, why do firms choose such different degrees of compatibility? There have been many formal and informal discussions on how asymmetric positions between firms, depending on their installed bases, their reputations and their product offerings, lead to different degrees of compatibility. In this paper, I will investigate the relationship between quality and the choice of compatibility and explore a new role of product compatibility, the quality-signaling effect. To this purpose, I consider an oligopoly situation in which a firm has generated a product of some unknown quality and introduced it into the market where there is another firm supplying established products of quality that is known to all consumers. If both products generate network externalities, the entrant must decide how compatible its product will be made with the established one. Its compatibility decision, however, will depend on the private information regarding the quality of the product it sponsors, and thus some useful information on the product quality may be reflected in the compatibility decision. In this article, I will demonstrate that high quality can be signaled through low compatibility. This possibility comes from the fact that the cost of a change in compatibility is different between a high-quality firm and a low-quality firm. High compatibility is disadvantageous to the entrant who introduces a new high-quality technology, since it gives users of the established technology large network benefits from the new technology.4 Moreover, this disadvantage becomes more
1 By compatibility, I mean that each firm continues to produce according to its own technology, but the products of the two firms can use the same software or communicate directly with one another. 2 A well-known example is the proprietary Macintosh operating system. Apple used its copyright on its operating system software to prevent competitors from producing an Apple-compatible clone so as to deny them access to applications software written for its computers. 3 Many later entrants have taken this strategy; Microsoft Word against WordPerfect in word processors, Quattro Pro, Excel against Lotus 1-2-3 in spreadsheets for personal computers, Compaq against IBM in personal computers, etc. 4 In fact, high compatibility may be advantageous to the entrant, since the quality becomes important relative to the network benefit in determining the demand for a technology as the degree of compatibility is increased. Due to this effect, I may obtain the opposite result that high compatibility signals high quality in a model of purely vertical differentiation. For a detailed discussion, see Kim (1998).
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severe as the quality of the new technology increases. This is the main force that enables low compatibility to signal high quality. There are some examples found in practice that support this argument. In 1982, Satellite Software International introduced WordPerfect 2.0, run on personal computers, that was made incompatible with WordStar by designing it specifically for the new standard MS-DOS. Satellite Software International did not design WordPerfect for the obsolete standard CP/ M that WordStar is designed for, nor did it go to pains to introduce another version that was redesigned for CP/ M so as to attract consumers loyal to WordStar. Similarly, in the early 1980s, Apple introduced the Macintosh computer using GUI (Graphical User Interface)-based Mac OS without any concern about compatibility with the IBM-PC using MSDOS which was popular at that time. In these examples, neither WordPerfect nor Mac OS was in a superior position in terms of its installed base or its reputation, so it is hard to say that their compatibility choices were a consequence of strategic motives other than quality consideration. Several authors have addressed the issue of firms’ incentives to make their products compatible when introducing a new product in a market with network externalities. Katz and Shapiro (1992) show that the firm introducing a new technology with cost advantage prefers incompatibility if the market grows rapidly, since incompatibility enables the firm to enjoy an installed base advantage that will come soon. Regibeau and Rockett (1996) show that the firm contemplating entering the market prefers incompatibility and this preference for incompatibility increases over time for a similar reason as shown by Katz and Shapiro (1992). They also point out the possibility of time inconsistencies that, before the precursor introduces its technology, the potential entrant may prefer compatibility since it may affect the time when the precursor introduces the technology in a way that increases its profits. Other than those works, Katz and Shapiro (1986) assert that the sponsor of a superior technology, whose costs are falling relative to those of its rival, may choose incompatibility to gain control of the market by taking advantage of the nature of increasing returns to scale, and Farrell et al. (1998) discuss how firms’ asymmetric strategic positions with respect to cost can lead them to different preferences about compatibility. Also, some works (e.g. Economides, 1991, 1996) have pointed out that a stronger firm in terms of demand prefers incompatibility. In particular, Economides (1991) asserts that the private network with a large demand prefers incompatibility while the smaller private network prefers compatibility. However, no author has explored the role of product compatibility as a signal of the quality of the new product. By incorporating asymmetric information, this paper shows that, under asymmetric information, the firm with a superior technology may attempt to signal its high quality by choosing low compatibility. There has been much literature on signaling the quality of experience goods. Judd and Riordan (1994) and Daughety and Reinganum (1995) present a model of prices as signals of quality. Nelson (1974); Schmalensee (1978) and Kihlstrom
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and Riordan (1984) argue that advertising can signal quality. Milgrom and Roberts (1986) and Hertzendorf (1993) consider two potential signaling instruments, price and advertising, simultaneously. Also, Grossman (1980) offers an interesting model of warranty as a signal of quality. This paper suggests the possibility of another signaling device that has not been paid attention to. The article is organized as follows. In Section 2, I describe the model. In Section 3, I analyze the model under full information as a benchmark case. The main theorem is derived in Section 4. Section 5 discusses the robustness of the results, and concluding remarks follow in Section 6.
