Adoption of new online services in the presence of network externalities and complementarities

Electronic Commerce Research and Applications 8 (2009) 3–15

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Electronic Commerce Research and Applications journal homepage: www.elsevier.com/locate/ecra

Adoption of new online services in the presence of network externalities and complementarities Woonam Hwang a, Jungsuk Oh b,* a b

KAIST Business School, 87 Hoegiro, Dongdaemun-gu, Seoul 130-722, Republic of Korea College of Business Administration, Seoul National University, San 56-1, Silling-dong, Gwanak-gu, Seoul 151-742, Republic of Korea

a r t i c l e

i n f o

Article history: Received 20 June 2006 Received in revised form 17 March 2008 Accepted 4 April 2008 Available online 8 April 2008 Keywords: Mixed-usage Online services Complementarities Network externalities Technology adoption Punctuated equilibrium

a b s t r a c t A typical online user utilizes multiple services in the same service category concurrently due to the fact that many online service markets are characterized by the coexistence of multiple services offering complementary features. Along with an inherent network externality feature, this complementary nature among competing online services complicates predictions of adoption patterns in these markets. This paper extends the adoption function model of Arthur [W.B. Arthur, Competing technologies, increasing returns, and lock-in by historical events, The Economic Journal 99 (1989) 116–131] and applies it to the online service market in an attempt to explain various cases of adoption behavior. The proposed model predicts that there exists a first-mover’s advantage in this market. Specifically, when network externality is large enough, the follower is confined to a low market share, even though it provides the same level of service as that provided by the leader. However, this first-mover’s advantage can be overcome in cases where perturbations are caused by the heterogeneity of consumers or by service value uncertainty. In addition, a two-step punctuated equilibrium may exist: under specific conditions, market share distribution may be stable for a while at certain levels and then move into actual equilibrium. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction A peculiar feature of online services is that multiple, similar services in a single service category can be utilized simultaneously. For example, a typical online user possesses multiple e-mail accounts from different service providers. Also, many users subscribe to more than one instant messenger service or join several blog websites. Many online services in the same service category offer slightly or moderately differentiated features in order to avoid direct competition. Consequently, users can enjoy differentiated features of multiple services offered by multiple service providers. For instance, a typical Internet user utilizes multiple search engines due to the fact that each search engine possesses unique features and yields different search results. Google is famous for its huge size of web coverage and reliable popularity ranking. On the other hand, Yahoo provides shortcuts that give quick access to dictionary, synonyms, patents, and other related information. Ask.com is strengthened by its subject-specific popularity ranking which suggests broader and narrower terms than the search terms already submitted. Utilizing these slightly different features and strengths together, an Internet user can enjoy more accurate search results, with broader web coverage and access to a rich * Corresponding author. Tel./fax: +82 2 880 2528. E-mail addresses: [email protected] (W. Hwang), [email protected] (J. Oh). 1567-4223/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.elerap.2008.04.002

set of related information that can enhance utility from search activity. Many online users take advantage of this situation by utilizing multiple services depending on the context. Since utilization of these similar services with moderately differentiated features together has a potential to give a higher utility than the sum of utility of each individual service to users, these services are complementary in nature from the users’ perspectives. For instance, as an online information repository, content from multiple portal services used together can endow users with a wider range of knowledge that can enhance and deepen the knowledge of users. The services of each of these categories are complementary since combined usage of these services provides more features, or more content that can provide larger utility than the mere sum of utility from each service to users. Along with this complementary nature, many online services are provided free of charge. A typical online service thrives on indirect revenue sources such as advertisement instead of direct sources such as application software charges or usage fees from its users. In addition, a new online service typically requires a minimal level of user adoption cost in terms of downloading, installation, registration or trial efforts. This minimal adoption cost in addition to the complementary nature among services in the same online service category entails ‘‘mixed usage” behavior, in which a typical online user adopts multiple services in the same service category and utilizes them concurrently. Recognizing that mixed

4

W. Hwang, J. Oh / Electronic Commerce Research and Applications 8 (2009) 3–15

usage behavior is frequently observed in the online service market, scholars need to reflect this in a study on user adoption dynamics of an online service. From a consumer’s perspective, there are a number of factors that contribute to the adoption decisions regarding a particular online service. The quality of the online service in consideration will be important. In addition, the network size of the online service will also be important due to the inherent network externality effect in online service markets. Finally, the extent of complementarity of the online service in conjunction with other online services in the same market is expected to play an important role. In this paper, a utility model that incorporates these features of online services is utilized to explore various adoption patterns in the market. Later in this paper, this model is extended, incorporating a feature of quality improvement over time as well as inflow of new users. The rest of this paper is organized as follows. In Section 2, the literature on the areas of network externality and complementarity as well as online services is explored. In Section 3, a mixed usage model of online services is constructed and equilibrium conditions are analyzed with simulations and introduction of adoption function. In Section 4, various characteristics of online services are explored and the basic mixed usage model is further developed in order to account for additional factors on market conditions such as cumulative network externality and growing market size. Section 5 speculates on the managerial implications of the results of Sections 3 and 4. Lastly, Section 6 provides conclusion and discusses limitations of the paper. 2. Literature review Many online services exhibit positive network externalities. For instance, consumers consider the size of the consumer base of messenger services by firms such as AOL and Microsoft to be very important, as the size of the consumer base determines the potential number of people consumers can communicate with. In addition, an online community with a large number of members is likely to be filled with lively communications and user-contributed content, thereby yielding high value for its users. Essentially, most online services provide values based on communication and information exchanges that are normally positively correlated to the number of people using the same service. However, the possibility of mixed usage in an online service context, as described in Section 1, allows for a number of interesting features of adoption patterns of online services that differ from those observed in other markets. The main objects of consideration from previous literature concerning network externality have been products or industrial technologies. Katz and Shapiro [9] distinguish direct and indirect network externalities. The extent of direct externality is proportional to the number of purchases of other users as exemplified by telephone or fax machine markets. In contrast, an indirect externality arises when the likelihood of a benefit for a potential consumer depends on the size of the existing consumer base through product support. For example, a PC architecture with a large consumer base has a high probability of a greater level of support from software vendors compared to that with a smaller consumer base, thereby awarding its user a higher benefit. Furthermore, the quality of post-purchase services ordinarily depends on the number of product purchases. Compatibility decision has also been regarded as an important determinant for adoption patterns in markets with externality [7–10,15]. The lock-in phenomenon and its effect have also been explored [2,19]. Regarding the entrance of a new service in the market with network externality, uncertainty and expectations about the new service are deemed important [9,12]. Katz and Shapiro [9] proposed the ‘‘ful-

