www.elsevier.nl / locate / econbase
Forecasting the success of telecommunication services in the presence of network effects
Detlef Schoder*
University of Freiburg i.Br., Institute for Informatics and Society (IIG), Department of Telematics, Friedrichstr. 50, 79098 Freiburg i.Br., Germany
Abstract
Historical examples (ISDN, Teletex, telefax, telex) show us that forecasting efforts in the telecommunication sector can go awry – not only by a few percentage points but by large magnitudes. We maintain that with strong network effects it is not possible to forecast the success of telecommunication services with a high degree of confidence. This paper reviews the role played by network effects for the adoption of telecommunication services, which lead to diffusion phenomena including critical mass, lock-in, path dependency, and inefficiency. To improve forecasting practices, we propose the master equation approach as an appropriate modelling technique incorporating network effects. A case is made for
‘‘thinking in probability distributions’’ rather than deriving misleading linear extrapolations of trend patterns. At base, the paper argues why these phenomena require a shift, away from a static, to a dynamic analysis; the paper also identifies a formal method suitable for the dynamic analysis. 2000 Elsevier Science B.V. All rights reserved.
Keywords: Telecommunication services; Forecasting; Diffusion; Network effects JEL Classification: C0; D7; L86
1. Introduction
Forecasts concerning the success of telecommunication services and technology, in general, are difficult to make. Historical examples (ISDN, Teletex, telefax, telex) show us that forecasting efforts in the telecommunication sector can go awry – not only by a few percentage points but by large magnitudes (Werle, 1994). As
* Tel.:149-761-203-4928 or -4964; fax:149-761-203-4929.
E-mail address: schoder@iig.uni-freiburg.de (D. Schoder)
0167-6245 / 00 / $ – see front matter 2000 Elsevier Science B.V. All rights reserved.
P I I : S 0 1 6 7 - 6 2 4 5 ( 0 0 ) 0 0 0 0 6 - 8
pointed out in the literature, network effects can significantly influence adoption and hence the diffusion of goods and services (Katz and Shapiro, 1985; Church and Gandal, 1993; Witt, 1997). This paper investigates the role and implications of network effects. After defining direct and indirect network effects we sketch their interrelationship with the usage of telecommunication services (Section 2).
Building on a large body of literature we briefly review and formally sketch the underlying feedback processes of the adoption dynamics that characterize new telecommunication service (Section 3.1). With this, we explain the resulting patterns of diffusion including critical mass, path dependency, lock-in, and inefficiency (Section 3.2). This review leads to the conclusion that the open, non-linear and stochastic diffusion process requires modelling techniques which can successfully incorporate network effects, to sketch the various patterns of diffusion. Accordingly, we propose the master equation approach and show qualitatively its application (Section 4). As a contribution to the field we conclude that ‘‘thinking in probability distributions’’ should replace the more typical linear extrapolation of trends or function forms, which has repeatedly led to considerable test errors in forecasting the diffusion of telecommunication services (Section 5).
Accordingly, prediction of the likely success of any telecommunication service should be expressed in scenarios and associated diffusion paths, rather than per cent of market share at a given point in time. Generally, we conclude that a dynamic analysis is essential.
2. Network effects and telecommunication services
The literature discusses several historical innovations whose diffusion processes were strongly dependent on network effects or increasing returns to adoption.
Amongst these are programming languages, operating systems, and telecommuni- cation services (David, 1985, 1987; Arthur, 1989; David and Greenstein, 1990). In order to better understand network effects it is helpful to distinguish between direct and indirect network effects.
Direct network effects are caused by demand side user externalities. Positive direct network effects result in an immediate utility gain for the participants, with an increasing number of users operating the same (compatible) system commodity.
A classical example is the telephone system, a more recent one is electronic mail (‘‘e-mail’’). Direct network effects occur only with use; purchasing the relevant good is not sufficient. A significant factor in the occurrence of direct network effects is the definition of standards as well as the deployment of gateways (Farrell and Saloner, 1992), which provide compatibility at a cost. The term gateway represents here a proxy for numerous compatibility creating mechanisms, such as converters and adapters (see David and Bunn, 1988, for the related term ‘‘gateway technologies’’). Direct network effects arise from a technical network (e.g. a communications network).
Indirect network effects are caused by supply side user externalities. Positive indirect network effects occur from the realization of returns to scale (i.e. falling unit costs in mass production, learning by doing, learning by using) which are passed on to users in the form of price cuts or quality increases (Woeckener, 1992a). Further ‘‘sources’’ of indirect network effects are complementary goods and services which are arranged by suppliers, and which allow a functionally, temporally and spatially diversified supply of software and hardware components.
