Economic Network Dynamics

As networks come to play an ever more important role in our economies, the study of networks structure and dynamics will inevitably become a key part of economic theory and analysis

Economic network dynamics is the study of how economic systems change over time through the analysis of the changes in their structure of connections; in particular how the network comes to form, strengthen and disintegrate over time.1 Today in advanced economies, how to develop networks is of great interest to many, both in business management – as they try to develop new business models and products built upon connecting people and goods – and also very important for research economists and policy makers in order to try and understand how networks affect economic growth within post-industrial economies that are increasingly fueled by the networking of information and knowledge activities.2 Whereas much economic growth in the industrial age was driven by economies of scale that reduced the marginal cost of producing goods, in a network economy growth is driven more by the network effect. This is a very different model and it requires us to understand the dynamics of networks, that is, how they develop, which can be quite counter-intuitive.

Network Dynamics

The study of how networks form, grow and eventually disintegrate is a relatively new area of research, but it is, of course, critical to understanding how to foster the development of some types of networks and reduce the development of others. For example, researchers have studied innovation as a process of diffusion across a network.3 Research like this helps us to better understand how innovative clusters like Silicon Valley can be fostered in other locations, or inversely law enforcement agencies have studied the dynamics of terrorist networks in order to better understand how to disintegrate them. Thus, we are interested in both network growth and decay.
An important thing to note here is that most real-world networks are not random. During their formation, they were subjected to certain environmental and resource constraints that shaped their formation as they developed in a particular non-random fashion. Added to this, most economic networks are user-generated. They have been formed out of local nodes choosing to make connections. Thus, both the local rules under which agents are making these connections and the environmental constraints they are under are both defining factors in the network’s formation. If this is, for example, a trade network, we need to know what are the physical constraints and the socio-political constraints that are inhibiting the formation of the network, and inversely, what are the set of rules under which agents are choosing to make connections; this can be modeled in game theoretical terms.

Nonlinearity

The growth of a network may be nonlinear, meaning there will likely be sub-linear growth up to a certain tipping point, and then positive feedback will kick in to give us super-linear exponential growth. In this way, something like the Internet can lay relatively dormant for a long time and then take off rapidly. An important thing to recognize in the growth of a network is the fact that whereas the number of nodes in the network may grow in a linear fashion, as in one, two, three etc, the number of edges can grow in a super-linear fashion. With 1 node, we have 0 links. With 2 nodes, we can have 1 link. With 3, we can have 3 links. With 4 nodes, we can now have 6 links. With 5, there can be 10. With 6 nodes, we can have 15 possible links.4
Whereas the number of edges started off lower than the number of nodes, it will likely sooner or later catch up with it and then outgrow it rapidly. In this example, the number of edges caught up with the number of nodes very quickly because we were talking about the maximum possible number of links, but typically in reality not every node will be fully connected, and thus it may often take a lot longer for it to catch up. But once it does, we will start to move from a component-based regime to a relational regime and the connections will add significant value to the system. We will get a positive feedback loop and the system may then grow exponentially. This is called the network effect.5 For example, the network effect can be seen in stock markets and derivatives exchanges. Market liquidity is a major determinant of transaction cost in the sale or purchase of a security. As the number of buyers and sellers on an exchange increases, liquidity increases and transaction costs decrease.6 This then attracts a larger number of buyers and sellers to the exchange. Thus, we get a positive feedback loop that is behind the network effect. In the remainder of this article, we will go over each stage in this network development process to try and understand it a bit better.

Sub-Linear Growth

Web servers with cables

The development of the internet is an example of nonlinear growth within a network, as it stayed relatively dormant for decades before experiencing exponential change

In the initial phase of a network’s formation, due to the limited number of nodes and connections in the network, the value of joining that network may, in fact, be negative because of the opportunity cost. Joining this network may well exclude you from joining another more mature network that already has a lot of network value. For example, if you choose to adopt a Linux operating system, you will be limiting your capacity to interoperate with over one billion users of Windows. Thus, in terms of opportunity cost, you are actually having to pay to be part of this burgeoning Linux network, and the same would be true for a social network, digital currencies and many other types of networks that have not reached a critical mass. These early adopters are typically special interest users, what we might call “geeks” that particularly care about this service and are prepared to pay the opportunity cost.8
Thus, it is these early enthusiasts that really matter because with them the network may be able to reach the critical mass; without them, it may not. And reaching this critical mass beyond which the network effect will take hold is the key factor in the early formation of the network. A key parameter here is how much of the value of using this system is in the components vs. the connections. So if there is value inherent to the product without connecting it, such as would be the case for a washing machine, then early adoption is not very difficult. But other things are very much dependent upon their connections such as the telephone, where it will be very difficult to get the original users because there is no value in the system without the existence of others to connect to. The role of expectations is very important here, as if people don’t expect the network to grow they will not join and it will not reach the critical mass. If their expectations are positive then it may well reach this threshold.9

One thing to note here is that within the industrial model of economies of scale it is all about the mean, average user. Because people were not connected, there was no value in the network. There was only value in the individual. In order to scale, you had to focus on the mass of individuals, that is to say, the normal average person. The geeks and outliers were of no interest. We produced products, services, and advertisements for the average people in the middle. Everyone on the fringes just had to try and fit in. It was the dog that wagged the tail. When we switch from the industrial model of economies of scale with isolated consumers to the post-industrial model of the network effect with connected users, this changes, as it is now the geeks and outliers that matter. Because of the thresholds and feedback loops, they are the ones driving the process of change. Thus, in networked economic systems, the tail is wagging the dog. Behind this is the power law distribution which is common to all kinds of complex systems because of nonlinear feedback that is able to amplify some small phenomenon on the fringes and turn it into a macro mainstream phenomenon.10

