 In this video we'll be introducing you to the basics of systems dynamics as we discuss causal link diagrams. We'll try to show how causal link diagrams can be used in the modelling of many microeconomic phenomena that involve the interaction between agents such as zero and positive sum games. The model of causal links and feedback loops is fundamental to understanding the dynamics of complex systems as they capture and describe the basic types of relations between components within nonlinear systems. Causal links and feedback loops are one of the best examples of the key premise within complexity theory. The idea that complex phenomena can in fact be the product of simple rules, but it cannot be the direct product of these simple rules. We can only get this complex emergent phenomena out of the nonlinear interactions between these simple rules as they are iterated upon over many cycles. Causal loop diagrams, CLD, is a causal diagram which aids in visualising how different variables in a system are interrelated. The diagram consists of a set of nodes and edges. Nodes represent the variables and edges are the links that represent a connection or a relation between the two variables. A link marked positive indicates a positive relation and a link marked negative indicates a negative relation. A positive causal link means the two nodes change in the same direction. That is to say, if the node in which the link starts decreases, the other node also decreases. Similarly, if the node in which the link starts increases, the other node increases as well. An example of this might be the relation between manufacturing output and electrical consumption within an economy. They will both move together, the more of one, the more of the other. A negative causal link means the two nodes change in the opposite direction. That is to say, if the node in which the link starts increases, the other node decreases and vice versa. An example of this might be the relationship between the amount of driving one does and the amount of fuel in your car. The more driving, the less fuel will remain. Negative links are additive. Thus, as we previously discussed, we can create an equation around them. Whatever we add or subtract from one side, we add or subtract from the other. Positive links, in contrast, are non-additive. When we add or subtract from one element, we also add or subtract from the other. Thus, they will not sum up to zero. And we cannot create a closed form equation around them. They will give us non-linear solutions. Positive links and positive feedback are behind almost all non-linear phenomena. They are very important to understanding the dynamics of non-linear systems. I will now illustrate how this basic formal language can be used to model economic phenomena such as those in game theory. Just to refresh our memory of what a zero sum game is, we'll borrow this definition from Wikipedia. In game theory and economic theory, a zero sum game is a mathematical representation of a situation in which each participant's gain, or loss, of utility is exactly balanced by the losses or gains of the utility of the other participants. If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero. Those negative links are linear, and sum up to zero, they define zero sum games. If we have a cake and divide it up between two people, the more one gets, the less the other will get. Zero sum games are also called strictly competitive, as competition is always the optimal strategy for an agent. Thus, a negative link defines a relationship of competition between two agents. What one agent gains, the other loses. Thus they are pitted against each other, and we get a dynamic of competition. Negative links are what we might call neutral. The interaction itself does not add or subtract from the whole. In these zero sum games, the whole pie is staying the same. What is changing is who gets what. The interaction defines who gets what. In contrast, positive links define non-zero sum games. A non-zero sum game is a situation in which the interacting parties aggregate gains and losses can be less than or more than zero. Thus it is non-linear. Through positive links, the whole pie that is being divided up between agents can grow or diminish. That is to say the interaction is not neutral, the interaction itself is adding or subtracting something from the whole pie, so we need to understand how that's happening. If the interaction between the two components adds value to the whole, this is called a synergy. If the interaction subtracts value from the whole, it is called interference. A synergy is a constructive interaction, meaning the output to the interaction will be more than the sum of its parts. There are many examples of synergies in our world. From the cooperation of cells and organs in the human body, to many different kinds of synergies produced by socially organized groups, or for example, all trade is thought to be positive sum, because if you are prepared to part with something, you must value what you are exchanging it for more, and if both value what they are getting more than what they give up, then some value has been added to the entire system through this interaction. The word synergy comes from the Greek word meaning working together. This working together involves the constituent components differentiating their activities with respect to each other, and also coordinating these activities towards a common end. One of the best examples of this is our global economy. Many millions, or even billions of people, performing different specialized functions, but these functions are then coordinated within firms and markets, so that we can get something