filled-expectations equilibrium” concept which asserts that consumer expectations regarding a product’s demand size decide the actual market size. Additionally, the nature of products and services in the online environment is completely different from that in the physical world [4,6,14]. Many firms have failed to survive online because they did not consider the Internet to be an entirely new medium [14]. Usually, a single online service offers a mix of services from different categories [18]. From the perspective of users, different online services offer differentiated services in a single category. Accordingly, people usually find themselves using multiple services in a single service category, in contrast to cases of physical products or industrial technologies in which different uses are normally exclusive. In addition, a lack of significant adoption cost in many online service markets implies that market equilibrium based on consumer expectations (such as the fulfilled expectation equilibrium) can be perturbed more easily than in the case of physical products. The primary adoption decision factor for a given online service is its quality [11]. In addition, due to the mixed usage characteristic of the online service market, complementarity is another important adoption decision factor. Complementarity has been regarded as an important factor in the context of brand extension [1,17], including cases of online services [18]. In this paper, the complementary nature of online services within the same service categories by different service providers is modeled through the use of bundling literature [3], because of their similarity. However, in the online service context, time resources are limited for consumers in terms of using more than two services simultaneously. Such time resource limitations have been reflected in the utility model of this paper. The concept of ‘‘punctuated equilibrium”, which originated in biology [5] and later was adopted in the business literature [12,13,16], has been widely utilized in this paper. Specifically, Loch and Huberman [12] showed that a market characterized by a combination of positive network externality and technology uncertainty can lead to a punctuated equilibrium. In this paper, such punctuated equilibrium is observed under certain market conditions. The distinctive features of punctuated equilibrium in this paper are that the proposed model considers a mixed usage model, and that punctuated equilibrium is observed in the absence of product quality uncertainty. In addition, punctuated equilibrium is also observed in the presence of consumer heterogeneity or quality uncertainty when there are quality improvements over time. 3. The model In this section, a basic model is constructed, and equilibrium conditions and simulation results are provided. In Section 3.1, the mixed usage model is defined. In Section 3.2, a brief user survey on the parameters is presented to assess the applicability of this model to the real world setting. Section 3.3 demonstrates equilibrium conditions of the model. In Section 3.4, adoption process with various sets of parameters is simulated and a modified form of adoption function that was introduced by Arthur [2] is utilized to characterize equilibrium from simulation analysis. 3.1. The mixed usage model It is assumed that there are two complementary online services (Service A and Service B) in the same service category that are provided for free and that their perceived basic service qualities by the users are QA and QB, respectively. Also assumed is that Service A is the incumbent service and Service B is a potential entrant. There

W. Hwang, J. Oh / Electronic Commerce Research and Applications 8 (2009) 3–15

are N users indexed from 1 to N. Since our model considers an online service market near its saturation such as instant messengers or e-mail services, the possibility of new users without any experience of either of the two services is not considered for now. This assumption signifies that all users have used Service A before Service B enters. This ‘‘market maturity assumption” is rather restrictive in that an incumbent online service rarely covers the entire market. On the other hand, the penetration speed of an online service is often very fast so that an online service occupies a significant market coverage by the time a new entrant arrives. Moreover, the market maturity assumption renders a more intuitive insight into the adoption process depicted in our framework. In Section 4.5, the market maturity assumption is relaxed and an explanation of this more realistic scenario is presented based on the understanding of previous scenarios with market maturity assumption. The total amount of time each user spends using the online services is fixed, and users allocate this amount of time between two services according to the utility maximization process. Let bi be the ith user’s proportion of the total amount of online service usage devoted to Service B; that is, the usage rate of Service B. The ith user’s perceived market shares in terms of usage rates for the two services are then P P j–i ð1  bj Þ j–i bj ; i; j ¼ 1; . . . ; N: ð1Þ and fiB ¼ fiA ¼ N1 N1 Note that ith user’s perceived market share excludes the own usage rate, because the user will adjust the own usage rate according to the perceived market share of each service. We also denote the total market shares of Service A and Service B as fA and fB, respectively, which include all users’ usage rates. As the market share of Service B is the focal point, fiB will be simply denoted as fi, and fB as f henceforth, except where distinction is necessary. The utility of each service perceived by the ith user is then defined as U pi ¼ Q p þ cp fip ;

p ¼ A; B;

where c is the externality coefficient for each service. Complementarity effects are incorporated into our model following the approach by Bakos and Brynjolfsson [3]. Adoption of both services is assumed to yield utility of 0 6 wðbÞ 6 1

ð3Þ

to a consumer where c > 0 is the degree of complementarity and U is an independent utility of each service. Due to the limited time resource assumption, the degree of complementarity between the two services is expected to be affected by the specific proportion of the total time budget that is allocated between them, which is represented by w(b) (see Appendix A for details). Note that when b = 0 or 1, it is an exclusive usage of Service A or Service B, so that w(0) = w(1) = 0, in which case two services are not complementary with each other. Also, if we designate bc as the usage rate that maximizes complementarity so that w(bc) = 1, this complementarity function becomes analogous to the one utilized by Bakos and Brynjolfsson [3]. With this model setup, the adoption of both services yields utilities of 2cw(b)UA and 2cw(b)UB, for Service A and Service B, respectively. Considering the time allocation between these two services, the final mixed utility function of an individual user is now defined as follows: U i ¼ ð1  bi Þ  2cwðbi Þ U Ai þ bi  2cwðbi Þ U Bi ;

i ¼ 1; . . . ; N

ð4Þ

Without loss of generality, it is assumed that the extent of complementarity is the largest when the two services are used equally. In this case, w(b) = 4b(1  b) and bc = 1/2. With this simplification, the individual mixed utility function becomes U i ¼ 24cbi ð1bi Þ fð1  bi ÞU Ai þ bi U Bi g;

Following Loch and Huberman [12], the adoption process for Service B with this mixed usage utility function is modeled as follows. Users evaluate two online services by their utility function asynchronously according to the Poisson process with an arrival rate of k, and at each time the evaluating user is selected according to the uniform distribution since every user is assumed to be homogeneous in his/her evaluation attempt. For example, when Service B enters the market, a user arriving according to the Poisson process evaluates his/her optimal usage rate of both services. Then, taking this evaluation by the user into account, the total market share f is updated, affecting the next user to result in different optimal usage rate for both services. This successive evaluation changes the market share f continuously, eventually leading to equilibrium. In reality, the users’ reevaluations can occur by many events, such as peer recommendations, encounter of links from other sites, accidental trials, trials by curiosity, or simple realization of the changed qualities of services already in use. In this regard, successive evaluations are assumed to be random and asynchronous. At each evaluation, a user perceives UA and UB as constants because they are already determined by the perceived market share fiA and fiB . Solving the consumer utility maximization problem by applying a first-order condition on Eq. (5) yields the following individual optimal usage rate of Service B at each evaluation, qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðDðfi Þ  2U Ai Þ þ ðDðfi Þ þ 2U Ai Þ2 þ c ln2 2 Dðfi Þ2 ; 0 6 bi 6 1 ð6Þ bi ¼ 4Dðfi Þ where Dðfi Þ ¼ U Bi  U Ai –0 and c – 0. When D(fi) = 0, bi is simply 1/2. Since the final market equilibrium is not analytically obtainable, numerical simulation will be extensively utilized in various equilibrium analyses in the subsequent sections. Also, variable definitions are summarized below (see Table 1).

