On the identification of critical mass in Internet-based services subject to network effects

Abstract

In many Internet-based services, network effects have a significant impact on the evolution of the market. In particular, critical mass is a fundamental element due to its relevance to the growth process of these kinds of services. The objective of this paper is to set out some of the difficulties concerning the identification of critical mass. According to more conventional approaches, the critical mass is defined by the product's demand curve and its price. However, as shown in this paper, it is not possible to define a critical mass in such a simple way, since market structure and companies' entry strategy will substantially modify the mass adoption process starting point. Results also have an impact on determining the value of a network. Conclusions and directions for further research are also discussed.

Keywords:

• network effects
• critical mass
• utility function
• Internet-based services

Notes

As an example of the relevance of this topic, many research papers linked to network in services have been published recently (see, for example, Chang & Chen Wang, 2008; Zurbano, 2005).

At least until the emergence of congestion externalities, effects which appear as a result of using shared resources, and which cause each new user to provide negative utility due to the increase in the congestion of these resources. It is a very significant effect in the study of certain networks, and some authors (Gupta, Jukic, Stahl, & Whinston, 2000; Gupta, Stahl, & Whinston, 1999; Sohn, Joun, & Chang, 2002; Westland, 1992) have studied the need to introduce a proper pricing policy for the use of communication networks (e.g. Internet) to prevent precisely these problems.

Nevertheless, other authors prefer the term winner takes most (e.g. Amit & Zott, 2001; Economides, 2003). In fact, Varadarajan and Yadav (2002) consider more appropriate the term tippy markets, due to the term winner takes all inducing the idea that only one standard can survive, while in real markets coexistence is possible, although the market shares are typically very different.

For a detailed study of the competition between the VHS and Betamax standards see Cusumano et al. (1992).

The case of the QWERTY keyboard (invented by Christopher Sholes) versus the Dvorak (invented by August Dvorak) has caused some controversy in academic circles. This case is often held up as an example, especially after David's (1985, 1986) studies, of how an inferior technology (QWERTY) becomes standard against a superior technology (Dvorak) as a consequence of network externalities. Liebowitz and Margolis (1990), however, postulated that this was not in fact the case, since, among other reasons that the authors set out, in their opinion there existed no real evidence to support the superiority of the DVORAK keyboard, or at any rate the latter did not compensate the cost of changing. These same authors (Liebowitz & Margolis, 1995) subsequently harshly criticised most of the theoretical literature produced on this subject for continuing to use the case of the QWERTY keyboard as a paradigmatic example despite their article of 1990.

See, for example, Clements and Ohashi (2004), Zodrow (2003), Amit and Zott (2001), Goolsbee and Zittrain (1999), Keilbach and Posch (1998), Yoffie (1996) and Katz and Shapiro (1985). These authors analyse one or several of the network effects mentioned.

Complementary products play a critical role in network markets, as numerous academics have pointed out (see, for example, Church & Gandal, 1992; Gandal, 1994; Keilbach & Posch, 1998; Schilling, 1998, 2002; Yoffie, 1996).

For example, the empirical work of Goolsbee and Klenow (2002) on the spread of computers in the United States showed that a much greater probability existed of purchasing the first computer in cities with a large number of computer users, a fact they attributed to learning externalities.

The concept of critical mass appears in different areas of the social sciences and has been a subject of study for a large number of researchers.

Although this paper, together with that of Oren and Smith (1982), is widely considered as one of the first to characterise critical mass, there are previous papers such as Rohlfs's (1974), where this concept was also introduced.

Specifically that of Briscoe et al. (2006), which is one of the latest proposals, does not enable the emergence of congestion externalities, inasmuch as it is a logarithmic-type law. Moreover, as it does not include the network structure, the different degrees of influence and the problem of multiple uses, it is perhaps an over-simplified exposition of the problem.