This relationship may be described in terms of a ‘‘hardware / software-paradigm’’
(Katz and Shapiro, 1994). Examples are the development of service networks e.g.
resourcing spare parts and repair services (the existence of a complementary technical infrastructure). Indirect network effects work through a virtual network (generally arranged through the market).
An increasing variety of telecommunication services have appeared in recent decades, such as electronic data interchange (EDI), video conferences, videotex, electronic mail, electronic funds transfer (EFT), on-line-database services and Internet or World-Wide Web-based applications. Depending on the predominant usage type of a telecommunication service, the impact of direct or indirect network effects may vary between negligible to decisive, for adoption and diffusion. For example, while using home-banking services, at best indirect network effects are at work. The extent to which others use the service is largely unimportant for the adoption decision, i.e. there are no direct network effects. Using telecommunica- tion services for interactive communications with others, i.e. sending and receiving messages, entails direct network effects. Examples include Internet-based chat services, online-auctions, or online-multi-player games. In these cases, the more the participants who respond through a given network, the more utility they gain and the more effective is the service.
3. A brief review: Network effects, adoption dynamics and patterns of diffusion
The following paragraphs briefly review parts of the large body of literature concerned with network effects. We start with a micro-level analysis, i.e. the adoption process in Section 3.1. Moving to a macro-level perspective in Section 3.2, we can explain the resulting patterns of diffusion. This review is motivated to understand the strong implications of network effects for adoption and diffusion and thus for the modelling of these phenomena.
3.1. Networks effects and adoption dynamics
In observing adoption dynamics it should be considered that, with network effects, the adoption decision of early demand depends on the expected behaviour
of potential, later users. This horizontal feedback, in the sense of the mutual influence of (potential) adopters, for instance through reciprocal observation, can be aptly described as ‘‘everybody watching [the group] while being watched’’
(Allen, 1988, p. 20).
Apart from this horizontal feedback at the micro-level, vertical feedback processes between micro and macro-level constitute the other influence. The analysis of the dynamics of feedback processes are often related in the literature to concepts such as vicious cycle, increasing returns, non-convexity, critical mass effect, cumulative causation, catastrophies, bifurcation, etc. Fig. 1 presents these relationships.
A particularly interesting form of (vertical) feedback processes in this context is the frequency dependency effect (Arthur et al., 1987; Witt, 1988, 1994): If individuals take their bearings in purchasing decisions from other members of a population who have already made their decision, then the marginal change in the relative frequency of behaviour within the population will depend itself on the macroscopic variables of the relative frequency itself (and thus not on microscopic variables at individual level, which have already eventuated). In simple terms this means that the choice of a certain attitude by individuals in a population depends
Fig. 1. Horizontal feedbacks (within the micro-level) and vertical feedbacks (between micro-level and macro-level).
on how frequently this behaviour in the population has already been pursued. Thus a form of interdependence between individual behaviour and macroscopic vari- ables arises.1
The following diagrams, using a simplified example with network effects, elucidate this relationship between individual and macrosocopic, which determines the diffusion pattern of innovation. In the simplified case, two alternatives are available, and the choice of one alternative excludes the other. The potential adopters make their decisions successively. The presentation closely follows Witt (1994, pp. 507–508).
F (t) describes the relative frequency of behaviour 1 in the population at time t1 and f (t) the probability that the individual making a decision in t will decide for1 alternative 1. The frequency dependency effect can be assumed according to the following relationship between these functions:
f (t)1 5c(F (t))1 (1)
Two fundamentally differing specifications of the function c will be considered.
In the first case (Fig. 2) the probability of choosing behaviour 1 falls as its frequency (its prior choice) increases. An example of this case is imitative behaviour which becomes less attractive as the number of imitators increases.
* Within the observed population behaviour 1 spreads in time until point F1 is reached. The relative frequency there is exactly the probability that behaviour 1
Fig. 2. Equilibrium with decreasing attractiveness of an alternative.
1One of the first economists to draw attention to this phenomenon, although he did not name it as such, was apparently Veblen, 1899 (cf. Witt, 1991).
*
will be chosen in time t. F1 is thus a (stable) equilibrium point (the 458line marks the equilibrium points).
A fundamentally different result obtains if the probability of choosing alter- native 1 increases nonlinearly with F (t). This can be assumed in the case of1 competing telecommunication services, where the utility of the services increases the more a service has already been chosen by its adopters. Starting in Fig. 3 from
0 0
the point f(0)5F150.5, then to the right of F1 the probability f (t) increases1 beyond the respective value of F (t), so that the process moves towards a stable1
*
point F *51 1 as soon as a tendency has developed in this direction. The same applies to the reverse case, when a tendency develops in the ‘‘other’’ direction. In
*
this direction F150 is the point where the system becomes stable.