2. Model Users are located uniformly on an interval [0,1]. The established firm A sponsoring technology A is located at one extreme of the interval, x 5 0. Another firm B, which has just developed a new technology B, is located at the other extreme x 5 1. Both technologies generate network externalities but they are not compatible with each other. Users know that the quality of technology A is r, but they are not sure of the quality of technology B, rB , which is private information of firm B. I assume that rB is either r H or r L where r H . r L . r and that Prob(rB 5 r H ) 5 l.5 Here, the quality of a technology reflects how well it performs the designated job.6 I define the type of firm B, v, as its quality. If its quality is r H (r L ), firm B will be called to be of type H (L).7 Each firm is assumed to have identical, constant marginal cost. In fact, this assumption implies that the unit production cost of firm B is the same whether the type of firm B is either L or H.8 Without loss of generality, I will normalize it to 0. A user’s valuation of a technology consists of a stand-alone component and a compatibility component. First, a user gets utility directly from the quality of the technology he adopts. Also, a user incurs a transportation cost t per unit of length, which represents the user’s preference over the technology. Then, the stand-alone component for a technology is the sum of direct utility from the quality and disutility from the transportation cost. Additionally, a user derives benefits from compatibility with other users. For simplicity, I will assume that benefits from
5
I am assuming that a new technology is always superior to an old technology. It is plausible that the later a technology is developed, the higher quality it has, since technological progress is ongoing. 6 Some authors (Milgrom and Roberts, 1986; Hertzendorf, 1993) measure quality as the probability that the product in question will turn out to be satisfactory. Daughety and Reinganum (1995) refer to various dimensions of product quality. 7 On this account, I will use H, L interchangeably with r H , r L if there is no possibility of confusion. 8 Low quality with the same production cost may be due to poor architecture design or inefficient software programming.
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network is linear in the network size. Therefore, if the network size of technology i is z i , a user’s benefit from the network when he adopts technology i is a z i , where a . 0. Also, if a technology is partially compatible with another technology, a user adopting one technology can derive some benefits from the network of the other technology. If b denotes the degree of compatibility, where b [ [0,1], I assume that he derives a fraction b of the full compatibility benefits from the network of the other technology. These are compatibility components of a user’s valuation for a technology. Then, the overall valuation of a user located at x on technology A is r 2 pA 2 tx 1 a zA 1 ab zB and the valuation on technology B is rB 2 pB 2 t(1 2 x) 1 a zB 1 ab zA . I consider the following two-period price competition model. In the first period, firm B decides how compatible it will make its technology with technology A by choosing b. It incurs extra costs c( b ) to achieve compatibility.9 The cost of achieving compatibility c( b ) is assumed to be continuous with respect to b with c9( b ) . 0, c0( b ) . 0, c(0) 5 0, c9(0) 5 0.10 After the compatibility decision by firm B, firm A modifies its belief that v 5 H by lˆ and then two firms choose their prices simultaneously based on the updated posterior belief. After observing the compatibility decision and the prices, users decide which technology to adopt based on the posterior belief.11 In the second period, firms compete again in a Bertrand fashion.12 In this period, all users are replaced by new users who are again uniformly distributed on the unit interval, but they are all informed of the quality of technology B.13 I assume that, at each period, a user adopts at most a single unit of the technology. For the analysis of the two-period model, I will use the following notation:
pi 5per-period profit of firm i given the compatibility cost is sunk.
