Complexity economics sees the economy as not necessarily in equilibrium, its decision makers (or agents) as not super-rational, the problems they face as not being well-defined. The economy becomes something not given and existing but constantly forming from a developing set of actions, strategies and beliefs. For past 150 years, economic theory has viewed economy as an evolving complex system, and out of this exploration has come complexity economics.

Complexity economics is not a science, rather it is a movement within science. It studies how elements interacting in a system create overall patterns. These patterns, in turn, cause the elements to change or adapt in response. The economics I will describe here drops the assumptions of equilibrium and rationality.

Equilibrium assumes that the aggregate outcome is consistent with agent behaviour. It gives no incentive for agents to change their actions. Over the past 120 years, economists such as Thorstein Veblen, Joseph Schumpeter and Friedrich Hayek have objected to the equilibrium framework. All have thought a different economics was needed.

Companies in a novel market may have different technologies, different motivations and different resources. They may not know who their competitors will be or, indeed, how they will think. As a result, the decision problem faced by agents is not logically defined. It follows that rational behaviour is not well-defined.

Agents could be implemented as small, individual computer programs that could differ, explore and learn to get smart. In economic problems, agents could start with their own arbitrarily chosen beliefs, learn which ones worked and explore new ones occasionally, dropping ones that did not perform well and replacing them with new ones to try out. They could, in this way, operate and explore in an ill-defined setting and become more intelligent as they gained experience.

In the El Farol problem, agents' forecasting methods vie to be valid in a situation that is dependent on other agents' forecasts. Behavioural economics gives insights into how real human agents respond. Agents act in a way like species, continually competing or mutually adapting and co-evolving.

In a classic study57, a computerized tournament was constructed in which strategies compete in randomly chosen pairs to play a repeated prisoner's dilemma game. Simple strategies such as tit-for-tat dominate but, over time, more sophisticated ones show up that exploit them. Evolution enters in a natural way that arises from strategies mutually competing for survival and mutating as they go.

The standard, neoclassical theory of financial markets assumes identical investors adopt identical forecasting models. In a new model, 'investors' generate their own individual forecasting methods, try out promising ones, discard those that don't work, and periodically generate new methods to replace them. At low rates of investors trying out new forecasts, the market behaviour collapsed into the standard neoclassicals.

Phenomena we see in real markets are not 'departures from rationality' They are the result of economic agents discovering behaviour that works temporarily in situations caused by other agents. In real markets, after all, that is where the money is made. A word on agent-based computational economics: it studies how solutions or structures form. Agent-based computational economics could be a key method within the framework of complexity economics, says David Frum. Frum