Tipping Points

If enough nodes join the network, then we may reach the critical mass and get a tipping point. The tipping point is the critical point in the system’s development as it defines where positive feedback will gain traction leading to a rapid and irreversible state change.11 The term critical mass is said to have originated in the field of epidemiology; where the spreading of an infectious disease reaches a point beyond any local ability to control it from spreading more widely. The term is in many ways analogous to a phase transition. Marketers use the term to denote a threshold that, once reached, will result in additional sales.12 At the point of critical mass, the value obtained from the good or service is greater than or equal to the price paid for it. Beyond this, it becomes much more attractive for people to join as the value is continually going up as each new user joining creates a higher surplus value for the next prospective user. With this positive feedback loop, we can get the bandwagon effect where agents couple to the network without any intrinsic evaluation for, or knowledge of the actual phenomena, but simply join to gain the benefit of the network effect in the way that someone might adopt a certain ideology or fashion without knowledge of it, simply to be socially accepted.13

People waiting to cross street

Nonlinear change involves distinct tipping points.
The tipping point is the point before positive feedback takes hold to drive the network’s development forward rapidly as with every new member of the network it becomes more attractive for others to join

The bandwagon effect can lead to over capacity, as the increasing number of users generally cannot continue indefinitely. After a certain point, many networks become either congested or saturated, stopping future uptake. Congestion occurs due to overuse. As an example, we might think about the telephone network. While the number of users is below the congestion point, each additional user adds additional value to every other customer. However, at some point, the addition of an extra user exceeds the capacity of the existing system. After this point, each additional user decreases the value obtained by every other user. If this is the case, then the next critical point is where the value obtained goes back down to where it approximates the price paid. The network will cease to grow at this point, and the system must be enlarged to enable future growth.14 This is the case for centralized systems, but may not be the case for distributed networks. New peer-to-peer network models such as Bitcoin may always defy congestion. True peer-to-peer networks are designed to distribute out the network’s load amongst their users. This theoretically allows peer-to-peer networks to scale somewhat indefinitely, at least until market saturation.14

Negative Externalities

But there is also a flip side to the network effect and network development, which is crowding out and the lock-in effects. Due to the importance of interoperability within network economies, there is a strong attractor toward everything converging onto the same network, the same set of standards or protocols resulting in lock-in.15 Network effects are notorious for causing lock-in with the most-cited examples being Microsoft products and the QWERTY keyboard. Going back to our previous example where the network effect created liquidity in a market, it is also apparent in the difficulty that startup exchanges have in dislodging a dominant exchange. For example, the Chicago Board of Trade has retained overwhelming dominance of trading in US Treasury bond futures despite the startup of Eurex US trading of identical futures contracts. Mitigating these negative externalities mean maintaining an open vendor-neutral network within which new standards and protocols can be incorporated. The success of the Internet is in many ways in its openness, net neutrality and the fact that no one owns it.

Diffusion

The rules under which a network was created and developed will play a large role in how something will spread across it and ultimately how robust it is to failure. The first thing to note with respect to network diffusion and robustness is that connectivity can both add and reduce to the system’s robustness. It works both ways. Connectivity is important for integrating the system and it is this integration that gives the system its overall robustness, but connectivity is also a potential pathway for disaster spreading. For example, in a recent paper entitled Systemic Risk and Stability in Financial Networks16 one of their authors summarizes their findings as such: “We show that financial contagion exhibits a form of phase transition as interbank connections increase. As long as the magnitude and the number of negative shocks affecting financial institutions are sufficiently small, more ‘complete’ interbank claims enhance the stability of the system. However, beyond a certain point, such interconnections start to serve as a mechanism for propagation of shocks and lead to a more fragile financial system.”17
Failure propagation within these complex economic networks might be financial as in this example or it might be within a logistic and supply network. Either way, there are a few key parameters that will greatly affect this process of spreading. Firstly, how contagious is the phenomenon that is spreading? An important consideration here is whether this is being powered by some negative feedback loop as is typically the case within financial markets where loss of confidence begets more loss of confidence. Secondly, how resistant are the nodes in the network to this phenomenon? So for a financial institution facing a mass of defaults, this resistance might represent how much capital they are holding. Thirdly, we need to consider the topology to the network; is it centralized or decentralized? Centralized networks are more susceptible to certain kinds of attack. This is one of the great benefits of distributed ledger technology. It reduces the current cyber security vulnerability of having large amounts of financial data within centralized repositories. Lastly, we need to also take into account whether this failure is being spread strategically or at random, as different network topologies exhibit different vulnerability characteristics depending on how random the failure is.18
The study of network diffusion and robustness has become a hot topic of research since the previous financial crisis, as it has become clear that it was the network of connections between assets and liabilities on different balance sheets that caused the breakdown of the whole system and there is a strong correlation between deregulation of cross-border capital flows and financial instability. It has thus been recognized by many that trying to understand this opaque and dense set of connections is important to identify the system’s future robustness and failure tolerance.19 


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2017-07-23T19:01:06+00:00