9 These include costs of developing a compatible product and the costs of inventing converters that allow one product to utilize software designed for another product. Here, I assume implicitly that the cost of achieving compatibility is the same regardless of the quality of technology B. However, it is possible in practice that it is more costly for a highly developed technology to be made compatible with the other technology using a different standard. This assumption disregards the possibility. 10 For instance, c( b ) 5 Kb 2 , where K . 0, satisfies all these conditions. 11 In fact, users update their posterior belief from pB as well as b. However, I do not need to distinguish users’ posterior belief from firm A’s posterior belief, because, in equilibrium, the price charged by firm B does not convey any informative message, so that users’ posterior belief does not differ from firm A’s posterior belief. See Section 4 for detailed discussion. 12 The established firm may increase the degree of compatibility with the new technology in the second period if the new technology turns out to be so strong as to threaten the market dominance of the established firm. However, considering the established firm’s possible reactions would make the analysis extremely complicated. Therefore, throughout the article, the established firm is assumed to be passive in determining the degree of compatibility. 13 This may be the result of learning by word of mouth from the first-period users or by reading Consumer Reports.
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P i 5present discounted value of two-period profits of firm i net of the compatibility cost. p ti 5price charged by firm i at period t. s 5type that firm B is perceived to be in the first period.14 d 5discount factor; d,1. In order to solve the model explicitly, I need a behavioral assumption on how users’ expectations on the network size of each technology are formed. Throughout the paper, I will assume that users have rational expectations, i.e. users’ expectations on the network size of each technology are actually fulfilled.15
3. Analysis under full information: benchmark case Suppose all users are informed of the quality of technology B. Given that b is chosen, two firms make their pricing decisions simultaneously. As a result of price competition, either both technologies survive (nonstandardization equilibrium) or only one technology survives, i.e. the market may be standardized by one technology (standardization equilibrium). A standardization equilibrium will occur if all users believe that others will adopt the same technology, whereas a nonstandardization equilibrium will occur otherwise. Throughout the paper, I will focus only on the nonstandardization equilibrium,16 assuming that the market is covered.17 In a non-standardizatio in equilibrium, some users adopt technology A, while
s is determined directly from lˆ ; s 5 H corresponds to lˆ 5 1, while s 5 L corresponds to lˆ 5 0. Katz and Shapiro (1985) calls the solution concept with this property the Fulfilled Expectations Equilibrium in the context of full information. 16 There may be standardization equilibria as well. For example, an equilibrium in which the market is standardized by the new technology B is viable if the user located at x 5 0 prefers adopting technology B, i.e. rB 2 pB 2 t 1 a > maxhr 2 pA 1 ab,0j. In this equilibrium, firm B does not benefit at all from achieving compatibility, so as to choose b 5 0. Therefore, if I assume that pA 5 0, firm B will charge pB 5 rB 2 r 2 t 1 a, the maximum price at which all users will adopt its technology, so long as pB > 0. 17 The Editor suggested that it would be worthwhile to discuss the case in which firms are located strictly inside [0,1] so that the market is possibly not covered at the edges while firms compete for consumers between them. If firms become closer to each other, the positive effect of an increase in b on the entrant is strengthened since the quality advantage becomes more important, whereas its negative effect on the entrant with the larger user size is weakened because demands for two firms could be both increased in the presence of backyard consumers. Thus, in the extreme case that both firms are located at the center of the interval, which corresponds to the case of no horizontal differentiation, high-quality firm B will prefer high compatibility as I put in Footnote 4. This implies that the main result of this paper could be reversed when the market does not have full coverage. Yet, if firms are located far enough, my result still holds. 14 15
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others adopt technology B. Let the cutoff user, given b, be x b* . Then, x b* must satisfy: r 2 pA 2 tx *b 1 a x *b 1 ab (1 2 x *b ) 5 rB 2 pB 2 t(1 2 x *b ) 1 a (1 2 x *b ) 1 ab x *b .