The point denoted with F01 in Fig. 3 is unstable. It can be interpreted as the critical mass point. Deviations from this point can drive this initially open
* *
development permanently to one of the stable points F1 or F *. This develop-1 ment path is characterised by the term lock-in. Due to the formation of multiple equilibria the specific diffusion or market-share development is open at the beginning and can only be forecast in the sense of the possible paths.
Increasing and decreasing returns to adoption
The frequency dependency effect as sketched here can occur in two basic forms:
• Decreasing returns to adoption: the more widespread an alternative already is, or is used, the lower its utility will be. For example, connecting a further subscriber to a heavily frequented computer network results in a utility decrease for all the remaining subscribers because the increased burden on the network causes the computer network performance to sink further.
Fig. 3. Equilibria with increasing attractiveness of an alternative.
• Increasing returns to adoption: the more widespread an alternative, the more attractive it will be. Increasing returns to adoption are an important explanation for the creation and the existence of standards.
Increasing and decreasing returns to adoption mean a departure from a more static and strict cause-and-effect analysis. The effect (output) of a cause (input) becomes reflexively itself an input again, for a reinforcing effect, and thus can only be adequately characterized with a dynamic viewpoint and analysis.
Eq. (1), in the interpretation so far, expresses the frequency dependency effect without considering time. A dynamic analysis of the frequency dependency effect is instructive. Every adopter’s decision causes a marginal change in the relative frequency of alternative 1. On average this change amounts to the difference between f (t) and F (t). The marginal change in the relative frequency of1 1 alternative 1 is obtained by the differential equation with f(0)50:
]dtdF (t)1 5f( f (t)1 2F (t))1 (2)
The following results correspond to Figs. 2 and 3:
Figs. 4 and 5 can be presented as potential functions (cf. Figs. 6 and 7). The use of potential functions has the advantage that the developmental dynamics of a2
Fig. 4. Differential of the relative frequency with decreasing attractiveness of an alternative.
2In general the dynamic behaviour of a variable, e.g. x(t) can be described with the help of a potential which can be derived from the following relationship:
≠V(x) ]dx5 2]]
dt ≠x
Integrating with respect to x we obtain the potential V(x) (with an additive constant). Cf. Haken (1990) and Weidlich and Haag (1983).
Fig. 5. Differential of the relative frequency with increasing attractiveness of an alternative.
Fig. 6. Potential of the relative frequency with decreasing attractiveness of an alternative (schematic illustration).
Fig. 7. Potential of the relative frequency with increasing attractiveness of an alternative (schematic illustration).
variable (in this case, relative frequency of the choice of behaviour 1) can be visually deduced from the form of the curves. One can visualise a ball laid on a section of the potential function. The form of the potential function then resembles a hilly landscape. The ball will roll to the nearest low point. If the ball remains at a point, without being moved further by external forces and no small disturbances drive it permanently from this position, then it has reached a stable point. In every other case the position reached is unstable. The slope provides information on the
‘‘rolling speed’’, in other words the speed with which the time dependent variable changes (‘‘the steeper, the faster’’).
While one can observe a certainty in accordance with natural laws in the system dynamics of physical or chemical systems (Haken and Wunderlin, 1991), this only applies with restrictions in social systems. In social systems one can imagine
¨
‘‘counter-measures’’ – e.g. market introduction strategies (Schoder and Hellbruck, 1994) – which can reverse an emerging development.
3.2. Network effects and patterns of diffusion
The vertical and horizontal feedback processes have a considerable, and possibly determining, influence on adoption and thus diffusion. Empirical studies on electronic data interchange (EDI) serve as an example. In this case network effects are a large explanatory factor in the observed diffusion (Bouchard, 1993;
Banerjee and Golhar, 1994; Mackay and Rosier, 1994).
The literature is concerned with several elements in the diffusion pattern which is empirically observed for telecommunication services. The phenomena described can be interpreted as a consequence of the horizontal and vertical feedback processes, i.e. they are the result of diffusion via the frequency dependency effect.
Several of the elements in these diffusion patterns can be more precisely explained by reference to the relationships illustrated in the above diagrams.
Critical mass, path dependency, lock-in, and inefficiency
• The critical mass or the critical mass point can be interpreted as the turning point between positive and negative returns to adoption (Markus, 1990). The field around the unstable critical mass point is ‘‘critical’’ in the sense that smaller fluctuations can have a large effect upon the continued development of diffusion. Only a deviation from this value can bring about the transition from an unstable to a stable diffusion phase. As long as the critical mass point is not exceeded, demand synergies can only develop to a limited extent.
