 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 on connecting people and goods, and also very important for research economists and policymakers 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. Whereas much economic growth in the industrial age was driven by economics of scale that reduce the marginal cost in producing goods. In a networked 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. 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. 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're interested in both network growth and decay. As we've previously noted, most real-world networks are not random. During their formation, they were subject 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've 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're under are both defining factors in the network's formation. So if this is for example a trade network, we need to know what are the physical constraints and the sociopolitical 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. So this can be modelled in game theoretical terms. The growth of a network may be non-linear, meaning there will likely be sub-linear growth up to a certain tipping point and then positive feedback will kick in to give a 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 recognise 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 1, 2, 3 etc. The number of edges can grow in a super-linear fashion. With one node, we can have zero links. With two nodes, we can have one link. With three, we can have three links. With four nodes, we can now have six links. With five, we can have ten. With six nodes, we can have fifteen possible links. So 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. For example, the network effect can be seen in stock markets and derivatives exchanges. Liquidity is a major determinant of transaction costs in the sale or purchase of securities. As the number of buyers and sellers on an exchange increases, liquidity increases and transaction costs decrease. This then attracts a large number of buyers and sellers to the exchange. Thus we get a positive feedback loop that is behind the network effect. So we'll go over each stage in this network development process to try and understand it a bit better. In the initial phase to the 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 lots of network value. For example, if you choose to adopt a Linux operating system, you will be limiting your capacity to inter-operate with over 1 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 currency and any other type of network that has not reached a critical mass. These early adopters are typically special interest users, or we might call geeks, that particularly care about this service and are prepared to pay the opportunity cost. Thus, it is these early enthusiasts that really matter, because with them your network may be able to reach the critical mass, without them you will 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 versus 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 would 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 critical mass. If their expectations are positive, then it may well reach this critical mass. One thing to note here is that within the industrial model of economics of scale, it's all about the mean average person. Because people weren't 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 of the distribution. 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 economics 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're the ones driving the process of change. Thus, in networked economic systems, it's the tail that wags the dog. Behind this is the power law distribution that we've met many times already, which is common to all kinds of complex systems, because of nonlinear feedback that is able to amplify some small phenomena on the fringes and turn it into a macro mainstream phenomena. 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 rapid and irreversible state change. 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. It 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. 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 continuously 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. The bandwagon effect can lead to overcapacity, as the increasing number of users generally can't 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 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. At 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 again. The network will cease to grow at this point, and the system must be enlarged to enable future growth. 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. But there's also a flip side to the network effect and network development, which is crowding out and lock-in effects. Due to the importance of interoperability within networked economies, there is a strong attractor towards everything converging onto the same network, the same set of standards or protocols resulting in lock-in. 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 liquid markets, 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 UX-US trading of identical futures contracts. Mitigating these negative externalities means 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. The rules under which a network was created and developed will play a large role in how something was 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 subtract 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 Networks, one of their authors summarized their findings as such, quote, 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. Failure propagation within these complex economic networks might be financial, as in this example, or it might be in 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 that's spreading? 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 cybersecurity vulnerabilities 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. We've only just begun to touch upon the subject of financial or economic network resilience, but we'll be talking about robustness in a future lecture, so we'll move on for now. We'll just note that the study of network diffusion and robustness has become a hot topic of research since the previous financial crisis, as it became 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's 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 identifying the system's future robustness and failure tolerance. In summary then, we've been talking about network dynamics that looks at how networks are formed and develop over their life cycle. We firstly noted that the formation of economic markets and institutions that are networked is very different in nature to our traditional industrial age model that is focused on economics of scale, the mass production of products that is focused on the average mean user in the market. In contrary, we talked about how connections can grow at an exponential rate, giving rise to a nonlinear pattern of development that requires a certain threshold to be overcome before the positive feedback loop of the network effect takes hold from where the system can grow very rapidly. We talked about how this can lead to negative externalities of crowding out and a lock-in effect due to convergence. Finally, we touched upon the subject of failure propagation and looked at some of the factors involved in analyzing a network's resilience.