(1)
This yields: pB 2 pA 1 t 2 a 1 ab 2 rB 1 r x *b 5 ]]]]]]]]] 2(t 2 a 1 ab ) Then, firm A’s profit function is: pB 2 pA 1 t 2 a 1 ab 2 rB 1 r pA 5 pA qA 5 pA x *b 5 pA ]]]]]]]]] 2(t 2 a 1 ab )
(2)
Differentiating it with respect to pA , I obtain pA 5 ]21 ( pB 1 t 2 a 1 ab 2 rB 1 r).18 Similarly, I have pB 5 ]21 ( pA 1 t 2 a 1 ab 1 rB 2 r) by differentiating pB with rB 2 r rB 2 r respect to pB . Thus, I get p A* 5 t 2 a 1 ab 2 ]], p *B 5 t 2 a 1 ab 1 ]], 3 3 and thus q *A 5 x b* 5 p *B 2 p *A 1 t 2 a 1 ab 2 rB 1 r / 2(t 2 a 1 ab ) 5 ]12 2 rB 2 r / 6(t 2 a 1 ab ), q *B 5 1 2 x *b 5 ]21 1 rB 2 r / 6(t 2 a 1 ab ), provided that t 2 a 1 ab . rB 2 r / 3.19 In turn, I have r 2r t 2 a 1 ab 2 ]]D S 3 p * 5 p * q * 5 ]]]]]]] and 2
B
A
A
A
2(t 2 a 1 ab ) rB 2 r 2 t 2 a 1 ab 1 ]] 3 p B* 5 p *B q B* 5 ]]]]]]]. 2(t 2 a 1 ab )
S
D
Notice that p B* . p A* and that q B* . q A* . The firm with higher quality charges the higher price and gets the higher market share.20 Also, as the technologies become more compatible, the price for the new technology increases, whereas the demand for it decreases. It is also worth noticing that prices become lower in the presence of network externalities. This is because it makes the competition for market shares more severe. If b 5 1, the network size no longer becomes important to firms, so that they charge the same prices as in the absence of network externalities.
18
The second order condition is satisfied if t . a (1 2 b ). Of course, this is the case only if the net valuation of the cutoff user is nonnegative, i.e. r 2 rB 2 r / 3 1 ab > 0, so that the market is covered. 20 In this model, even in the presence of network externalities, a late-comer like firm B can be a dominant firm as soon as it enters the market, insofar as the technology it sponsors is superior to the rival’s. Under the assumption of rational expectation, the installed base does not matter at all in determining the market share in the current period. 19
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Now, I will consider the compatibility decision by firm B. The following proposition will be useful to characterize the compatibility decision. Proposition 1. ≠p B* ≠ 2 p *B ≠p B* ( b,H ) ≠p B* ( b,L) (i) ]] . 0. (ii) ]] (iii) ]]] , ]]] 2 . 0. ≠b ≠b ≠b ≠b Proof. See Appendix A. This proposition says that the profit of the entrant increases as its technology becomes more compatible with the established one, but increases less when its quality is higher. Firm B of type v will choose b 5 b * (v ) to maximize PB ( pA , pB , b,v ) 5 (1 1 d )pB ( pA , pB , b,v ) 2 c( b ). Assuming that the second order condition is satisfied, i.e. ≠ 2 P B* ( b,v ) / ≠b 2 , 0 where P B* ; PB ( p *A ( b,v ), p *B ( b,v ), b,v ), I have the following proposition: Proposition 2. Under full information, either b * (H ) , b * (L) or b * (H ) 5 b * (L) 5 1. Proof. Direct from Proposition 1 and assumptions on c( b ) (See Fig. 1.) This proposition implies that either firm B prefers lower compatibility when the quality is higher or it chooses full compatibility regardless of the quality. The former case occurs when the optimization problem for firm B of type H has the interior solution and the latter case does when it has the corner solution. The intuition for the former case is as follows. As mentioned above, increasing compatibility has both the price effect and the market share effect on firm B. As b becomes larger, firm B can charge a higher price, but at the same time it loses its market share, since compatibility gives users of technology A larger network benefits than users of technology B which becomes dominant in the market.21 On this ground, if the quality of technology B is higher, an increase in b gives users of technology A much larger network benefits, so that the negative effect of an increase in b on the market share is larger, while the effect on its price is the same. This makes it in the interest for firm B with higher quality to keep a lower degree of compatibility than for firm B with lower quality. 21
In fact, compatibility does not bring the benefits of superior quality of technology B to users of technology A. Rather, it allows them to benefit from the network externalities enjoyed by the users of technology B. Therefore, it is not because a user can enjoy virtually all the benefits of superior quality of technology B with cheaper technology A that firm B loses its market share as b is increased.