ð2Þ

p

2cwðbÞ  U;

5

i ¼ 1; . . . ; N:

ð5Þ

3.2. Example cases In order to assess the applicability of the utility model of 3.1, we conducted a brief survey on user assessment of key parameters on representative online services in the South Korea. Although these results are not rigorous measurements, they provide a sense of how levels of quality, network externality and complementarity of each service are perceived and relatively compared by users. Table 2 presents the survey results. The survey contains user ratings on these key parameters in online service categories such as search engines, blogs, e-mail services and others by 18 participants.

Table 1 Summary of notation Notation

Description

Service A Service B QA, QB N bi bi bc fiA ; fiB ð¼ fi Þ fA, fB (=f) cA, cB U Ai ; U Bi c w(b)

Incumbent service with initial market share of 100% New entrant service with initial market share of 0 % Basic quality of Service A and Service B Total number of users ith user’s usage rate of Service B ith user’s individual optimal usage rate of Service B at each evaluation A usage rate that maximizes complementarity ith user’s perceived market share of Service A and Service B Total market share of Service A and Service B Externality coefficient (degree of externality) ith user’s perceived utility of each service when used exclusively Degree of complementarity A function that adjusts the usage rate division that affects the extent of complementarity Arrival rate of the Poisson process U Bi  U Ai

k D(fi)

6

W. Hwang, J. Oh / Electronic Commerce Research and Applications 8 (2009) 3–15

Table 2 Survey results on representative online services Category

Quality (out of 10)

Network externality (out of 9)

Complementarity (out of 9)

Search engine 1 Naver.com 2 Google.co.kr

6.9 7.6

4.5 3.4

1.78

Blog 1 Blog.naver.com 2 Cyworld. com

4.6 7.1

4.3 5.5

0.44

E-mail service 1 Daum.net 2 Paran.com

4.7 3.8

2.4 1.9

0.83

Internet community service 1 Cafe.daum.net 5.6 2 Cafe.naver.com 4.3

5.1 3.6

0.83

Online game 1 Nexon.com 2 Hangame.com

3.9 4.1

3.1 3

0.83

7.2

5.8

1.33

5.6

5.2

5.1 4.8

3.8 2.8

Instant messenger 1 MSN Messenger 2 NateOn Messenger Internet shopping 1 Gmarket.com 2 GSestore.com

From Proposition 1, it is important to notice that when the two services are complementary (when c > 0), Service B can be adopted even when U Bi is smaller than U Ai due to its complementary nature. Moreover, even when U Bi is larger than U Ai , Service B does not always dominate the entire market. Note that U Ai and U Bi change as f changes during the evaluation process. As c gets larger, there is a higher chance of survival for Service B as well as a lower chance of its dominance of the entire market. Corollary 1 implies that when the degree of complementarity between Service A and Service B exceeds some level, Service B will always be adopted regardless of its quality or degree of network externality, but it will never dominate the entire market. When there is a strong complementarity between services, users need to use both services. Fig. 1 graphically summarizes these results. 3.4. Simulation and adoption function

0.78

Fig. 2 exhibits a Matlab simulation result of a typical adoption process in which the quality of Service B is higher (QB = 11) than that of Service A (QA = 10), and in which both services have the same level of moderate network externality (cA,cB = 7) and complementarity (c = 0.2). The number of total users N is 100, and the reevaluation happens with a rate of k = 1 according to the Poisson process. (N and k will remain unchanged throughout the simula-

Utility Ratio UB UA

UB UA

From Table 2, search engines and instant messengers show relatively high complementarity than the other service categories. Also, e-mail services and Internet shopping websites exhibit relatively low network externality, which seems to be a reasonable result since for these services, users do not derive value directly from other users’ usage. With these brief survey results, one can get a sense of how results and implications of subsequent analyses can be applied to real world situations.

0 < f <1

1

UB UA

γ 1 4 ln 2

U Bi

1 > A 1  4c ln 2 Ui

and

1  4c ln 2 > 0

1

40 Market Share of B ( f )

0.75

35 30 25

0.5

B

20

A

15

Utility of Service B (U ) Utility of Service A (U )

0.25

Utility

Market Share of B ( f )

Furthermore, the new online Service B will dominate the market with complete market share when the following condition is satisfied at some point during the adoption process:

Complementarity

Fig. 1. Graphical representation of equilibrium condition.

Proposition 1 (The new online service adoption proposition). The new online Service B will be adopted when the following condition is satisfied for the first evaluating user: > ð1  4c ln 2Þ

= 1 − 4γ ln 2

f =0

In order for Service B to survive, bi should be larger than 0 for the first evaluating user after Service B has entered the market. For Service B to dominate the market, the evaluator’s optimum usage rate bi should grow to 1 at some point during the adoption process. These two conditions translate into the following necessary condition.

U Ai

1 1 − 4γ ln 2

f =1

3.3. Equilibrium conditions

U Bi

=

10 5

Proof 1. Proofs for all of the main results are provided in Appendix B. h Corollary 1 (The co-existence condition corollary). The new online Service B is always adopted but can never dominate the market with complete market share when c satisfies c P 4 ln1 2.

0

0

1000

2000

3000

4000

0 5000

Time Fig. 2. An example of new service adoption. (When N = 100, k = 1, c = 0.2, QA = 10, QB = 11, cA,cB = 7).

7

1

0.8

Equilibrium

0.6

β* i

0.4

βi*= fi

0.2

0 0

0.2

0.4

0.6

0.8 Perceived Market Share of B ( f )

1

i

Fig. 3. ith user’s adoption function with a stable equilibrium. (When N = 100, k = 1, c = 0.2, QA = 10, QB = 11, cA, cB = 7).

1

0.8 B QB = 16 Q = 13

0.6

0.4 QB = 10 QB = 7

0.2

0 0

0.2

0.4

0.6

0.8

1

Perceived Market Share of B ( fi ) Fig. 4. ith user’s adoption functions for differing quality levels of service B. (When N = 100, k = 1, c = 0.2, QA = 10, cA, cB = 10).

patterns of changes in the shapes of adoption functions in response to changes in the quality level of Service B when complementarity is moderate (c = 0.2) and network externality is relatively high (cA, cB = 10). An increase in the quality of Service B from 7 to 16 while the quality of Service A is 10, entails a parallel upward shift in the adoption function. Such a parallel increase in the adoption function will affect the overall speed of adoption. For example, when QB is 16, the difference between the adoption function and the dashed line is roughly twice that of when QB is 13. Note that for both cases, the final equilibrium is f = 1, while the equilibrium for QB = 7 is f = 0. Fig. 5 shows the impact of the changing extent of network externality on the shape of the adoption function, in which the quality of Service B (QB = 12) is higher than Service A (QA = 10) with a moderate level of complementarity (c = 0.2). As c(c = cA = cB) increases from 2 to 18, the adoption function rotates counterclockwise with changes in its shape. When the network externality is relatively small or moderate (c 6 10), the equilibrium market share of Service B is very high, but as it increases to 18, Service B’s market share drops to 0. Fig. 5 signifies that, in a market with strong network externality, an entering online service will not be adopted; whereas in a market with a moderate level of externality, an

