Complexity economics is an alternative paradigm within economic science based upon complexity theory and nonlinear models. Within this theoretical framework the economy is modeled as an open system composed of heterogeneous agents with bounded rationality, which gives rise to networks of interactions that we call institutions, and macro level non-equilibrium state to the economy that is in constant change driven by internal dynamics.1
Complexity Theory studies open systems, that is to say, systems that are so embedded within their environment, interconnected and interdependent with other systems, that we can no longer define them by their boundary conditions and their static internal components.2 With linear systems theory we use the process of reasoning called analysis that starts by isolating the system from its environment so as to hold inputs and output to the system constant. This is what we do when we take things from their environment and put them in a lab. It is only by doing this that we can describe the system in terms of the additive properties of its internal constituent elements, creating equations based on invariant transformations between the properties of its constituent elements. Complexity theory does not use this method of analysis. Because this method of analysis is very fundamental to modern science, complexity theory results in a very different way of looking at systems. Because it does not use analysis it allow for the study a system as being open, that is in terms of its function and relations within its environment. This is a process of reasoning called synthesis and it is the opposite from analytical reasoning.3
Unlike standard economics where the economy is modeled as a closed system, complexity theory gives us a model to the economy as fundamentally an open system. Standard economic models will not describe how the system interacts with other systems external to it such as the social or ecological domains. It exists in isolation. If anything is going to be incorporated into the model it has to be represented as being inside the economy. With complexity economics, because we are using open system models, we can represent the economy as one component interacting with other components within its environment. From this perspective we will be able to identify the economy as taking in resources from other components as in social capital and ecological capital, processing these in order to generate outputs that represent both resources of a higher value and also resources of a lower value, what we might call entropy.4
Closed Form Solutions
When modeling the economy as an open system, there will typically be no single closed form solution. Isolated systems tend towards a single equilibrium. Open systems, in contrast because there is a constant input and output of energy and matter, they do not tend towards a single equilibrium. They may have multiple equilibria, which is characteristic of nonlinear systems, and it does not mean that they are random. They are certainly not, they are just governed by different dynamics. What this means is that the end result of our model will typically not be a closed form solution, that is to say an equation. Even if we do create an equation, these nonlinear equations typically have multiple solutions and they may exhibit chaos. In general, because we are dealing with open systems that are really defined not by any equilibrium or equation but instead by their inputs and outputs, these inputs and outputs are going to be defined by the system’s relations within its environment and its function.
These functions are most appropriately modeled as algorithms, that is to say a set of instructions that define how the component or system maps an input to an output. What is of interest here is trying to understand and capture the algorithm that the agents or institutions are operating under, which may then be used to create a high fidelity model through computer simulation. This simulation can then be run in order to get a simulation of the system’s behavior over time and from this we may get all the information we want to know about the system without ever needing an equation. The power behind this technique is one of the basic premises within complexity theory, that is, the idea that simple rules can create complex phenomena. We are defining simple rules and then using the computer to iterate on these simple rules to give us nonlinear interactions and feedback that will generate a model with a structure that is both complex and intricate – a high fidelity representation of real world economic phenomena.
Unlike standard economics where the interactions between agents have to be additive in order to get general equilibrium, meaning the relations add or subtract no value to the system and thus can be largely ignored. But in complexity economics we are not trying to get an equilibrium outcome, and thus these relations don’t have to be additive. Because this is a nonlinear framework, they can be non-zero sum, which means they may add or subtract value to the system and these non- additive relations will be important to the overall make up of the system.
Because these interactions are non-additive, they give rise to non- equilibrium macro scale patterns of organization that will have their own internal dynamics and structure, what are called emergent properties. This is going to give a heterogeneous macro scale topology to the system. Thus within this paradigm institutions are important, and this is in contrast to standard economies, where they are primarily seen as markets or clearing houses, they don’t really have any internal dynamic, they are seen essentially as equilibrium point.5
By not focusing on general equilibrium and the idea of individual atomized agents, and instead focusing more on these interactions, what we see is that these institutions are in fact networks, and the structure to these networks is very important because it largely defines how things flow through the network. Because we are dealing with open systems this is about input and output, where a component is in a network, the network’s structure and what is flowing through that network is going to be decisive in defining the inputs and outputs to any of its components or subsystems.
These internal emergent structures or institutions will add or subtract value to the whole system creating a macro level disequilibrium. Because the system is open and resources are coming in and out of it from a larger environment that it is a part of, the flow of resources in and out of the system will change over time. This will add to this state of non-equilibrium. When we allow for non-equilibrium on the macro level, we can start to think about how the whole system changes over time and complexity economics uses the model of evolution in order to describe this macro process of change.