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Fig. 1. Optimal compatibility levels under full information.
Before I finish this section, let me identify the set of parameters for which the above results hold. For this purpose, I will use a specific functional form of c( b ) 5 Kb 2 . As already seen, the condition for concavity of pi is that t 2 a 1 ab . 0, and the condition for the existence of the nonstandardization equilibrium in which the market is covered is that t 2 a 1 ab . rB 2 r / 3 and r 2 rB 2 r / 3 1 ab > 0. Also, a sufficient condition for concavity of P B* in b is that K . 3a 2 (1 1 d ) /(rL 2 r)3 .22
4. Analysis under incomplete information In this section, I will analyze the model under incomplete information set up in Section 2 by focusing mainly on separating equilibria. In separating equilibria, each type of firm B makes a different choice, so that the type is revealed by its decision. Since all uncertainty is resolved at the beginning of the second period, the analysis for the second period is trivial. My interest thus will focus only on the
22
This is immediate, since ≠ 2 P *B / ≠b 2 5 (1 1 d ) 2a 2 / 9(t 2 a 1 ab )3 2 2K , 6a 2 (1 1 d ) /(rB 2 r) 2 2K , 0 for all b [ (0,1). 3
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first-period compatibility decision and price decisions by firms and on the concomitant beliefs of firm A and users, which enables me to suppress the superscript t. Therefore, hereafter, I will write the first-period price of technology i simply as pi . Suppose firm B of type H chooses bH and firm B of type L chooses bL with bH ± bL in equilibrium. Once firm B reveals its type through its compatibility decision, it does not need to engage in costly signaling by prices. As a result, prices must be equilibrium ones under full information given the compatibility decision. To avoid the trivial case, I will assume that there is no separating equilibrium in which each type of firm B behaves as under full information, i.e. assume that the low-quality type of firm B would wish to pool if bH were equal to b * (H ). Put ˆ B ( b * (H ),H,L) . P ˆ B ( b * (L),L,L), where formally, it is assumed that P ˆ * * * PB ( b,s,v ) 5 pB ( p A ( b,s ), p B ( b,s ), s ) 1 dpB ( p A ( b,v ), p *B ( b,v ),v ) 2 c( b ) and p *i ( b,s ) is the equilibrium price of technology i given the compatibility level b and firm B’s first-period perceived type s.23 Since the low type does not have to worry about being mimicked, it will choose bL 5 b * (L), its full-information compatibility level. Then, bH must be chosen so as to satisfy the incentive compatibility conditions of both types. Let b *I (s,v ) be the optimal compatibility level when firm B’s perceived type is s and its true type is v.24 Then, the incentive compatibility conditions are ˆ B ( bH ,H,H ) > P ˆ B ( b *I (L,H ),L,H ) P
(3)
ˆ B ( bL ,L,L) > P ˆ B ( bH ,H,L) P
(4)
The incentive compatibility condition for H-type firm B, given by inequality (3), requires that H-type firm B should not deviate from bH by choosing the compatibility degree, b I* (L,H ), that is most favorable to it if users in the first period believe that it is of type L. The inequality (4) is the incentive compatibility condition for L-type firm B, implying that L-type firm B should have no incentive to mimic the type H by choosing bH instead of bL . L-type firm B may charge a deviant price after it chooses bH . Such a price, however, cannot be a best response to the price of firm A, p A* ( bH ,H ). The intuition behind these conditions are as follows. First, H-type firm B can enjoy high demand by choosing bH that is distorted from b * (H ) so as to persuade users that it is of type H. If it chooses a different b, it may make users believe that it is producing a low-quality technology, which yields lower profits. The first condition requires that, when the high-quality type gives up revealing its type, the
23 24
It is obvious that firm B of type H has no incentive to mimic one of type L. Notice that b I* (H,H ) 5 b * (H ), b I* (L,L) 5 b * (L).