Individual Optimum Usage Rate of B (βi*)

Individual Optimum Usage Rate of B ( βi*)

tions henceforth.) The simulation result shows that the usage rate of Service B converges to 0.8036 after about 2500 units of time. UA is initially higher than UB even though QA is lower than QB because of its network externality, but evaluations and adoptions of Service B by successive users causes UB to increase while instigating the decrease in UA. After about 2500 units of time, equilibrium has been reached in which no more changes in the usage rate occur. At this point, each user attains the maximum utility level, collectively. In this case, the result is quite intuitive in that Service B gained higher market share because of its higher quality. Fig. 3 illustrates how the equilibrium in Fig. 2 is reached. The horizontal axis is fi, and the vertical axis is the optimum bi of an individual user i. During the adoption process, the qualities of both services are fixed, so the optimum bi only depends on the perceived market usage rate of B at each time. The dashed line on the graph is an equality line where the optimum bi and fi coincide. When Service B enters the market with a zero usage rate, the first evaluating user chooses to allocate about 0.16 of his time to Service B, and this increases other users’ fi slightly, moving fi to the right on the horizontal axis. Following this, the next user allocates more time than the first user did to Service B, moving fi farther to the right. This process will be continued by successive users until they arrive at the point where the optimum bi line meets the dashed line. From this point on, evaluating users continue to follow the market usage rate, resulting in an equilibrium in terms of usage rate, where fi is equal to f. If any user allocates more time to Service B than the market equilibrium, fi will move to the right side of the axis; but when this occurs, the optimum bi line will become lower than the dashed line, forcing a move back to equilibrium. In this regard, the equilibrium in Fig. 3 is stable. This framework of service adoption represented by Fig. 3 bears a structural similarity to that of Arthur [2]. However, the work by Arthur is different from this framework in that his model focused on adoption patterns of industrial technologies which are characterized by exclusive usage. In addition, competing technologies were assumed to enter the market simultaneously while the current model deals with a situation in which there are incumbent and entering services. Following Arthur [2], the optimum bi line of users is referred to as an adoption function. Note that the speed of adoption is proportional to the difference between the adoption function and the dashed line. Utilizing this adoption function framework, the impacts of perturbations of various utility function parameters have been assessed via multiple runs of simulation. First, Fig. 4 exhibits

Individual Optimum Usage Rate of B (βi*)

W. Hwang, J. Oh / Electronic Commerce Research and Applications 8 (2009) 3–15

1

0.8 c=2

c=6

c = 10

0.6

0.4 c = 18

0.2

0 0

0.2

0.4

0.6

0.8

1

Perceived Market Share of B ( fi ) Fig. 5. Adoption functions for differing levels of network externality (When N = 100, k = 1, c = 0.2, QA = 10, QB = 12, c = cA = cB).

W. Hwang, J. Oh / Electronic Commerce Research and Applications 8 (2009) 3–15

0.7

1

0.6

c=2

0.8

Market Share of B ( f )

Individual Optimum Usage Rate of B ( βi*)

8

γ = 0.35

0.6

γ = 0.45

0.4 γ = 0.25 γ = 0.15

0.2

0.5 c=6

0.4 0.3

c = 10

0.2 c = 12

0.1 c = 18

0

0 0

0.2

0.4

0.6

0.8

1

0

1000

entering service may benefit from the externality through the expansion in its market share provided that the entering service is of high quality. Fig. 6 illustrates the effect of complementarity on the shape of the adoption function, in which the quality of Service B (QB = 12) is higher than Service A (QA = 10) with relatively high network externality (c = 10). An increase in c from 0.15 to 0.45 causes the adoption function to rotate clockwise, which is the opposite of the effect of network externality. This implies that a market externality effect is offset by that of service complementarity. As c increases, the market equilibrium approaches f = 0.5 at which point the degree of complementarity and the difference between the adoption function and the dashed line are the largest. Thus, as the two online services exhibit stronger complementarity, the new service will be adopted faster and the market will be split in half. 4. Equilibrium analysis In this section, we derive some new findings on the online service markets from the mixed usage model, and we extend the basic model to relax some restrictions made before, with further analysis. In Sections 4.1 and 4.2, the existence of first-mover advantage and two-step punctuated equilibrium are presented, respectively, along with their rationales. In Section 4.3, we observe an equilibrium jump in the extended model with the introduction of consumer heterogeneity and uncertainty of decision in quality measurement. In Section 4.4, cumulative network externality is taken into account and another form of punctuated equilibrium is found. Finally, Section 4.5 relaxes the mature market assumption made before and observes how it works differently from the previous model. 4.1. First-mover advantage With the same quality and same degree of network externality, two online services offer the same value to users. In this case, the market will be split in half between the two services. On the other hand, with a large degree of network externality, the new Service B is entitled to a market usage rate of less than 0.5. Fig. 7 shows the situation in which the qualities of both services are the same (QA,QB = 12) and the complementarity is moderate (c = 0.2), with various degrees of externality. When network externality is small or moderate (c = 2 or 6), the market usage rate of B approaches

3000

4000

5000

Fig. 7. An example of first-mover advantage. (When N = 100, k = 1, c = 0.2, QA = 12, QB = 12).

0.5. However, when the degree of externality is relatively high (c = 10 or 12), the market share of B converges to approximately 0.27 or 0.1, respectively, and when c is 18, Service B is never adopted. Fig. 8 illustrates the rationale behind this distinction clearly. When c is 2 or 6, the only stable equilibrium is f = 0.5, where the adoption functions are relatively flat. However, as the degree of network externality increases, the adoption function gets curved and increases the possibility of multiple equilibria. When c is 12, there are two stable equilibria of f = 0.1 and 0.9 and one unstable equilibrium of f = 0.5. The point f = 0.5 is unstable equilibrium because any small deviation will lead to either of the other stable equilibria. As Service B is an entrant, f = 0.1 is the actual equilibrium, since the adoption process starts from f = 0. At c = 18, there is only one unstable equilibrium, so Service B is not adopted. In sum, a network externality of a certain level or higher endows Service A with the first-mover advantage even if the quality levels are identical between the two services. With a high c value, the adoption function has more of a curve, as the benefit from a high network externality exceeds that from service complementarity, which leads consumers to use only one service. As a result, with a proper balance between externality and complementary effects, two stable equilibria occur whereas

Individual Optimum Usage Rate of B (βi*)

Fig. 6. Adoption functions for differing levels of complementarity. (When N = 100, k = 1, QA = 10, QB = 12, c = cA = cB = 10).

2000

Time

Perceived Market Share of B ( fi )

1

0.8

0.6 c=2

c=6

0.4 c = 12

0.2

c = 18

0 0

0.2

0.4

0.6

0.8

1

Perceived Market Share of B ( fi ) Fig. 8. Adoption functions for the example of first-mover advantage. (When N = 100, k = 1, c = 0.2, QA = 12, QB = 12, c = cA = cB).

