Reconsideration of the winner-take-all hypothesis: complex networks and local bias.

1. Introduction

The literature on network effects has had considerable impact on managerial practices recently (Farrell and Klemperer 2001). It has indicated that, in a market that demonstrates network effects, a firm or technology that gets ahead tends to increase its market share, cornering the market over time (e.g., Arthur 1989, Shapiro and Varian 1999); a firm or technology that lags behind is likely to lose its market share. It may even be driven out eventually.

This extreme possibility has been called the "winner-take-all" hypothesis in the popular literature (Arthur 1996, Kelly 1998, Shapiro and Varian 1999). This literature suggests that the winner-take-all markets would be more common in the New Economy, where networks play an increasing role in shaping customer choices and technology competition. Practitioners interpreted the hypothesis and often took action in the form of implementing the "get-big-fast" strategy. In the midst of the late 1990s Internet bubble, dot-com companies rushed to build large installed bases ahead of the competition in emerging markets (Liebowitz 2002). Some Internet start-ups even gave away free PCs just to attract customers. Frequently, the size of an installed base was used for valuation of an Internet start-up.

However, the unconditional, winner-take-all hypothesis has baffled many practitioners, as incompatible technologies often persist (Shapiro and Varian 1999). In such a situation, the implementation of the get-big-fast strategy by all players could lead to a costly war with no clear benefit. Obviously the field could benefit from boundary conditions regarding when the hypothesis will work and when it will not. The objective of this paper is to take a step toward identifying these conditions.

Much of the prior work on network effects has emphasized an installed base (e.g., Katz and Shapiro 1985, 1992; Farrell and Saloner 1986; Arthur 1989). The typical assumption has been that customers value the general connectivity of an entire network. (1) That is, customer benefits of adopting a product depend on how many other customers in the market also use this product. This global network effects assumption may not be a bad approximation when compatible complements indirectly reinforce the benefits of a given product; these benefits are called indirect network effects (Katz and Shapiro 1985). In the markets for VCRs and CD players, for example, hardware products alone offer little value to customers. The benefits of using them come mainly from the availability of diverse complements such as prerecorded tapes or CDs. The diversity of complements is largely affected by the number of units sold for each hardware platform (Katz and Shapiro 1986, Langlois and Robertson 1992), because independent producers of complements prefer to develop more prerecorded tapes or CDs for a hardware platform with a larger installed base. In these sorts of markets, we do not doubt that control over an installed base is often crucial for waging a standards war (Farrell and Saloner 1986, Shapiro and Varian 1999).

However, we also believe that a customer's selection of a technology is sometimes influenced more by the opinions and choices of his or her acquaintances than by the size of an installed base. Exchanging files or advice with others is often a key source of benefits for complex hardware or software. Such benefits are called direct network effects (Katz and Shapiro 1985) and are realized through interactions among customers. In sharing experiences or files with others, a customer is more likely to contact his or her acquaintances (e.g., coworkers or friends) than the majority of unknown others in a network of all previous adopters. Usually, the customer maintains relationships with a small number of acquaintances. It is quite possible that some of these acquaintances will adopt a lagging technology even when a lead technology has built a large installed base. This situation is called local bias. Such a local bias may, over time, act as a brake on the winner-take-all process. A lead technology may then find the winner-take-all process limited, leaving room for smaller rivals to survive.

Consider an example of local bias. In the 1990s, MCI, a small long-distance carrier, initiated a marketing campaign called "Calling Circle" to foster local bias deliberately. If a customer built a friends-and-family network using MCI's service, he or she was promised a discount (or a customer benefit) for calls to any member of this local network. On the other hand, no discount was offered for calls between the customer and the majority of irrelevant others in the network as a whole. MCI's Calling Circle was very attractive to individuals who needed to communicate frequently over long distances with their significant others. By launching this campaign, MCI was able to expand its share of the long-distance service market dominated by AT & T (Strouse 2001). The upshot was that this local bias could sustain customer benefits within the bound of acquaintance networks.

This paper confirms such local bias effects by developing a model of diverse network topology. In the past, it was difficult to study these effects because of the lack of appropriate tools for analyzing complex social networks. Researchers had little choice but to ignore them. Recent advances in complexity theory, however, have provided us with a tool to examine the dynamics of complex social networks (e.g., Watts and Strogatz 1998). By developing network effect models with this tool, we show that incompatibilities persist under locally clustered networks, for example, a friends-and-family network. However, we also show that the winner-take-all markets are possible even when each consumer interacts with a small number of acquaintances. The different outcomes of market dynamics are explained by whether or not a network topology allows local bias to arise and persist in a social network.

This paper proceeds as follows. The second section reviews recent progress in complexity theory and introduces a tool for specifying diverse social networks. In the third section, we develop simulation models. The fourth section shows the results of our simulations. In the last section, key findings are highlighted, and their implications are discussed in light of the extant literature.

2. Networks of Interactions

This section briefly reviews the recent progress in complexity theory, which offers a tool for us to reinvestigate the winner-take-all hypothesis. As Strogatz (2001) noted, the current interest in networks could be considered part of a broader movement toward research on complex systems, where interactions among component parts make it difficult to understand the behaviors of whole systems. A network, in this view, is a blueprint for how those component parts interact. We present the related literature by dividing it into two categories: simple networks and complex networks. Then we briefly survey the burgeoning complexity research in the management area and discuss how our work is similar to and distinct from it.

2.1. Simple Networks

Until very recently, researchers could not work with the structure and dynamics of complex networks (Strogatz 2001). In the 1980s and 1990s, most mathematical models attempted to highlight the complexities arising from the dynamics of large interactive systems while …