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loss from the decreased demand exceed the gain from picking up the optimal b. On the other hand, the low-quality type of firm B may increase its first-period net profit by mimicking the compatibility of the high-quality type and thereby increasing the demand for its technology. However, mimicking it may be costly to the type L with regard to its profit realized in the second period. The second condition requires that the second-period loss of mimicking the type H exceed the first-period gain. To characterize the set of bH satisfying inequalities (3) and (4), it is sufficient to note that the high-quality type must make its technology sufficiently less compatible with the established technology than under full information. This is because it is more costly for the low-quality type to make compatibility low in the light of Proposition 1 (iii). Therefore, I have a continuum of separating equilibria ] ] if there is a nonempty interval [bH ,bH ] , [0,1],25 where bH satisfies inequality (4) ] with equality and bH satisfies inequality (3) with equality (Fig. 2 and Table 1). ] Theorem 1. The following strategies and beliefs constitute separating equilibria: ] ] (i) H-type firm B chooses bH [ [bH ,bH ] where bH , b *(H ) and L-type firm B chooses bL 5 b * (L). (ii) Firm A]and users update their belief lˆ ( b ) 5 1, or
Fig. 2. Set of separating equilibria.
25
The Editor and an anonymous referee raised a question of whether this condition could be compatible with other conditions derived in the analysis. Table 1 provides the result of a numerical ] simulation showing when the interval [bH ,bH ] exists and how it is changed with varying values of ] parameters (a and t). It indicates that H-type firm B chooses a lower level of compatibility than the optimal level under full information, b * (H ), or the equilibrium compatibility level for L-type firm B under incomplete information, b * (L).
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Table 1 Range of equilibrium bH (calculated on the basis of d 5 .61, K 5 3.28, r 5 4.2525, r L 5 8.01 and r H 5 9.01) ] a t b * (L) b * (H ) bH bH ] 5.01 7.595834 0.582007 0.560791 0.171798 0.186329 5.01 8.595834 0.591365 0.577020 0.210563 0.218673 5.01 9.595834 0.597047 0.586555 0.210563 0.218673 6.01 7.595834 0.701303 0.677847 0.276621 0.296051 6.01 8.595834 0.711073 0.695162 0.324706 0.334578 6.01 9.595834 0.717088 0.705388 0.347792 0.354237
equivalently, s ( b ) 5 H if b < bH and lˆ ( b ) 5 0, i.e. s ( b ) 5 L if b . bH . (iii) At each period, firm i charges p i* ( b,s ), s 5 L,H, i 5 A,B. Proof. See Appendix A. This theorem implies that a low degree of compatibility signals high quality and that the compatibility degree chosen by high-quality firm B is downward distorted from its optimal degree under full information because the high-quality type wants to reveal its good quality by making its technology too incompatible for the low-quality type to mimic.26 However, it is not difficult to see that not all separating equilibria are reasonable. In Appendix A, I will prove that only the least-cost separating ] equilibrium involving b 5bH passes the intuitive criterion proposed by Cho and Kreps (1987). One may wonder if there exists a separating equilibrium in which only prices convey an informative message, while the compatibility decision does not. However, it can be easily shown that there is no such equilibrium, since the type L could be always better off by mimicking the price of the type H. In fact, this is a direct consequence of the assumption that production costs are the same regardless of the quality. As a consequence of this assumption, the per-period profit is not affected directly by the true type but only through the price charged. Thus, both types of firm B, either L or H, must prefer one price to another and, consequently, the type L can always increase its first-period profits by mimicking the price of the type H; otherwise, the price would not be the best for the type H, either. Thus far I have considered separating equilibria in which users become fully informed of the quality of a new technology through the behavior of its sponsor, but there can also exist pooling equilibria in which they learn nothing at all from observing the compatibility choice and prices. In a pooling equilibrium, both types
26
The analytic methodology employed in this section is a standard one in the signaling literature. See Fudenberg and Tirole (1986) for a typical treatment of a signaling game with two types.