• The concept of path dependency is used to describe competing paths of development under the influence of network effects. Examples are to be found
in the field of technical standardising (keyboard definition, interfaces in computers), in institutional regulations (driving on the right- or the left-hand side of the road) and in spatial economic topographies (the pooling of similar, specialised firms spatially near to one another, for example the pooling of computer firms in ‘‘Silicon Valley’’ in California). In all these situations there were several development paths available at the outset. The history of the frequency shares, which is partially the result of small events and historical coincidence, is seen to be decisive for the ultimate success of the different alternatives each competing for choice (David, 1988, 1991).
• The phenomenon lock-in is closely linked to path dependency. If an (unstable) critical phase – this is the phase in which no persistent trend in favour of an alternative has been established – has initially been overcome, then the alternative under consideration will be ‘‘locked-in’’ on a stable successful or unsuccessful path, from which departure is not really possible even with large fluctuations (Arthur, 1989). If a successful path, the large number of adopters, over time, effect sufficiently large utility for further, later adopters. Competing innovations are no longer able to build up a sufficiently large installed base, in order to be attractive enough to their potential adopters. From the viewpoint of each utility maximizing individual adopter, it is rational to remain with the relatively successfully diffused innovation. The continuing diffusion form is predetermined. Switching costs may even enforce lock-in (Klemperer, 1987;
Farrell and Shapiro, 1988).
• Inefficiency: Related to a lock-in, one can ask if an established technology is
‘‘optimal’’. Would an innovation that appeared later be more advantageous, or would an unsuccessful alternative have been ‘‘better’’? Examples in the literature attempt to provide evidence that the market does not automatically select the ‘‘best’’ alternative over time (Foray, 1997).3
Although an innovation may be superior to alternatives, fluctuations in critical phases, e.g. in the early market introduction phase, can cause an innovation which is superior to fall behind. The competing product, which establishes itself, is not necessarily Pareto optimal (David, 1985; Arthur, 1987). Producers and consumers alike commit themselves relatively quickly to a few, manageable technical solutions. The market does not have resources to test every conceivable solution (David, 1985). Lock-in may lead to an inefficient market solution.
Fig. 8 depicts some resulting patterns of diffusion when network effects are present.
3Cf. the discussion concerning the advantages of the QWERTY keyboard against Dvorak (David, 1985). For a contrary opinion see Liebowitz and Margolis (1990) and in particular Liebowitz and Margolis (1994). A less controversial example is the operating system MSDOS, which in its first years was not accredited with technical superiority and whose success was probably attributable to favorable licensing terms agreed by IBM (Besen and Farrell, 1994).
Fig. 8. Idealized successful and flop-like diffusion with network effects, compared to the typical S-shaped diffusion pattern. Adopted from Wilhams et al., (1988).
4. Modelling network effects and the diffusion process of telecommunication services
In summary it can be established that non-linear feedback, both horizontal and vertical in nature, can lead to special phenomena in diffusion. Models which aim to explain the diffusion of services where network effects are present must be able to capture these dynamics. The so-called master equation approach can provide this type of model.
The first applications of the master equation approach were aimed at explaining the macro behaviour of physical, chemical and biological systems composed of a large number of elements, which at the microscopic level were subject to identical interaction patterns (e.g., in thermodynamics, molecular- and population-biology, etc.). In recent years the number of sociological and economic models based on the master equation has continued to increase (cf. survey in de Greene, 1989; Schoder, 1995). Applications in the context of marketing examine the stimulation of diffusion of electronic data interchange, the explanation and forecasting of failures and the analysis of the effects of alternative market creation strategies while
¨
introducing goods with network externalities (Schoder and Hellbruck, 1994;
¨
Hellbruck and Schoder, 1994).
The mathematical formalization of the master equation approach can be best introduced while proceeding from the microlevel of individuals with their attitudes to the macrolevel of collective variables and their dynamics (the following presentation follows Weidlich (1990), see for a comprehensive introduction and
more detailed treatment of this approach Weidlich and Haag (1983), Haken (1990), Weidlich (1991), or Weidlich and Braun (1992)). Starting from the microlevel, a given population (e.g. consumers) consisting of N members can be constructed with N (a 5a 1, 2, . . . , P) homogeneous sub-populations.
O
P Na5N (3)a 51
A homogeneous subpopulation N is defined by the verifiable assumption that itsa
members exhibit the same probabilistic decision behaviour. An aspect space Q may comprise A aspects for which the N members of a subpopulation can have aa
certain attitude i, i[h1, . . . , Aj, expressed formally:
A
O
nai 5N ,a (4) i51where n denotes the number of individuals of a subpopulationai a with the same attitude i. The dynamics on the microlevel of a population is generated, if individuals decide to change their attitude within a given aspect space. Such decisions can be described in probabilistic manner using individual probability transition rates. Given a utility maximizing rationale amongst the individuals, it is
a a
assumed that there exists a measure ui and uj of the subjective ‘‘utility’’ to a member of a subpopulation of the ‘‘old’’ attitude j and the ‘‘new’’ attitude i respectively, in order to specify the individual probability transition rates between attitudes, thus
a a a a
p (n;ij ©k)5f(u (n ;i ij©k), u (n;j ©k)) (5) where ©k denotes a vector of exogenous influence, often called trend or order parameters.