Because we have an open model that is actually embedded within some real environment, we can begin to recognize the complexity to the real world. As the economist Axel Leijonhufvud once remarked, Neoclassical models give us a view of, quote “smart people in unbelievably simple situations, while the real world involves simple people [coping] with incredibly complex situations.” The implicit expectation of standard economic models is that agents are seen as almost supercomputers that are able to run an optimization algorithm over thousand or even millions of different choices within a fraction of a second. Complexity economics based on this idea of simple rules, instead ascribes individuals with only a very finite amount of computing power, what is called bounded rationality, the idea that when individuals make decisions, their rationality is limited by the information they have, the cognitive limitations of their minds, and the time available to make the decision.6
Behavioral economics gives us a much-expanded and more complex conception of motives that are driving the individuals as it studies the effects of psychological, social, cognitive, and emotional factors on the economic decisions of individuals. Agents are still seen to be efficiently pursuing their valued ends as part of our definition of economics, but these valued ends can represent a much wider spectrum not just purely industrial capital. Because we are not constraining our model of the individual towards achieving equilibrium, we can begin to think about the individual agent as being in a real environment embedded within a multiplicity of different networks, each exerting its own force over the agent’s behavior, and thus linear causality, where A causes B, begins to break down. The net result of bounded rationality and a complex set of motives means that agents may come to hugely non-optimal economic solutions.7
This leads to a discussion to what theory of value can this nonlinear modeling framework offer. Because we are looking at the economy within the context of its connections with other systems within its environment, we can begin to recognize the value of those other things that are not necessarily inside the economy. Using analytical methods, we can only ascribe value to anything that is inside of the system. Ecological capital is defined within the model as the mining or agricultural industries. It can’t have value outside or independent from the economic system.
By flipping this model around and seeing these other domains outside of the system and in relation to them, then we can begin to reason about their independent value and how this might translate into primary economic value. As long as we are using analytical methods focused on looking inside the system, we will only be able to ascribe value to anything that is inside the model. When we use synthetic reasoning to create models for the whole environment, we can then ascribe some value to all the different domains and begin to reason about how to create a metric for translating between domains, thus incorporating both extrinsic primary economic value and intrinsic secondary value. And this will be congruent with our model of agents as being under the influence of many different motives and value systems, as they respond to social capital, cultural capital, environment capital and so on. It is a much more complex model where we are trying to take account of value in all its different forms. Value is not homogeneous, a single price determined by market equilibrium. It is instead heterogeneous, a network of different interacting variables.
Complexity theory is very much focused on the non-zero sum(nonlinear) interactions between agents. Game theory models both zero sum games and non-zero sum games. Zero-sum games give linear solutions and are thus central to standard economics. Non-zero sum games result in nonlinear outcomes, and thus the nonlinear study of economics is mainly concerned with these non-zero sum dynamics. It allows us to incorporate relations of cooperation or interference into our model. Both will give us non-equilibrium results. Interference between components means some form of conflict between the agents that make the combined system less than the sum of its parts. As an example of this, we might think about price wars between different businesses.
Inversely, cooperation is a form of synergistic interaction between agents. Synergies involve the components both differentiating their functions and coordinating them towards the common end. Through synergies value is added to the composite organization. Through these relations, we get an organization that is greater than the sum of its parts. Synergies form the basis for the process of emergence that gives rise to different levels in the economy with diverse institutions serving diverse functions on these different levels.
In the complexity paradigm, macroeconomic patterns are emergent properties of micro-level interactions and behaviors. But because of the nonlinear interactions between components that we previously mentioned, we cannot analytically derive the properties of the macro system from those of its constituent parts. Although we can apply computational techniques to model the behavior of the emergent properties, that is to say, agent-based models can simulate these emergent phenomena in high fidelity. Agents within the complex economy are embedded within many overlapping networks, social, cultural, technological, financial etc. How an organization or individual succeeds or fails within this economy is a product of these different many interacting variables across different networks and the makeup of those networks.
From this perspective, there is no such thing really as efficient markets that allocate resources in an optimal fashion. This whole idea is only really relevant when we are thinking about agents in isolation, agents as price takers in a pure market, where they face an impersonal price structure and they are computing their rational choices. From the complexity perspective, people are interconnected they are embedded within networks of production and consumption. Resources flow through these networks, and how those resources get distributed out depends on the structure of the network and where you lay in the network. There doesn’t have to be any equilibrium here. The distribution of resources across the network can be hugely heterogeneous, and may remain in a non-equilibrium state indefinitely.8
Complexity economics sees the economy as a complex adaptive system that evolves over time. In standard economic theory, there is no mechanism for creating novelty or qualitative change within the economy. In the complex economy, the evolutionary process of diversification, selection, and amplification provides the system with novelty and is responsible for the growth in order and complexity over time. Eric Beinhocker in his book The Origin of Wealth describes this process as “an evolutionary search mechanism. Markets provide incentives for the deductive- tinkering process of differentiation. They then critically provide a fitness function and selection process that represents the broad needs of the population… Finally, they provide a means of shifting resources toward fit modules and away from unfit ones, thus amplifying the fit modules’ influence.”
Complexity economics focuses on the non-equilibrium processes that transform the economy from within, such as technological innovation and new business models created by entrepreneurs that lead to a process of creative destruction, within an economy that is constantly changing as it grows in a somewhat organic fashion. Changes in one part leads to new opportunities and niches within another as the whole thing co-evolves with different industries and sectors becoming interdependent and self-organizing. And out of this process of evolution, we get what we might call economic growth, not so much in our traditional sense of an increase in the gross throughput to the systems but more in terms of its qualitative structural transformation in becoming both more differentiated and integrated to exhibit greater complexity.9