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of firm B select the same degree of compatibility and the same price, and users base their adoption decision on the average quality of technology B, (1 2 l)r H 1 lrL ; rl . In this equilibrium, L-type firm B wants to mimic the type H by choosing a lower degree of compatibility than the optimal degree of compatibility when it would be perceived to be the type L, and he actually succeeds in pretending the type H by doing so. This equilibrium can occur when it is too costly for the type H to separate itself from the type L type by choosing a very low level of compatibility. However, all the pooling equilibria can be eliminated by universal divinity 27 which is a more refined concept than the intuitive criterion.28 This can be easily seen from the observation that a deviation to a slightly lower level of compatibility than a pooling equilibrium one is more profitable to type H, implying that such a deviation must be believed to come from type H.
5. Discussion In this section, I briefly discuss the robustness of the results derived in this article by considering alternative models. First, I have assumed that two technologies are both horizontally and vertically differentiated. If, instead, I consider a model of purely vertical differentiation, the result is turned over. The difference is essentially due to the fact that quality is relatively more important than market share in determining the demand for a technology in the case of purely vertical differentiation. For this reason, a high-quality firm prefers higher compatibility and signals its good quality by making its technology excessively compatible with the existing one. Second, I asserted in Section 4 that the price would have no signaling effect and that this was due to the assumption of cost parity for different-quality technologies. Suppose I modify this assumption and, instead, assume that the unit production cost of a high-quality firm is higher than that of a low-quality firm. Then, it can be shown that even without repeat purchases this asymmetric cost condition can generate an equilibrium in which quality is signaled through price alone. The intuition is simple. Generally, in a two-period setup, there are two effects involved in signaling through prices. On the one hand, from a dynamic perspective, the high-quality firm may have more incentive to offer a low price to encourage users to experiment and thereby induce more repeat purchases. This is the so-called Nelson effect. On the other hand, from a static point of view, the low-quality firm may have more incentive to charge a low price because, given a price, low quality yields high profits due to lower production cost. This is the
27 Roughly, universal divinity proposed by Banks and Sobel (1987) requires off-the-equilibrium beliefs to place positive probability only on those types that are most likely to deviate. 28 I am grateful to an anonymous referee for pointing this out.
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Schmalensee effect. If the model is of one period, only the Schmalensee effect exists and high quality is signaled through a high price. Even with considering the two-period model, as long as I retain the assumption that all users are informed of the quality of both technologies in the second period, the Nelson effect does not exist, since the first period pricing decision cannot affect the behavior of users in the second period.29 Moreover, if I relax the assumption that the second-period users all are informed of the quality, the price-signaling result could be obtained even without the assumption of cost asymmetry. Third, if increasing compatibility is more costly to the high type than to the low type, i.e. c( b ;H ) . c( b ;L), the high-quality firm will make its technology even less compatible with the established technology. This will make it more difficult for the low-quality firm to mimic the compatibility level the high-quality firm chooses and thus separating equilibria will more likely exist. Finally, this paper avoids technological complexities arising from intertemporal interaction by assuming that there is no market inertia and, obviously, a more realistic model would be one in which there is market inertia due to the presence of switching costs or some users who have myopic expectations. If there are switching costs involved, for instance, a firm can milk away some customers loyal to the rival by making its technology more compatible with the established one so as to lower the costs of switching from the rival’s technology to its own. Also, by choosing high compatibility or equivalently low switching costs, a firm can credibly commit not to extract rents from the consumers in the second period and increase the demand for its technology.30 Thus, the incentive of a new entrant to achieve higher compatibility will become stronger regardless of its type. Such a consideration, however, would not affect the qualitative nature of the results.