On the macrolevel the microvariables and microdynamics create the sociocon- figuration which can be described in a compact form:
1 1 a P P
n5(n ; . . . ;n ; . . . ;n ; . . . n ; . . . )i A i i A (6) The socioconfiguration characterizes the distribution of attitudes within the total population in a given moment. If one individual of a subpopulation changes its attitude from j to i it induces a change of the socioconfiguration from n to n :aij
a 1 a a P
n→nij5(n ; . . . ;(ni i 11); . . . ;(nj 21); . . . ;n )A (7) Since each of the naj members of a subpopulation with attitude j can make its transition to i statistically independently, the configurational probability transition rate is given by:
a a a
vij(n;©k)5n pj ij (8) Of interest now is how will P(n, t), the probability that the socioconfiguration n
exists at time t, change? The master equation can formally describe the change in time of probability of configuration n through a dynamic probability balance consideration:
d a a a a
]P(n, t)dt 5
O
vij(n ;ij ©k)P(n ; t)ij 2O
vji(n;©k)P(n, t) (9)j,i,a j,i,a
( j±i ) ( j±i )
The first term describes the probability flow per unit of time from all neighbouring configurations into the configuration n, and the second term subtracts the probability flow from n into all neighbouring configurations. The solution of the master equation not only yields the evolution of the most probable configurations but also the width and form of the probabilistic fluctuations around them.
Considering network effects, the corresponding formal expression of the interdependence of micro-level and macro-level can now be incorporated into the individual transition rates through macrovariables (e.g. market shares of the attitudes under consideration). Hence, the individual probability transition rates become a function of the macrostate. Thus, there exists a nonlinear, cyclic coupling between both levels: The individual decisions merge into the collective state and dynamics of the population and, vice versa, the latter leads to an adjustment of individual behaviour, so that micro-behaviour and macro-dynamics are coupled selfconsistently. The nonlinear dynamics now lead – depending on initial conditions and on exogenous control parameters – in general to a complex variety of self-organizing dynamic patterns within a given population.
This paper will focus on important ramifications of this modelling approach when forecasting the success of telecommunication services in the presence of network effects.
In the classical diffusion literature, adoption and diffusion are handled as separate aspects. Broadly speaking, adoption research attempts to explain diffusion processes at the individual leve. Diffusion research, in the stricter sense anyway, usually examines the linear aggregate of individual uptake decisions; processes which occur at the individual level are not commonly taken into account in diffusion work (Weidlich, 1991).
However, for goods with network externalities strong dependencies can be observed, not only at the micro-level, i.e. at the level of the (individual) adopter, but also between the micro-level and the macro-level. It is out of the question in this case to predict phenomena at the macro level using simple (linear) addition of adoption decisions at the micro-level (Schelling, 1978). On the contrary it is necessary to consider the interdependencies between the levels in addition to the factors determining diffusion at the individual levels.
It is precisely for this type of model that the master equation approach is very promising. The master equation assumes that the macro variables (e.g. market shares) have an influence on the adoption decisions of the members (consumers) of independent subpopulations (consumers groups). Conversely, the dynamic of macro variables is determined from the numbers of adoption decisions made by
consumers. The problem of aggregation can be elegantly solved by the master equation. This provides the dynamic equations for the macro-level variables based on the dynamic of the micro-level (Haag, 1990).
There are additional advantages to using the master equation approach for diffusion theory:
• It is well grounded in behavioural science (Erdmann, 1990),
• it allows simultaneous treatment of several innovations which compete with one another, and
• it permits model-based generation of a broad palette of empirically observed diffusion patterns for goods with network externalities, including flops (Schoder, 1995).
Figs. 9 and 10 show schematically qualitative changes in the probability distribution calculated with the master equation approach, for alternative parame- ters in time (Woeckener, 1992b). The underlying model represents one population whose members can choose among two attitudes (e.g. alternatives or innovations).
The socioconfiguration therefore reads:
n5(n , n )1 2 (10)
For the purpose of a compact illustration the two variables are transformed into one difference variable x which can be interpreted as market shares of the two attitudes under consideration.
Fig. 9. Development of the probability distribution without micro-macro-interdependences.
Fig. 10. Development of the probability distribution with micro-macro-interdependences (typical for network effects in presence).
n12n2
x5]] with21,x,1 (11)
2n
For x50.0 this means a uniform distribution of market shares, for x5 20.5 no market share (flop) for attitude 1 and 100% market share for attitude 2 and vice versa for x50.5.