like a laptop computer that no one person could create. It's only through this process of differentiation and then reintegration that value is added to the system. Synergistic relations are pervasive phenomena in our universe, as they form part of all complex organizations, and of course they are non-linear. The whole will be more than the sum of its parts, because value is being added by these synergistic interactions. These are just one type of positive link, where both components value will move in the same positive direction as the whole pie grows, but we can also get the inverse phenomena. They can both move in the negative direction, due to what is called interference. The classical example of this being the interference between two sound waves as they cancel each other out. Interference is the opposite from a synergy, that is to say the failure to differentiate and coordinate. For example, if a society doesn't provide proper education and training for its people, while they choose not to take it, there will be too few high skilled, specialized workers and too many people looking for undifferentiated, unskilled labor. Because of the failure to differentiate, there will be a failure to coordinate and we will get interference and crowding out. Because of this destructive relation of interference, the whole pie will get smaller and the variables associated with all the components in the relation will go down together. Negative links define closed systems. As such, they are representative of a dynamic surrounding a rival good. The more that one person uses of a rival good, the less that another one can. Value is excludable, thus we get a well bounded, well defined system. Marginal cost will approximate marginal benefit with a trade off between agents and an equilibrium out of which we can create the market mechanism of supply and demand. Because nothing is being added or subtracted from the entire system, negative links have no externalities. Non-rival goods are goods that have externalities. With non-rival goods, marginal cost or benefit approaches zero. The benefit to the additional consumer may be substantial, thus resulting in a non-zero interaction and positive externalities. Because positive links are non-zero sum, they have externalities, both positive externalities where through synergies the system becomes greater than its parts and thus adds value to its environment and inversely through interference it can subtract value from its environment what is called negative externalities. When a company achieves internal synergies between employees or departments, it will be able to deliver a better product that would be of more value to the economy and society which is a positive externality. With synergies and positive externalities, social value is higher than the private value. With interference, the system will be less than the sum of its parts and thus the input of resources to the system must be more than the output in order to maintain the system, meaning the system's environment is paying the cost for running the system. The social cost is higher than the private cost. Some of the cost is being externalized to the environment and negative externality, thus the system will overproduce because the marginal cost to the system will be less than the marginal benefit. A negative link is a description of the market mechanism where the benefits and costs of each agent in the relation are balanced against each other giving an equilibrium of supply and demand through which to regulate the quantity of goods and services produced and consumed and their allocation it's a self-regulating mechanism. The market mechanism breaks down when we have both positive or negative externalities because marginal cost and marginal benefit are out of equilibrium. The two are not moving in the opposite direction or there is a weak correlation between them. As for example might be the case with digital products where the marginal cost of producing one more copy is very small and the marginal benefit can be very large and thus the two are not directly correlated. This is even more extreme with the network effect where both the producer and consumer can be gaining value at only a very small marginal expense to one, meaning both variables are moving in the same direction, a positive link. Civil war is another example of a positive link. We have interference in the system as the two components are in conflict. The marginal cost of one of waging war is also a marginal cost to the other. Thus the two variables are moving in the same direction. There is no balance thus it cannot be regulated through the market mechanism. In this module we've been taking a quick look at the basics of causal link diagrams as applied to microeconomics. Causal link diagrams help us to formalize nonlinear phenomena in that they divide the world into linear additive interactions as described by negative feedback and nonlinear interactions as described by positive feedback that looks specifically at relations that add or subtract value from the entire system through synergies or interference between the agents. We've briefly touched upon how they can be used as a basic formal language for capturing many game theoretical microeconomic phenomena such as zero sum games, externalities and non-rival goods or market failures. It's in causal link diagrams that involve the interaction between many causal links that we can see how complexity may emerge from very simple local rules. We've only just touched upon the subject here but it should hopefully be suffice to illustrate how nonlinear models can give us a new perspective on these fundamental dynamics within microeconomics.