6. Conclusion In the real world, we observe an infinite variety of compatibility levels among substitutable technologies. This may be a natural consequence of technological constraint, but, in many cases, a consequence of strategic decisions by firms. This paper shows that a newly introduced technology can signal its quality by how compatible it is with the existing technology. Most papers consider a firm’s compatibility decision as a means of increasing its market share directly by allowing its users to enjoy the network benefits of the competitor’s technology, but this paper suggests that it can be also used as a way of conveying its private information that it is of good quality.
29
See Kim (1998) for the detailed analysis. A similar issue can be found in Choi and Thum (1998). Also, see Kim (1996) for price competition after a firm’s strategic decision to reduce switching costs. 30
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Real market situations are much more complex than the one assumed in this paper. In particular, technologies that were initially incompatible may be made compatible ex post either by the new firm or by the established firm. Incorporating the reaction of the established firm to the entrant’s compatibility choice remains an interesting extension for future research.
Acknowledgements I would like to thank Jay Pil Choi and the audiences at the conference of Korean Industrial Organization Association and at the Economic Theory Workshop at Yonsei University, and Jong Hee Chung for her superb research assistance. I am especially grateful to Nicholas Economides and two anonymous referees for their extensive comments on earlier drafts. Research support from Dongguk University is gratefully acknowledged.
Appendix A Proof of Proposition 1. Let s ; rB 2 r and n 5 a (1 2 b ) . 0. Then, I have s p B* 5 (t 2 n 1 ] )2 / 2(t 2 n ). Differentiating it yields 3 2 ≠p *B a (t 2 n 2 ]3s )(t 2 n 1 ]3s ) ≠ 2 p B* 2a ]] ]] ]]] 5 ]]]]]]] . 0, 5 . 0, and ≠b 2(t 2 n )2 ≠b 2 9(t 2 n )3
≠p B* ( b,H ) a a s 2H a s 2L ≠p *B ( b,L) a ]]] 5 ] 2 ]]]2 , ] 2 ]]]2 5 ]]] , ≠b 2 18(t 2 n ) 2 18(t 2 n ) ≠b where s H 5 r H 2 r, s L 5 r L 2 r. Proof of Theorem 1. Given lˆ specified in (ii), if H-type firm B chooses b . bH , ˆ B ( bH ,H,H ) > then lˆ ( b ) 5 0, which would be unprofitable, since P ˆ ˆ PB ( b *I (L,H ),L,H ) > PB ( b,L,H ) for any b from (3). If it chooses b , bH , then ˆ B ( b,H,H ) / ≠b . 0 so long lˆ ( b ) 5 1, but it would not be profitable, either, since ≠P as bH , b * (H ). On the other hand, the most profitable deviation for L-type firm B would be to bH . But, it is direct to see from (4) that it would not be profitable. This completes the proof. ] Claim. bH 5bH and bL 5 b *I (L,L) are the only separating equilibrium compatibility level satisfying the intuitive criterion.
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] ] ˆ B (] Proof of Claim. For any bH [ [bH ,bH ), choose b 5bH . Then, (i) P bH ,L,H ) . ] ] ˆ B ( bH ,H,H ) ; P ˆ B* (H ), (ii) P ˆ B (b ˆ ˆ * P ,L,L) < P ( b ,L,L) ; P (L) by the definition H B L B ] of bH . This completes the proof.
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