Second, another reason to follow other nodes comes from network effects, which can be direct benefits or indirect benefits. As explained in Chap. 3, direct benefits occur when more people join a network, increasing the value of joining to subsequent users. If more people use the payment mechanism Venmo, then the direct benefit of participating increases since you have a wider network of people to access. Indirect benefits are due to the benefits of coordination. If all users are on the same system, then there will be more complementary products produced, increasing the total benefit of the system. An example of this is the operating system, iOS. When more people use the iPhone or iPad, the more apps there are, increasing the value of the device.
Diffusion of an idea or financial innovation in networks works along the same principle as network effects. The benefits of synchronization increase not only as more members of a network adapt to the new innovation, but as more of a given individual’s immediate neighbors adopt this new innovation. This idea is subtly different from network effects described above, where the fraction of the entire population that adopts a product is critical. Here, the threshold depends upon an individual node’s immediate neighbors. If more neighbors adopt an innovation or idea, then the likelihood of adoption increases.6 The switching threshold is reached when the fraction of trendy individuals exceeds the relative payoff from sticking to the old model.7
One can formulate examples, say a new mobile payment platform, where the sweeping diffusion of an innovation, called a complete cascade, depends upon the identity of the initial adopters and the network structure. A cascade will fail to sweep the entire network if there are dense clusters of individuals outside the set of early adopters. More strongly, we can say that a complete cascade will fail to take hold if and only if the the relative payoff from the new product is smaller than the fraction of non-adopting clusters [ 14].
Tightly knit communities, or clusters, can impede a cascade. Innovations from outside this tight community will find it difficult to find a way into this community. In Fig. 1.1(d), the local bridge G-A, linking networks with high clustering coefficients, may be a powerful way of conveying new information, but it also impedes cascades or diffusion of a risky new product. A bridge between networks only connects single nodes so its existence is not a compelling argument for switching products. Since the risk of adoption is mitigated if a high threshold of neighbors also adopts this innovation, risky new products and ideas are less likely to be transferred across local bridges.
An important example of impediments to the diffusion of ideas is the failure of collective action. Collective action is not simply a consequence of coordination problems, which requires access to localized and dispersed information. It also requires common knowledge, which is a higher order of information access. It is the assurance that all participants in the network have access to the very same body of information. For example, if a coordinated response is necessary to abandon a particular financial innovation or fire a CEO, then a critical minimum (threshold) number of neighbors or colleagues need to be in mutual agreement as to the action and the desired outcome. This action relies on the firm and secure knowledge that not only are other members acquiescent with the plan, but others know that they know and so on. Importantly, each individual is going to use immediate neighbors’ threshold as a signal for the participation of the entire network. And here is where the tricky part comes in. Suppose all residents of a village are located on a straight road so each resident has two neighbors. Also suppose that there is a plan to fire the village headman but that each resident will participate only if three other residents participate. If villagers know only the views of their immediate neighbors but not that of other members of the village, the idea may never get off the ground. This can happen even when most members of the village would otherwise have accepted the idea. The problem is one of common knowledge, not just coordination.