9

1

1

0.8

0.8

1st-mover advantage

0.6

Market Share of B ( f )

Individual Optimum Usage Rate of B ( βi*)

W. Hwang, J. Oh / Electronic Commerce Research and Applications 8 (2009) 3–15

Possible equilibrium

0.4 2nd mover equilibrium 0.2

c = 14

c = 14.5

0.6

0.4

c = 14.54

0.2

c = 15 0

0 0

0.2

0.4

0.6

0.8 Perceived Market Share of B ( f )

1

i

0

0.5

1

1.5

Time

2 x 10

4

Fig. 9. A general example of first-mover advantage. (When N = 100, k = 1, c = 0.19, QA = 12, QB = 10, cA = 8, cB = 12).

Fig. 10. An example of two-step punctuated equilibrium. (When N = 100, k = 1, c = 0.2, QA = 10, QB = 12, c = cA = cB).

with the domination by the externality effect over that of complementarity, only a single equilibrium prevails. Consider another scenario depicted in Fig. 9 in which Service A has higher quality (QA = 12, QB = 10) but Service B has a higher degree of network externality (cA = 8,cB = 12), with moderate complementarity (c = 0.19). There are two stable equilibria, but the actual equilibrium occurs at approximately 0.06 due to the fact that Service B is a new entrant with lower quality and that Service A possesses the first-mover advantage. If Service B can achieve the market adoption rate represented by the second, unstable equilibrium of approximately 0.5, the market equilibrium will occur at the upper right, stable equilibrium. In this regard, the difference between the lower left and the unstable equilibrium is the firstmover advantage that the second mover has to overcome. This first-mover advantage can be either big or small depending on the position and the shape of the adoption function. A first-mover advantage in online service markets is very commonly observed. For example, Google, the biggest online search engine, has the largest market share in the US and in many other parts of the world. However, its market share in the South Korea is comparably insignificant. First movers in the South Korean online search market, such as Daum and Naver, possess a large amount of local contents with high positive network externalities such as knowledge services and individual images uploaded by users. In contrast, the first movers in the US when Google debuted did not possess many contents with high network externalities. In this regard, Google overcame the first-mover advantage in the US but it has not in the South Korean market due to a larger firstmover advantage. In another example, regarding the instant messenger market, MSN’s messenger service was an entrant into the market dominated by AOL’s messenger service. While the market share of AOL Messenger had been ahead of MSN Messenger for some time in both the global and the US market, MSN Messenger eventually took the lead in the global market, whereas in the US market, AOL and MSN’s messengers were capturing roughly equal market share as of 2006. AOL’s strong first-mover advantage in the US, due in large part to its US focused communities and content services, has hampered MSN Messenger from dominating the market as fast as it has in the rest of the world.

higher value for quality than Service A (QA = 10) with a moderate degree of complementarity (c = 0.2), and each variation of c is relatively large, signifying a high level of network externality. In the adoption paths of Service B for various values of c, there are time periods in which the adoption speeds are slower compared to other periods. In this example, with larger values of c, this time period of the delay in adoption becomes longer. For c = 14.5 and 14.54, it may appear that an equilibrium is reached with a market share of B at 0.16. However, soon, a relatively abrupt increase in the adoption of Service B follows. Such an equilibrium followed by an abrupt surge in adoption is called a punctuated equilibrium [12]. With an even larger externality factor at c = 15, there is no punctuated equilibrium, and the usage rate of B stabilizes at approximately 0.09. Fig. 11 illustrates the adoption mechanism for Service B using the adoption function with the value of c at 14.54. The adoption function in this case is tangent to the dashed line at a market usage rate of approximately 0.16. At this point, there is a pause in the changes in adoption rate because the difference between the adoption function and the dashed line is small; consequently, the adoption of Service B is slow. In Fig. 11, it is observed that there are two sudden increases in the usage rate of Service B. The first surge occurs at the initial entrance of Service B and the second occurs after a relatively long pause at a market usage rate of nearly 0.16. As there are two punctuations before Service B takes over the entire market, this kind of profile in usage rates is referred to as a two-step punctuated equilibrium. An implication of a two-step punctuated equilibrium is that there is a chance that a service with an initially small market share can take over the entire market after a certain period of time to establish a seemingly stable market share structure. As is observed in this example, such a two-step punctuated equilibrium is likely to occur in a market characterized by a large degree of network externality, since a highly curved adoption function is achieved with a large externality coefficient.

4.2. Two-step punctuated equilibrium Under specific conditions, a time delay may precede an eventual equilibrium which is illustrated in Fig. 10. Service B (QB = 12) has a

4.3. Equilibrium jump by heterogeneity and uncertainty In a market with a relatively small first-mover advantage, a small perturbation in the market can result in the new entrant gaining more market share than might otherwise be expected. In Fig. 12, the quality of Service B (QB = 12) is larger than Service A (QA = 10), and they both have a very high degrees of externality (c = 15) with a moderate complementarity (c = 0.2). In this

W. Hwang, J. Oh / Electronic Commerce Research and Applications 8 (2009) 3–15

1

Individual Optimum Usage Rate of B ( βi*)

Individual Optimum Usage Rate of B ( βi*)

10

0.8 Equilibrium (B takes over A)

0.6 Slow transition of usage rate

0.4

0.2

0 0

0.2

0.4

0.6

0.8 Perceived Market Share of B ( f )

1

1

0.8

Critical mass for takeover

0.6

0.4

Equilibrium 0.2

0 0

0.2

i

Fig. 11. Adoption function for two-step punctuated equilibrium. (When N = 100, k = 1, c = 0.2, QA = 10, QB = 12, cA, cB = 14.54).

example, the adoption function is curved due to the high network externality, and is mostly above the dashed line because the quality of Service B is higher than that of Service A. A stable equilibrium occurs at approximately 0.1, and at 0.25 there is an unstable equilibrium after which the market share of B surges and dominates the market. In this case, the unstable equilibrium can be regarded as the critical mass necessary for Service B to take over the market. There are a number of factors that can cause such a perturbation in the market. On the supply side, a heavy investment in advertising and marketing promotions can lead to such a perturbation. From the demand side, factors contributing to the relaxation of the homogeneity and stability of consumer utility functions such as consumer preference heterogeneity and service quality uncertainty can bring about such a perturbation. First, in order to incorporate heterogeneity in the previous consumer’s utility function, the following heterogeneity function is assumed:     1 i  1 i  A B  h; h ðiÞ ¼  þ h; i ¼ 1; . . . ; N: ð7Þ h ðiÞ ¼ 2 N 2 N  is the level of heterogeneity and N represents the total popwhere h  and ulation. From Eq. (7), each user takes a position between 0:5h  For Service A, users on the positive side according to hA(i) pre0:5h. fer Service A, while those on the negative side prefer Service B; for hB(i), the opposite is true. The ith user’s utility function for each service is then defined as follows: p

U pi ¼ Q p þ cp fip þ h ðiÞ;

p¼A

or

B;

i ¼ 1; . . . ; N:

0.4

0.6

0.8

1

Perceived Market Share of B ( fi )

