PERSPECTIVES I will give a personal account of how this economics was arrived at, based on my Foundations of complexity economics own experiences. I will also not attempt to survey the hundreds of studies now in the W. Brian Arthur field. Rather, I will discuss how complexity economics came to be, what logic it is based Abstract | Conventional, neoclassical economics assumes perfectly rational agents on, what its major themes are and how it (firms, consumers, investors) who face well-defined problems and arrive at optimal links with complexity and physics. I will behaviour consistent with — in equilibrium with — the overall outcome caused by talk about ideas rather than technicalities, this behaviour. This rational, equilibrium system produces an elegant economics, and build from earlier essays of myself and 12–21 but is restrictive and often unrealistic. Complexity economics relaxes these others to illustrate the key points, noting that this approach has variants22,23 and assumptions. It assumes that agents differ, that they have imperfect information forerunners24,25, and it owes much to earlier about other agents and must, therefore, try to make sense of the situation they work by Thorsten Veblen1, Herbert Simon2 face. Agents explore, react and constantly change their actions and strategies in and Friedrich Hayek26. response to the outcome they mutually create. The resulting outcome may not be in equilibrium and may display patterns and emergent phenomena not visible to The logic of the approach equilibrium analysis. The economy becomes something not given and existing but Standard economics and fundamental uncertainty. Standard economics, called constantly forming from a developing set of actions, strategies and beliefs — neoclassical economics, studies how something not mechanistic, static, timeless and perfect but organic, always outcomes form in the economy from agents’ creating itself, alive and full of messy vitality. behaviour, and, to do so, it chooses to make several standard assumptions: For the past 150 years, economic theory Smith, economists noted that aggregate • Perfect rationality. It assumes agents each has viewed agents in the economy (firms, outcomes in the economy, such as patterns solve a well- defined problem using perfectly consumers, investors) as perfectly rational of trade, market prices and quantities of rational logic to optimize their behaviour. decision makers facing well-defined goods produced and consumed, form • Representative agents. It assumes, problems and arriving at optimal behavior from individual behaviour, and individual typically, that agents are the same as consistent with — in equilibrium with — behaviour, in turn, reacts to these aggregate each other — they are ‘representative’ — the outcome caused by this behaviour. This outcomes. There is a recursive loop. and fall into one or a small number view has brought much insight. But many It is this recursive loop that makes the (or distribution) of representative types. economists1–7 have pointed out that it is economy a complex system. Complexity, • Common knowledge. It assumes all based partly on assumptions chosen for the overall subject8–11, as I see it is not agents have exact knowledge of these mathematical convenience and, over the a science, rather it is a movement within agent types, that other agents are years, have raised doubts about whether it science, and it has roots in thinking developed perfectly rational and that they too is universally applicable. Since the 1990s, in the 1970s in Brussels, Ann Arbor and share this common knowledge. economists have instead begun exploring Stuttgart. It studies how elements interacting • Equilibrium. It assumes that the the economy as an evolving complex system, in a system create overall patterns, and how aggregate outcome is consistent with and out of this exploration has come a these patterns, in turn, cause the elements to agent behaviour — it gives no incentive different approach — complexity economics. change or adapt in response. The elements for agents to change their actions. Complexity economics sees the might be cells in a cellular automaton, or cars These assumptions are by no means economy — or the parts of it that interest in traffic, or biological cells in an immune perfectly rigid but they constitute an us — as not necessarily in equilibrium, its system, and they may react to neighbouring accepted norm. They are made not because decision makers (or agents) as not super- cells’ states, or adjacent cars, or concentrations theorists necessarily believe they are true, rational, the problems they face as not of B and T cells. Whichever the case, but because they greatly simplify analysis. necessarily well-defined and the economy complexity asks how individual elements The equilibrium assumption in particular not as a perfectly humming machine but react to the current pattern they mutually is basic to neoclassical theorizing. General as an ever-changing ecology of beliefs, create, and what patterns, in