In the first case (Fig. 9) the equation for the individual transition probability of using a given service is specified within the master equation so that there is no feedback between the macro state of the diffusion system and the micro behaviour which takes place. This case can also be approached with a single linear stochastic differential equation. The only solution provided is the most pobable one.
The case with interdependence between the macro- and micro-level is our interest; this is the case of goods with network externalities. In concrete terms this means that the individual transition probabilities are made to be dependent on the respective actual market shares.
Fig. 10 shows that, initially, development is open. With the continued effect of the strengthening feedback process, a lock-in becomes increasingly probable and an about-face, into the other half of the state area, becomes ever more unlikely.
Going through a critical phase (in Fig. 10 approximately between t5150 and t5350), the original unimodal probability distribution changes to bimodal. Two stable states are probable as the long-term solution in this scenario. However, the state which evolves cannot be predicted ex ante.
Applied to the diffusion of innovations, this ‘‘two possibilities’’ solution can be interpreted as a complete adoption or a complete non-adoption. An interim
solution of stagnation or a limit level of diffusion is not to be expected. This
‘‘dichotomy of diffusion outcomes’’ accords with the empirical penetration rates of videotex systems (Schneider, 1989).
´ ´
Videotex produced outcomes at the extremes. French Teletel, measured against the number of French households, has high penetration in both absolute and relative terms. State-backed subsidy played a key role in the start-up. In the eighties and early nineties all the remaining videotex systems in other countries have had a minute penetration level. This already clear ‘‘dichotomy of the diffusion outcome’’ would be even clearer if the deficit systems were not still subsidized by telecom companies and so would be completely out of the market.
The strength of the master equation approach is evident in its portrayal of the non-linear relationships between the micro- and the macro-level. This explains the ability to reproduce empirically observable diffusion phenomena in the presence of network externalities. The master equation approach accommodates the open- ended stochasticity of the processes. The stochastic formulation is more suited than are deterministic approaches when we take the complex nature of the adoption and diffusion process into account. Furthermore, the approach can handle several innovations which are competing with one another simultaneously. The study of such constellations is of enormous practical relevance, since it arises frequently.
Logistical approaches suffer a ‘‘pro-innovation bias’’ (cf. Rogers, 1983, p. 92) when they concentrate on observing the adopter’s behaviour alone. The master equation approach lessens this bias, when it takes into account adopter data covering all relevant competitive innovations. The approach thereby indirectly incorporates non-adopter influences.
Classical (deterministic) diffusion models, in particular those with a logistical construction, can be derived as a special class of models from the master equation, as long as the master equation models are only employed for the analysis of means (Weidlich and Haag, 1983). Conversely, a study oriented toward probability distribution, as with the master equation approach, offers an extension of the standard view of diffusion processes.
The application of the master equation approach also presents difficulties, however. One difficulty is the requirement to specify individual or group transitional probabilities. A further disadvantage is the type and quantity of data required, as well as demanding computational requirements.
5. Applying the approach
The non-linear interrelationships between the micro and macro-level play a significant role in the diffusion dynamics that arise from telecommunication services, notably via the frequency dependency effect. With such non-linearity, the
diffusion pattern at the macro-level is not amenable to a simple linear addition of adoption decisions at the micro-level. What are the ramifications, if we apply the master equation approach? How might the forecasting for new telecommunication services improve? Practical application tests the approach, and it may also yield unexpected insight.
• We need more concrete information about the relationship between penetration rates and individual adoption probabilities. Helpful questions would take the4
form, ‘‘Would you use the telecommunications service X, if Y% of your communication partners were already using it? ’’ Questions of this type need to be included in field studies for substantive analysis.
• A simulation tool to model the – open, non-linear and stochastic – diffusion of telecommunication services can be one product of the master equation approach. The simulation tool can help in assessing the likelihood of alternative diffusion scenarios: the probability distribution for possible development paths can be calculated. By changing parameters, alternative diffusion scenarios can be simulated. The locus and sensitivity of critical diffusion phases might be determined numerically. If the data are reliable, the ‘‘critical mass’’ can be calculated.
• Perhaps the most intriguing prospect: ‘‘Thinking in probability distributions’’
could replace the linear extrapolation of trends, which has repeatedly led to considerable error in forecasting the diffusion of telecommunication services.
As a result, potential development paths can be forecast, in contrast to the previous method of estimating the penetration level at a specific time.
Accordingly, prediction of the likely success of any telecommunication service should be expressed in scenarios and associated diffusion paths, rather than per cent of market share at a given point in time.