ð8Þ

With the heterogeneous utility functions of users, the first-mover advantage, such as that in Fig. 12, may be overcome. In Fig. 13, the values of parameters are same as those of Fig. 12 and only the heterogeneity factor has been added, so that we can find out how heterogeneity can help to overcome the first-mover advantage in  is 3, the heterogeneity is not large enFig. 12. In Fig. 13 in which h  is ough to overcome the first-mover advantage. However, when h 3.7, Service B achieves a two-step punctuated equilibrium after a  inrelatively long pause before taking over the entire market. As h  ¼ 4, the two-step punctuation creases, as illustrated in the case of h happens even faster. Thus, a big difference in consumer preferences may play an important role in overcoming the first-mover advantage from an entrant service provider’s perspective. In Fig. 14, the values of parameters are also the same as those of Fig. 12. However, instead of heterogeneity, users are assumed to

Fig. 12. An example of first-mover’s advantage. (When N = 100, k = 1, c = 0.2, QA = 10, QB = 12, cA,cB = 15).

have service quality uncertainty of N(0, 2) for each service in order to see how uncertainty can help to overcome the first-mover advantage. In this case, as can be seen in Fig. 12, an equilibrium without uncertainty occurs at approximately 0.1. However, due to the perturbation by uncertainty, the market share fluctuates for some time, and the usage rate of B accidentally reaches an unstable equilibrium at approximately 0.25. Subsequently, Service B takes over the market. 4.4. Competition in the presence of cumulative network externality Many online services provide value with cumulative content. For example, in the context of community websites or knowledge services, more posts and content accumulates as member activities continue. The accumulation of content increases the perceived quality of the service, which motivates successive users to participate in the service. In order to incorporate this ‘‘cumulative network externality” effect, it is helpful to assume that the quality of the online service increases in proportion to the network size with time t in the presence of a ‘quality ceiling’ which is denoted by Q A and Q B for each service. Following this, the rate of quality accumulation is assumed to be proportional to the amount of accumulated quality up to the quality ceiling, which signifies that the rate of increase in quality will slow as the quality gets closer to the ceiling [12]. Letting kA and kB be the rates of quality improvement for each online service, the service quality is defined as follows: p

Q ptþ1 ¼ Q pt þ k f p

Q p  Q pt Qp

;

p ¼ A or B;

t ¼ 1; 2; . . .

ð9Þ

This cumulative network externality coexists with the non-cumulative externality introduced earlier. For example, in community service markets, perceived content quality depends on the amount of cumulative content but the speed of the responses by other members of the community only depends on the network size of the service, which is an additional value source for users. In this regard, both the cumulative and non-cumulative externality effects are incorporated in this model. The heterogeneity assumption of the previous section is also maintained, which results in the following extended utility model, p

U pi;t ¼ Q pt þ cp fi;tp þ h ðiÞ;

p ¼ A or B;

i ¼ 1; . . . ; N:

ð10Þ

Fig. 15 exhibits a simulation result based on Eq. (10). In this example, the quality of Service B (QB = 12) is higher than that of Service A

11

1

1

0.8

0.8

h =3.7

0.4

0.2

h =3

50

40

Market Share of B ( f ) Utility of Service A (UA)

0.6

30

Utility

h =4

0.6

Market Share of B ( f )

Market Share of B ( f )

W. Hwang, J. Oh / Electronic Commerce Research and Applications 8 (2009) 3–15

0.4

20 B

Utility of Service B (U )

0.2

10

0 0

0.5

1

1.5

2 4

Time

0

0 0

x 10

1

2

3

Time

Fig. 13. An example of overcoming the first-mover’s advantage with heterogeneity. (When N = 100, k = 1, c = 0.2, QA = 10, QB = 12, cA,cB = 15).

4 x 104

Fig. 15. Punctuated equilibrium with cumulative network externality and heter ¼ 2:5; ogeneity. (When N = 100, k = 1, c = 0.2, QA = 10, QB = 12, Q p ¼ 2Q p , h p k ¼ 0:05; cp ¼ 10).

1

possibility of a punctuated equilibrium in a market with cumulative externality and uncertainty, in which the parameters of simulation are the same as those in Fig. 15. The adoption pattern closely resembles that depicted in Fig. 15 except for the constant perturbation of market usage rate for Service B.

Market Share of B ( f )

0.8

0.6

4.5. Adoption behavior with growing market size 0.4 Critical mass for takeover

0.2 Equilibrium without uncertainty

0 0

0.5

1

Time

1.5

2 4

x 10

Fig. 14. An example of overcoming the first-mover’s advantage with uncertainty. (When N = 100, k = 1, c = 0.2, QA = 10, QB = 12, cA,cB = 15, uncertainty: N(0, 2)).

(QA = 10), and the quality ceiling for both services are assumed to be twice their initial values. Note that the complementarity (c = 0.2) is moderate and the network externality (c = 10) is relatively high. Also the rate of quality improvement kp is 0.05, and the degree of  is 2.5. With its incumbent status, Service A reaches heterogeneity h its quality ceiling rapidly. Service B enters the market after 3,000 units of time. Initially, the quality of Service B is very low compared with that of Service A, which leads to a low level of adoption for Service B. As time progresses, the quality of Service B steadily increases due to the cumulative externality effect by those users who prefer Service B. When the quality of Service B reaches a certain level, the usage rate increases suddenly and a punctuation of the equilibrium to level f = 0.8 results. In this scenario, Service B would never have been adopted in a market with homogeneous users, as no one would try this service. In a market with consumer heterogeneity, the small number of users who try Service B initiates the quality accumulation process. In sum, the combination of cumulative network externality and heterogeneity enables this one-step punctuated equilibrium. As the effect of quality uncertainty is similar to that of consumer heterogeneity in stimulating a punctuated equilibrium, a similar adoption pattern is expected in a market with cumulative externality and quality uncertainty. Fig. 16 illustrates the

So far, it has been assumed that the market is already saturated when the new Service B enters, because markets for many popular online services such as search engines, e-mail, or instant messengers are rather mature and near saturation and the pool of potential users is small. However, there are also services that are new and growing in market size, so we briefly analyze such markets. We postulate a situation in which the market size at the time of B’s entrance is half the total market size. Half the users are using Service A, and the remaining users are not using any service at all. After Service B enters, existing users reevaluate the two services, and potential users also enter the market and evaluate the services. The usage rates of the services are then determined by the preferences of all users. This two-stage evaluation process is assumed to follow the Poisson process, and since the users’ motivation to reevaluate or to enter the market is conjectured to be similar, such as peer recommendation, links from other sites, or trials by curiosity, the process of reevaluation by existing users and entrance of new users is modeled as a single process following the Poisson process with an arrival rate of k = 1. With this market growth assumption, an interesting result is obtained that was not observed in previous analyses with market maturity assumption. The market share of Service B overshoots the equilibrium before it becomes stable. Fig. 17 shows several simulations for the case of Fig. 12 with the same parameter set. Every run in Fig. 17 shows that the market share of Service B at its adoption surge is higher than their final equilibrium, except the one that takes over the market. When Service B enters, the market is not near saturation, so the network externality is relatively less influential compared to the quality factor in evaluating the utility level of each service, despite the high value of the externality coefficient. Therefore Service B, with its higher quality, is more attractive than it would be if the market were nearly saturated, and people will use it more than they would if the market were nearly saturated. However, from newly arrived users’ perspectives,