turn, result. equilibrium theory asks what prices and organizing principles and behaviours. The economics I will describe here quantities of goods consumed and produced The approach, which has now spread drops the assumptions of equilibrium and would be consistent with (in equilibrium throughout the economics profession, rationality. But it did not come from an with) the overall pattern of prices and got its start largely at the Santa Fe Institute attempt to discard standard assumptions, quantities in the economy’s markets — that (SFI) in the late 1980s. But the basic ideas of rather it came from a pathway of thinking is, would pose no incentives for those overall complexity economics have an even longer about how the economy actually works. patterns to change. Classical game theory history in economics. Even before Adam So instead of giving a formal description, asks what strategies or moves of one player 136 | February 2021 | volume 3 www.nature.com/natrevphys PERSPECTIVES 100 on their ideas of what others’ predictions 90 will be, which depend, in turn, on their 80 ideas of others’ predictions, and there is an 70 infinite regress. Further, if a shared rational 60 forecasting model did exist, it would quickly 50 negate itself: if it predicted few will attend, all would go; if it predicted many will 40 attend, nobody would go. Agents, therefore, 30 Numbers attending face fundamental uncertainty: they do not 20 know how other agents will decide on their 10 forecasts, and, yet, such knowledge determines 0 attendance. The problem is ill-defined. 0 20 40 60 80 100 One can model this situation by assuming Time (weeks) agents act inductively: each creates their own Fig. 1 | Attendance at the El Farol bar in the first 100 weeks. Agents attend if they believe the total set of plausible hypotheses or predictors, attendance that week will be no more than 60. Each creates their own set of plausible hypotheses or and, every week, acts on their currently predictors of attendance, and, every week, acts on their currently most accurate one. Figure reprinted most accurate predictor. In other words, a with permission from REF.12, AAAS. framework for studying the economy should involve agents that form individual beliefs would be consistent with the strategies or first research programme8,36–38. I was asked or hypotheses — internal models (possibly moves their rivals might choose — that is, to lead this programme, and, after many several simultaneously) — about how to would be the best course of action for that discussions, we realized that we kept coming respond to the situation they are in. player. Rational expectations economics back to the same question: what would Such agents could be implemented as asks what forecasting methods would economics look like if we went beyond the small, individual computer programs that be consistent with the outcomes these standard assumptions? could differ, explore and learn to get smart. forecasting methods brought about — For one thing, agents differ39. Companies How they could do this — how they could that is, would statistically, on average, in a novel market may have different get smart — was inspired by the work of be validated by outcomes. technologies, different motivations and computer scientist John Holland, who Overall, this equilibrium approach has different resources, and they may not know had spent much of his career developing worked quite well. It is a natural way to who their competitors will be or, indeed, methods by which computer algorithms examine questions in the economy and how they will think. They are subject to what could learn to play checkers/draughts or open these up to mathematical analysis, economists call fundamental uncertainty40. chess. Holland’s algorithms could ‘recognize’ and it illuminates a wide range of issues As John Maynard Keynes described this in the current state of the game and learn to in economics. I admire its elegance; it has 1937, “the prospect of a European war… the associate appropriate moves with it. The yielded, in Paul Samuelson’s words27, an rate of interest twenty years hence…. About moves would be fairly random to start with “austere aesthetic grace.” But it severely these matters there is no scientific basis on and not very useful, but, over many games, limits what can be seen. By its definition, which to form any calculable probability the program would learn which moves equilibrium makes no allowance for whatever. We simply do not know.”41 worked in which situations, ‘explore’ new the creation of new products or new As a result, the decision problem faced moves and drop ones that did not work — arrangements, for the formation of by agents is not logically defined and, so, it would get smarter. In economic problems, new institutions, for exploring new strategies, it cannot have a logical solution. It follows agents could start with their own arbitrarily for events triggering novel events, indeed, for that rational behaviour is not well-defined. chosen or random beliefs, learn which ones history itself.