Acknowledgements
I am grateful for the helpful comments provided by Everett M. Rogers at the workshop ‘‘Diffusion and Innovation’’, 1994, Bonn, and at the ‘‘Scientific Symposium 1996’’ at Schloß Thurnau, Germany, and detailed comments by David Allen, also by two anonymous reviewers, on an earlier draft. Furthermore I am thankful for critical suggestions by Norman Archer and Mark Ginsburg at UC-Berkeley on a revised version.
4A complementary approach is Granovetter’s idea of threshold models of collective behaviour, cf. in particular Granovetter (1978) and Valente (1985).
References
Allen, D., 1988. New telecommunications services – network externalities and critical mass.
Telecommunications Policy 12 (3), 257–271.
Arthur, W.B., 1987. Competing technologies: an overview. In: Dosi, G., Freeman, C., Nelson, R., Silverberg, C., Soete, L. (Eds.), Technical Change and Economic Theory, London, pp. 590–607, Chapter 26.
Arthur, W.B., 1989. Competing technologies, increasing returns, and lock-in by historical small events.
The Economic Journal 99, 116–131.
Arthur, W.B., Ermoliev, Yu.M., Kaniovski, Yu.M., 1987. Path-dependent processes and the emergence of macro-structure. European Journal of Operational Research 10, 294–303.
Banerjee, S., Golhar, D.Y., 1994. Electronic data interchange: characteristics of users and nonusers.
Information and Management 26, 65–74.
Besen, S.M., Farrell, J., 1994. Choosing how to compete: strategies and tactics in standardization.
Journal of Economic Perspectives 8 (2), 117–131.
Bouchard, L., 1993. Decision criteria in the adoption of EDI. In: deGrow, J.J., Bostron, R.F., Robey, D.
(Eds.), Proceedings of the Fourteenth International Conference on Information Systems, Dec. 5–8, 1993, Orlando, Florida, pp. 365–376.
Church, J., Gandal, N., 1993. Complementary network externalities and technological adoption.
International Journal of Industrial Organization 11, 239–260.
David, P.A., 1985. Clio and the economics of QWERTY. In: Papers and Proceedings of the 97th Annual Meeting of the American Economic Association, Dallas, Texas, Dec. 28–30, 1984, American Economic Review, Vol. 75 (2), pp. 332–337.
David, P.A., 1987. Some new standards for the economics of standardization in the information age. In:
Dascupta, P., Stoneman, P. (Eds.), Economic Policy and Technological Performance, pp. 206–239.
David, P.A., 1988. Path-dependence: putting the past into the future of economics. Technical Report No. 533 of The Economics Series of The Institute For Mathematical Studies in The Social Science, Stanford University, California.
David, P.A., 1991. Path-Dependence and Predictability in Dynamic Systems with Local Network Externalities: A Paradigm for Historical Economics, Center for Economic Policy Research, Stanford University, California.
David, P.A., Bunn, J.A., 1988. The economics of gateway technologies and network evolution: lessons from electricity supply history. Information Economics and Policy 3, 165–202.
David, P.A., Greenstein, S., 1990. The economics of compatibility standards: an introduction to recent research. Economics of Innovation and New Technology 1, 3–41.
De Greene, K.B., 1989. Micro–macro interrelations and order parameter concept in the field theory of societal systems. Systems Research 6 (4), S277–S288.
¨ ¨ ¨ ¨
Erdmann, G., 1990. Evolutionare Okonomik als Theorie ungleichgewichtiger Phasenubergange. In:
¨ ¨
Witt, U. (Ed.), Studien zur Evolutorischen Okonomik I, Schriften des Vereins fur Socialpolitik, Bd.
195 / I, Berlin, pp. 135–162.
Farrell, J., Saloner, G., 1992. Converters, compatibility, and the control of interfaces. Journal of Industrial Economics 40 (1), 9–35.
Farrell, J., Shapiro, C., 1988. Dynamic competition with switching costs. RAND Journal of Economics 19 (1), 123–137.
Foray, D., 1997. The dynamic implications of increasing returns: Technological change and path dependent inefficiency. International Journal of Industrial Organization 15, 733–752.
Granovetter, M., 1978. Threshold models of collective behaviour. American Journal of Sociology 83, 1420–1443.
Haag, G., 1990. Die Beschreibung sozialwissenschaftlicher Systeme mit der Master Gleichung. In:
¨ ¨
Individuelles Verhalten und kollektive Phanomene, Okonomie und Gesellschaft, Bd. 8, Frankfurt a.M., u.a.O, pp. 128–179.
¨ ¨ ¨
Haken, H., 1990. Synergetik, Eine Einfuhrung, Nichtgleichgewichts-Phasenubergange und Selbstor- ganisation in Physik, Chemie und Biologie, Vol. 3, erw. Aufl, Berlin u.a.O.
