Complexity science is the study of complex systems. The difference between complex and complicated is usually misunderstood. Complexity is when a system has a reflexivity component, whereby feedback loops affect the behavior of the system—leading to unpredictable behavior. Complicated systems are structures that have many inter–links or intra–links, whereby it is hard to discern the actual mechanics of the system. I do not attribute reflexivity to a complicated system and self–organizing behavior is not present in this type of structure. A complex system does have self–organizing behavior. A complicated system can be called a cybernetic system.
There are three main behaviors of complex systems that I would like to explain: (a) agents have simple rules, (b) self–organization, and (c) interactions that can have magnifying effects. Agents can be described with simple rules but exhibit a vast array of behavior.When agents have the ability to interact with other agents and their surrounding environment emergence is exhibited. An example of a simple set of rules for an agent, in a financial paradigm, is the following:
Agents are traders in a financial market
Agents have a starting set of income
Agents can be influenced by surrounding agents trading behavior
Agents can lose all their income
Agents have a changing degree of risk taking
With the above agent rules complex market interactions can result that are quite unpredictable. The example is not an exhaustive rule set, just a mere example of the simplicity in agent’s rules.
Within the behavior of agents expressed with their respective rule set is the emergence of self–organization. Fractal patterns can emerge from complexity, whereby self-similarity is present. Within fractal designs there is a feedback loop that can magnify the pattern. We can see this magnifying effect in financial markets through herd effects. These herd effects can be negative or positive for asset prices, but eventually the energy in the system fades and a mean reversion usually results in these financial complex systems. Within behavioral finance this reflexive property is the main reason that financial markets are nonlinear and are impossible to fully predict with a high degree of accuracy—unlike Newtonian laws of motion.
Another property of reflexivity is the self fulfilling behavior of financial markets. If another agents move in the same direction then, no matter what the true value of the asset is, the market will move in speculative equilibrium. We will now transition to some more discussion of agents.