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W. Hwang, J. Oh / Electronic Commerce Research and Applications 8 (2009) 3–15

1

Market Share of B ( f )

5. Discussion: developing managerial interpretations for improved strategy

40

Many online services are competing with one another in the same service category, trying to attract more users and obtain a greater share of their time. In some service categories, the first mover may have a high market share even though its competitors offer superior or comparable services. As we previously mentioned, Google is having a hard time competing in South Korea because Naver, the dominant domestic search and portal service provider, has built up first-mover advantage and barriers to market entry with strong network externalities. However, in other cases, second movers have overcome first-movers’ advantage. In the United States, for example, Yahoo was a dominant search engine service provider during 1990s, but Google, with its superior search technology, took over the market and became the dominant player. As these examples show, both the first mover and the follower can acquire the dominant position in a market, provided that a suitable market strategy under the right market conditions is leveraged. This section provides additional managerial insights based on the analysis work that we have carried out in this article. First movers need to have content or features that can enable strong network externality effects in order to obtain a dominant market position relative to its competitors. In many online service contexts, this is a difficult task since service features are normally easy to duplicate but hard to protect by legal means and patents. From this perspective, Google’s core service, the search engine, whose strength stems from its high technical capabilities, may lack naturally high network effects. On the other hand, Google’s recent moves to acquire YouTube or its attempt to buy a stake in FaceBook show that its intent to complement its portfolio of services with those that bear high network externalities. In other cases, online services with cumulative content show strong network externalities. YouTube and Wikipedia are two exemplary cases in which an enormous amount of content from users has helped strengthen their market-leading positions. Market followers can also carry out strategies that bring higher market share or permit them to overtake the first mover. First, as we found from the analysis of the mixed usage model, a second mover’s superior service quality can help it to acquire higher market share. If the first mover has a low network externality, a second mover which is able to offer slightly better quality can achieve a higher market share. However, if the first mover has dominated the market with high network externality-bearing services, then the second mover’s service quality will need to be much higher. For example, MySpace, which has great network effects emanating from the features of its services, has achieved a position as a dominant service provider in social networking. There have been many competitors who challenged MySpace’s market share, but none of them were successful until FaceBook entered the market. Having high complementarities that derive from an existing service may also be a good strategy to gain market share, since the high complementarities between two services engender similar levels of use. Additionally, a follower can take advantage of differences among consumers. Consumer heterogeneity is known to be a factor that causes fluctuations in firm market shares, helping a second mover to overcome the first mover’s early entry advantage. Even in an environment with cumulative network externalities, consumer differences enable the second mover to gain a significant market share after a long period of product or service trials under certain conditions. Therefore, the second mover will differentiate its services from the first mover so as to appeal to users’ varied tastes within the same service category. Then, users who prefer the second mover’s offering may help it to achieve a higher market

Utility of Service A (UA)

0.6

30

Utility

Market Share of B ( f )

0.8

50

0.4

20 Utility of Service B (UB)

0.2

10

0

0 0

1

2

3

4

Time

x 104

Fig. 16. Punctuated equilibrium with cumulative network externality and uncertainty. (When N = 100, k = 1, c = 0.2, QA = 10, QB = 12, Q p ¼ 2Q p , kp = 0.05, cp = 10, Uncertainty: N(0, 1)).

1

Market Share of B ( f )

0.8

0.6

0.4 Critical mass for takeover

0.2

0 0

1000

2000

3000

4000

5000

Time Fig. 17. Dynamic adoption behavior with market growth. (When N = 100, k = 1, c = 0.2, QA = 10, QB = 12, cA, cB = 15).

Service A is still more attractive due to its greater market share (around 0.8 in Fig. 17) and hence, UA is raised to a greater degree than UB. The increasing UA causes users in general to choose Service B less than they did at first. This gradual change causes the subsequent drop in the market share of B, which converges around f = 0.1. On the other hand, during the early period, old users raise UB and lower UA, since they allocate some of their usage time for Service A to Service B. This contrasts with the effects of the inflow of new users. Therefore, the adoption pattern differs according to the arrivals of new users and the changes in the behavior of old users, and the resulting usage profile might show more than one equilibrium. Because the first-mover advantage in Fig. 12 is small, Service B can take over the market, if the surge in its market share during its adoption period reaches the critical mass, as in one of the runs shown in Fig. 17. Therefore, we can conclude that, during the early stage of adoption in an immature market, the quality factor affects the market share more than it does in a mature market, and this can lead the market to different equilibria under certain market conditions.

W. Hwang, J. Oh / Electronic Commerce Research and Applications 8 (2009) 3–15

share. This strategy seems straightforward, but is still noteworthy because many online services have imitated their competitors without any efforts to differentiate themselves. Finally, in a growing market with a small user population, the second mover early on might want to attract more of the users of the first mover rather than new users, through some specific marketing strategy. In a growing market, new users evaluate the available services to a greater extent than old users do, and the first mover then will have a higher chance of getting a larger market share. On the other hand, if a new service attracts old users who were using the incumbent service, before the arrival of new users, the market share of the new service may surge. New users may join, leading to a larger market share. This matches our intuition: when new users rush in before a new service takes off, they will tend to stay incumbent service due to the network externalities it creates. However, if the new service acquires sufficient market share before the bulk of the new user demand materialize, then we expect that new users will tend to give more of their time to the provider of the new service. 6. Conclusion This paper proposes a mixed usage utility model of online services to provide insights into online service adoption patterns. The online service market’s distinctive characteristic is that it is possible for users to adopt multiple services in identical service categories simultaneously without incurring a high cost. The utility model in this paper captures this feature of the online service market along with other salient features of the market such as network externality and service complementarity. Later, the model was extended to incorporate preference heterogeneity, quality uncertainty and cumulative externality effects. Utilizing Arthur’s adoption function approach [2], equilibria under various scenarios were explored and analyzed. The quality of service is the main determinant of the overall speed of the adoption of a service. Conversely, a strong network externality prevents a new service from being adopted whereas a moderate network externality may help the new service to take off provided that the service quality is high. When two services are highly complementary, it is likely that the equilibrium outcome will be that competitors have similar market shares. There are two noticeable market characteristics resulting from the mixed usage model. First, the advantage of the first mover is a given. With a strong network externality, there may be two stable equilibria, and the market will settle with the one in which the entrant receives a lower market share. In this situation, there is a critical mass for the entrant in terms of the market usage rate. Once the entrant achieves critical mass, it may be able to take over the entire market. This will result in a move toward a stable market equilibrium. In this regard, the gap between the initial stable equilibrium and the critical mass can be thought of as the first-mover’s advantage. A relatively small first-mover’s advantage can be overcome in the presence of certain market conditions. When consumer preferences are heterogeneous, the existence of users who prefer the new service may help in creating the basis for a new critical mass to emerge. In addition, uncertain service quality as seen from the consumers’ side may also be sufficient to affect the strength of the first-mover’s advantage. Second, a two-step punctuated equilibrium may exist. Under specific conditions, the speed of adoption could become very slow, and this may delay the onset of the eventual equilibrium. In this case, the new service exhibits an adoption pattern in which its adoption speed is initially fast, followed by a period of little change in the adoption rate, followed by an eventual jump to the equilibrium.

