What distinguishes “economics from complexity”? W. Brian Arthur offers a short readable overview in “The Foundations of the Economics of Complexity” (Nature Physical Notice 3: 136-145, 2021).

This is a personal essay rather than a review of the literature. For example, Arthur explains how the modern research agenda for the economics of complexity emerged from the work of the Santa Fe Institute in the late 1980s.

How is the economy of complexity different from the ordinary economy?

The economy of complexity sees the economy – or the parts of it that interest us – as not necessarily being in equilibrium, its decision-makers (or agents) as not surrational, the problems they face as not necessarily well-defined and the economy not as a machine but as an ecology in constant evolution of beliefs, organizing principles and behaviors.

How does a researcher economize with this in mind? A common approach is to describe, in mathematical terms, a number of decision-making agents in a certain context. Officers start with a set of rules for how they will perceive the situation and how they will make decisions. The rules that a given agent uses may change over time: the agent may learn from experience, or may decide to copy another agent, or the decision-making rule may undergo a random change. The researcher can then examine the path of decision-making and the outcomes that emerge from that process – a path that will sometimes turn into a relatively stable outcome, but sometimes not. Arthur writes:

The complexity, the global subject, as I see it, is not a science, it is rather a movement within science … It studies how the interacting elements in a system create global models, and how these patterns, in turn, cause elements to change or adapt in response. Elements can be cells in a cellular automaton, or cars in circulation, or biological cells in an immune system, and they can respond to states of neighboring cells, or adjacent cars, or concentrations of B and T cells. Whatever the case, the complexity asks how the individual elements react to the current pattern they mutually create, and what patterns, in turn, result from it.

As Arthur points out, an increasingly digitized world is likely to offer a number of demonstrations of complexity theory at work.

Today, with rapid digitization, the character of the economy is changing again and parts of it are becoming self-sufficient or self-sufficient. Financial trading systems, logistics systems and online services are already largely autonomous: they may have overall human supervision, but their instant actions are automatic, without a central controller. Likewise, the power grid becomes autonomous (the load in one region can self-adjust automatically in response to the load in neighboring regions); air traffic control systems become autonomous and independent of human control; and future driverless traffic systems, in which driverless traffic flows respond to other driverless traffic flows, are likely to be self-sustaining. … In addition to being autonomous, they self-organize, self-configure, self-heal and self-correct, so they show a form of artificial intelligence. These stand-alone systems can be thought of as miniature, highly interconnected and highly interactive economies in which agents are pieces of software “in conversation with” and constantly reacting to the actions of other pieces of software.

In other words, if we are to understand when these types of systems are likely to perform well and how they can derail or be manipulated, complexity analysis is likely to offer useful tools.

But what about the use of complexity theory for economics in particular? As Arthur writes: “A new theoretical framework in a science does not really work unless it explains phenomena that the accepted framework cannot. Can the economics of complexity make this claim?

For example, there has long been a question as to why stock markets see short-term patterns of boom and bust. Another headache of the stock markets is why there are so many stock transactions. Of course, stock traders will disagree on the underlying value of stocks and the significance of recent news affecting perceptions of future value. Such disagreements will lead to a modest stock trading volume, but it is difficult to see how they lead to the extremely high trading volumes seen in modern markets. John Cochrane made this point well in a recent interview with Tyler Cowen:

Why is there this immense volume of transactions? When was the last time you bought or sold a stock? You don’t do this every 20 milliseconds, do you? I will highlight this. If I get my list of the 10 Great Unsolved Puzzles that I hope our grandchildren have solved, why does getting the asset price information require the action to be flipped a hundred times? This is clearly what is happening. There is this large amount of transactions, which are based on information or opinions and so on. I hate to think of it as human madness, but it’s clearly what’s happening, but we don’t have a good role model.

Here’s Arthur’s description of how the economics of complexity examines these stock market puzzles:

We set up an “artificial” stock market inside the computer, and our “investors” were clever little programs that could differ from each other. Rather than sharing a self-fulfilling forecasting method, they were to somehow learn or discover forecasts that work. We allowed our investors to randomly generate their own individual forecasting methods, try promising methods, reject methods that didn’t work, and periodically generate new methods to replace them. They made offers or offers for a stock based on their currently most accurate methods and the stock price forms based on them – ultimately, based on the collective forecast of our investors. We have included an adjustable exploration rate parameter to govern how often our artificial investors might explore new methods.

When we did this computer experiment, we found two regimes, or phases. At low rates of investors trying new forecasts, market behavior has collapsed into the standard neoclassical equilibrium (in which forecasts converge to those that produce price changes that, on average, validate those forecasts). Investors became alike, and trade faded. In this case, the neoclassical result holds, with a cloud of random variation around it. But if our investors try new forecasting methods at a faster, more realistic pace, the system goes through a phase transition. The market develops a rich psychology of different beliefs that change and do not converge over time; a healthy volume of trade emerges; small price bubbles and temporary crashes appear; technical trading is emerging; and random periods of

volatile exchanges and a quiescence emerge. The phenomena that we see in real markets are emerging. …

I want to emphasize something here: Phenomena such as random volatility, technical trading or bubbles and crashes are not “exits from rationality”. Outside of equilibrium, “rational” behavior is not well defined. These phenomena are the result of the discovery by economic agents of a behavior that works temporarily in situations caused by other agents who discover a behavior that works temporarily. It is neither rational nor irrational, it just makes itself felt.

Other studies find similar regime transitions from equilibrium to complex behavior in non-equilibrium models. One could object that the emerging phenomena that we find are small: the price results in our artificial market only deviate from the standard equilibrium results by 2 or 3%. But – and this is important – the interesting things in real markets happen not with equilibrium behavior but with deviations from equilibrium. In real markets, after all, this is where the money is made.

In other words, the key to understanding stock market dynamics may lie in the idea that investors are continually exploring new ways of investing, which in turn results in high trading volumes and, in some cases, dysfunctional results. Of course, Arthur offers a variety of other examples as well.

For those who would like more information on the economics of complexity, a place to start would be the footnotes to Arthur’s article. Another starting point is trying to J. Barkley Rosser, “On the Intricacies of Complex Economic Dynamics,” in the Fall 1999 issue of JJournal of Economic Outlook (13: 4, 169-192). The summary reads as follows:

Endogenously complex nonlinear economic dynamics do not converge at a point, limit cycle or explosion. Their study developed from previous studies of cybernetic, catastrophic and chaotic systems. Complexity analysis emphasizes the interactions between dispersed agents without a global controller, entangled hierarchies, adaptive learning, evolution and novelty, and out-of-equilibrium dynamics. Complexity methods include interacting particle systems, self-organized criticality, and evolutionary game theory, to simulate artificial stock markets and other phenomena. Theoretically, bounded rationality replaces rational expectations. The theory of complexity influences empirical methods and restructures political debates.

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