Haken, H., Wunderlin, A., 1991. Die Selbststrukturierung der Materie, Synergetik in der unbelebten Welt, Braunschweig.
Hellbruck, R., Schoder, D., 1994. Explaining and forecasting flops. In: Business Research Yearbook:¨ Global Business Perspectives, Vol. 1, Lanham, University Press of America, pp. 594–598.
Katz, M.L., Shapiro, C., 1985. Network externalities, competition and compatibility. American Economic Review 75, 424–440.
Katz, M.L., Shapiro, C., 1994. Systems competition and network effects. Journal of Economic Perspectives 8 (2), 93–115.
Klemperer, P., 1987. Entry deterrence in markets with consumer switching costs. RAND Journal of Economics 18, 138–150.
Liebowitz, S.J., Margolis, S.E., 1990. The fable of the keys. Journal of Law and Economics 33, 1–25.
Liebowitz, S.J., Margolis, S.E., 1994. Network externalities: an uncommon tragedy. Journal of Economic Perspectives 8 (2), 133–150.
Markus, M.L., 1990. Critical mass contingencies for telecommunications consumers. In: Carnevale, M., Lucertini, M., Nicosia, S. (Eds.), Modelling the Innovation: Communications, Automation and Information Systems, IFIP.
Mackay, D., Rosier, M., 1994. Measuring organisational benefits of EDI diffusion in the Australian automotive industry. In: Proceedings of the International Conference on Information Technology (ICIT) 1994, August 9–12, 1994, Kuala Lumpur, Malaysia, pp. 415–433.
Rogers, E.M., 1983. Diffusion of Innovations, 3rd Edition, New York.
Schelling, T.C., 1978. Micromotives and Macrobehaviour, New York.
Schneider, V., 1989. Technikentwicklung zwischen Politik und Markt: Der Fall Bildschirmtext, Campus, Frankfurt a.M.
¨ ¨
Schoder, D., 1995. Diffusion von Telekommunikationsdiensten, Phanomenologie und Erklarung, Diss.
[PhD-Thesis in German], Univ. Freiburg.
¨
Schoder, D., Hellbruck, R., 1994. Telematic innovations – why do some fail and some not?
Conclusions for marketing. In: Proceedings of the International Conference on Information Technology (ICIT) 1994, August 9–12, 1994, Kuala Lumpur, Malaysia, pp. 399–414.
Valente, Th.W., 1985. Network Models of the Diffusion of Innovations, Cresskill, NJ.
Weidlich, W., 1990. Quantitative social science – the dynamics of social processes. In: Gladitz, J., Troitzsch, K. (Eds.), Computer Aided Sociological Research, Proceedings, Holzhau, GDR, Oct. 2nd to 6th, 1989, Akademie-Verlag, Berlin, Chapter 26.
Weidlich, W., 1991. Physics and social science – the approach of synergetics. Physics Reports (Review Section of Physics Letters) 204 (1), 1–163.
Weidlich, W., Braun, M., 1992. The master equation approach to nonlinear economics. Journal of Evolutionary Economics 2, 233–265.
Weidlich, W., Haag, G., 1983. Concepts and Models of a Quantitative Sociology, Berlin, Heidelberg, New York.
¨
Werle, R., 1994. Diese Angaben sind ohne Gewahr, Prognosen in der Telekommunikation. In: Kubicek,
¨
H., Muller, G., Raubold, E., Roßnagel, A. (Eds.), Jahrbuch Telekommunikation und Gesellschaft, Schwerpunkt Technikgestaltung, Band 2, 1994, Heidelberg, pp. 201–212.
¨
Witt, U., 1988. Eine individualistische Theorie der Entwicklung okonomiseher Institutionen. Jahrhuch
¨ ¨
fur Neue Politsche Okonomie 7, 72–93.
Witt, U., 1991. Reflections on the present state of evolutionary economic theory, in: Hodgson, G., Screpanti, E. (Eds.), Rethinking Economics: Markets, Technology, and Economic Evolution.
Aldershot, pp. 83–102.
Witt, U., 1994. Wirtschaft und Evolution, Einige neuere theoretische Entwicklungen, WiSt, 10, Oktober, pp. 503–512.
Witt, U., 1997. Lock-in vs. critical masses – industrial change under network externalities. Internation- al Journal of Industrial Organization 15, 753–773.
¨ ¨
Woeckener, B., 1992a, Innovationskonkurrenz bei Netzwerk-Externalitaten und beschrankter Infor- mation, paper presented at the Conference ‘‘Evolutorische Okonomik’’, Freiburg.¨
¨ ¨
Woeckener, B., 1992b. Zur Relevanz der Mastergleichung fur die Modellierung okonomiseher
¨ ¨
Prozesse. Jahrbuch fur Nationalokonomie und Statistik 210 (5-6), 412–426.