13

With an extension of the utility model with cumulative network externality, another adoption pattern characterized by a one-step punctuated equilibrium can arise in a market with a preference heterogeneity or quality uncertainty. In the presence of cumulative externalities and either heterogeneous consumer tastes or service quality uncertainty perceived by users, a new service can obtain occasional users who, in turn, contribute to enhancing the service quality. In the presence of a quality ceiling and a long enough time horizon, the new service may achieve critical mass, so that punctuated equilibrium arises. We also learned that product and service quality in an immature market is more influential than the network externalities that are present in the marketplace in determining the utility of users. We explored adoption behavior in a growing market, and our results show that market shares move over time, since the externality effect increases as the market matures. This can result in a different equilibrium, even with the same set of underlying simulation parameters that describe market competition. The mixed usage model can be applied to most online services that offer free services and that show complementarity with their competitors. However, if users have to pay for services or buy items from the online services, this model has almost no application. For example, online shopping malls such as Amazon or eBay would be evaluated by their product prices as well as service quality and network externality. If an online service involves any sort of payment, price should be taken into account. Therefore, this model cannot be applied to those services. This paper has introduced a mixed usage model of a service in the presence of externalities and complementarities. This is pertinent to the dynamically evolving characteristics of the online service market. The incorporation of the adoption function approach and the use of the punctuated equilibrium concept in this paper have enabled the observation and characterization of complex service adoption dynamics in this market. Also, an analysis of the model provides several strategic pieces of advice for the online industry. This paper contributes to the previous IS literatures by suggesting a new perspective on the usage of online services and by constructing a solid framework for analysis, providing various practical strategies that can be employed by online companies. In contrast, this paper also contains some limitations that could be improved upon in later work. First, certain assumptions underlying the utility model may be considered restrictive, such as the one in which the complementarities between the two services are maximized when they are used equally. This particular assumption can be relaxed by using w(b) in the simulation. Also, the proposed model is not fully developed in the immature market. Although we observed the adoption behaviors in a growing market in Section 4.5, the assumption is too restrictive and the analytical model is not fully developed to accommodate the growing market. The model requires further development particularly in this area. Further studies will provide more insightful results with greater implications. Appendix A. Complementarity function w(b) is used in the model setup because the degree of complementarity varies according to the proportion of time devoted to each service. There would be a proportion of usage time that maximizes the complementary effect that is not necessarily 1:1. Hence, if we assume that the complementarity is maximized when b = bc, w(bc) = 1 which is the maximum value of w(b) yielding the maximum bundling effect. If the user’s usage rate is different from b = bc, the complementarity and the bundling effect are not maximized, and the value of w(b) is between 0 and 1. When b = 0 or

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W. Hwang, J. Oh / Electronic Commerce Research and Applications 8 (2009) 3–15

Appendix B. Proofs of Proposition 1 and Corollary 1

1

Psi Function (ψ (β) )

0.8

Proofs of Proposition 1.

m =5

(1) Adoption condition In order for the new online service to be adopted, ffi   rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  

m =1

0.6

bi

0.4

m = 0.1

0 0.2

0.4

¼

Dðfi Þ þ 2U Ai

4Dðfi Þ

2

þ c ln2 2 Dðfi Þ2

>0

has to be satisfied. When Dðfi Þ ¼ U Bi  U Ai > 0, this condition is equivalent to sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðDðfi Þ  2U Ai Þ þ ðDðfi Þ þ 2U Ai Þ2 þ Dðfi Þ2 > 0 c ln 2

0.2

0

Dðfi Þ  2U Ai þ

0.6

0.8

1

which is in turn, satisfied if and only if U Ai ð1  4c ln 2Þ < U Bi . On the other hand, when Dðfi Þ ¼ U Bi  U Ai < 0, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðDðfi Þ  2U Ai Þ þ ðDðfi Þ þ 2U Ai Þ2 þ Dðfi Þ2 < 0 c ln 2

Usage rate of B ( β ) 1

m = 0.1

Delta Function ( δ (β) )

0.8

needs to be satisfied which, in turn, is satisfied if and only if UB U Ai ð1  4c ln 2Þ < U Bi . In both cases, UAi > 1  4c ln 2 is the rei quired condition. h (2) Dominance condition In order for the new online service to dominate the entire market,   qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dðfi Þ  2U Ai þ ðDðfi Þ þ 2U Ai Þ2 þ c ln2 2 Dðfi Þ2  >1 bi ¼ 4Dðfi Þ

m =1 0.6

m=5

0.4

0.2

0 0

0.2

0.4

0.6

0.8

1

Usage rate of B ( β ) Fig. 18. w(b) and d(b) functions.

When Dðfi Þ ¼ U Bi  U Ai > 0, it is equivalent to sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ðDðfi Þ  2U Ai Þ þ ðDðfi Þ þ 2U Ai Þ2 þ Dðfi Þ2 > 4Dðfi Þ c ln 2 which translatesB into U Bi ð1  4c ln 2Þ > U Ai . Therefore, when U 1  4cln2 > 0, U Ai > 14c1 ln 2 is the required condition. If i

1, usage is exclusively of either A or B and the complementary effect has to be zero. Therefore, w(0) = w(1) = 0. Thus, the w(b) function captures the complementarity effect according to each usage rate. Satisfying the above characteristics and using d(b) to vary the complementarity-maximizing usage rate bc from 0 to 1, we can define w(b) as follows: wðbÞ ¼ 4  dðbÞ  ð1  dðbÞÞ ( ðmþ1Þb when bc < 12 mþb where dðbÞ ¼ mb when bc > 12 mþ1b Fig. 18 shows the case of bc < 1/2. In the first graph, when m increases, the peak of w(b) moves closer to bc = 1/2, and as m decreases, the peak moves away from bc = 1/2 to the left side where bc < 1/2. The second graph of d(b) helps in understanding how the first graph works. When bc > 1/2, the converse is true. Therefore, as m increases the complementarity is highest when both services are used in similar proportions of time, and as m decreases the complementarity is highest when either of the services is used more than the other. Without loss of generality, it is assumed that bc = 1/2 in this paper, meaning that the extent of complementarity is the largest when the two services are used equally. In this case, m = 1 and d(b) = b, which simplifies the w(b) function to w(b) = 4b(1  b).

1  4cln2 < 0, the inequality does not hold. On the other hand, when Dðfi Þ ¼ U Bi  U Ai < 0, the above dominance condition of bi > 1 leads to a contradiction since U Bi 1 > 14c ln 2 implies U Bi > U Ai . Hence when D(fi) < 0, the UA i

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