A pioneering approach

Arthur pushed the boundaries of complexity science to uncharted territory. Arthur not only coined the term ‘complexity economics’ (Arthur, Reference Arthur1999b),Footnote ³ but he also significantly advanced research in the field (Axtell, Reference Axtell2007; Farmer, Reference Farmer2012; Kirman, Reference Kirman1989: 126).Footnote ⁴ This is not to say that all complexity economics is inherently Arthurian, given that, as we shall see, researchers have been working on the idea of complexity in economics for centuries. However, Arthur stands out as the main pillar of today's approach to complexity economics.

Arthur defines complexity ‘not [as] a science, [but] rather [as] movement within science’(Arthur, Reference Arthur2021) that ‘studies how elements interacting in a system create overall patterns, and how these patterns, in turn, cause the elements to change or adapt in response’ (Arthur et al., Reference Arthur, Beinhocker and Stanger2020: 124). The fact that simple interactions between agents affect their environment (and, in turn, those same agents) informs much of Arthur's work.

Applied to economics, complexity relaxes the neoclassical assumption that agents are all equal, have perfect knowledge of other agents, and collectively arrive at optimal behaviour consistent, or in equilibrium with, the overall outcome caused by that behaviour (Arthur, Reference Arthur2018a). Neoclassical economists usually agree that these assumptions do not represent the ‘real world’, but maintain them to make economic theory workable.Footnote ⁵ Complexity economists instead turn ‘to the question of how actions, strategies, or expectations might react in general to (might endogenously change with) the aggregate patterns these create’ (Arthur, Reference Arthur1999b). Economic agents ‘experiment, explore, adjust, readjust’ (Arthur et al., Reference Arthur, Beinhocker and Stanger2020). Their behaviours are unrestricted; they evolve over time and self-reinforce.

Arthur's book ‘Complexity and the Economy’ (Arthur, Reference Arthur2015b) and his article ‘Foundations of Complexity Economics’ (Arthur, Reference Arthur2021) are very comprehensive explorations of complexity economics. Looking at complexity economics years after the emergence of the field, they present economic systems as adaptive, biological colonies that should be approached with a park ranger mindset (Arthur, Reference Arthur2023a). They connect complexity economics to earlier studies by Adam Smith, Joseph Schumpeter, Thorstein Veblen, Friedrich Hayek, John Maynard Keynes, and Ken Arrow.Footnote ⁶ Perhaps more fundamentally, they identify the main breakthrough of complexity economics: economic problems are ill-defined (Arthur, Reference Arthur2021: 137).Footnote ⁷

Ill-defined problems are those for which there is no single optimal solution. Arthur defines economic problems as ill-defined precisely because agents are constantly adapting to what (temporarily) works. When they converge on a strategy, it creates opportunities to explore other strategies, which some agents do. Agents are constantly learning from the behaviour of other agents. They are in a state of perpetual novelty. Thus, one of Arthur's major contributions to economic theory is to provide ‘a framework for studying the economy [which] involve agents that form individual beliefs or hypotheses – internal models (possibly several simultaneously) – about how to respond to the situation they are in’ (Arthur, Reference Arthur2021: 137). More generally, his overall contribution to economics stands in contrast to the vast majority of publications in the economic field that is ‘very much based on mathematics’ (Arthur, Reference Arthur2023a).Footnote ⁸ Arthur rejects the ‘highly mechanical’ (Arthur, Reference Arthur2018a) perspective of the economy that often leads to ‘prim dreams of pure order’ (Venturi, Reference Venturi1966). Instead, he leans on the side of ‘messy vitality’ (Arthur, Reference Arthur2021: 137).

Beyond economics, Arthur's contribution to complexity science has important implications for the study of law and institutions as they also face ill-defined problems. Given the literature documenting the role of (legal) institutions in shaping markets and the pace of innovation, Arthur's impact in this area ends up being relevant to researchers interested in the design of institutions (Deakin et al., Reference Deakin, Gindis, Hodgson, Huang, Geoffrey and Pistor2021; Harper, Reference Harper2018).

Generally, Arthur conceives institutions as social technologies – complex objects within the broader economic system (Arthur, Reference Arthur2009: 205). He posits that the structure of an economy consists of a network of interdependent arrangements, such as firms, means of production, and institutions, all of which can be viewed as technologies in a broad sense. This framework challenges the equilibrium view of institutions as stable and uniform belief systems that dictate the expected behaviour of members of society in different situations (Aoki, Reference Aoki2001; Kingston and Caballero, Reference Kingston and Caballero2009). Instead, institutions are constantly evolving and adapting to the changing landscape of complex market dynamics (Arthur, Reference Arthur2023b). This perspective suggests that the task of designing institutions is inherently ill-defined; rather than seeking a static ideal, the focus should be on creating flexible, adaptive institutions capable of evolving with the economic and technological environments in which they are situated.

More specifically, Arthur's work informs three prospects. First, the legal system, like the economy, can be studied as a biological ecosystem. The combination of rules and standards exhibits a messy vitality that a complexity mindset can begin to comprehend. Using Arthur's methodology, scholars can document how small events trigger chains of legal responses, resulting in a complex network of laws, i.e. a complex adaptive institution. In a sense, Arthur's work on complexity economics informs the efforts of institutional scholars seeking to document the evolution of legal systems (Hodgson and Stoelhorst, Reference Hodgson and Stoelhorst2014; Ostrom and Basurto, Reference Ostrom and Basurto2011).

Second, the legal system is part of a larger institutional ecosystem – including the market, norms and architecture – that constrains everyone's behaviour (Lessig, Reference Lessig2006). Scholars may be interested in studying how agents respond to and in turn influence the dynamics between these constraints (Schrepel, Reference Schrepel2022). In a sense, Arthur's work on complexity economics provides a methodology for focusing on the evolution of institutional systems by looking at how agents' behaviour affects the combination of constraints (bottom-up). It nicely complements the more traditional institutional perspective used by policymakers, which typically focuses on how different arrangements within institutions shape the behaviour of agents (top-down).

Third, given that agents' experimentation evolves over time in response to ill-defined problems, legal scholars might consider creating complex adaptive regulations that co-evolve with technology to document and respond to their experimentation (Schrepel, Reference Schrepel2023a). Policymakers and regulators typically ignore the strategies and resources of the agents they regulate (Lourenço and Turner, Reference Lourenço and Turner2019). But the ability to adapt to how agents respond to new regulations makes them more effective. It makes the law inductive rather than treating rules and standards as perfectly informed solutions to well-defined problems. To be clear, complex adaptive regulation does not make the initial state of regulation a bottom-up, agent-informed approach. Regulation remains top-down, but should policymakers go down the wrong path, leading to inefficiency or overreach, complex adaptive regulation corrects by responding to its own effects. Ultimately, this approach to the regulatory process helps address a phenomenon often observed by policymakers and legal scholars. Given the complexity of the systems they often regulate, rules and standards cannot repeatedly achieve a singular optimum using similar methods and provisions. Thus, instead of relying solely on experience to write new rules and standards, the introduction of complexity adaptive rules allows for more flexible regulations that adapt to current events and observations (Kupers and Colander, Reference Kupers and Colander2014).

For example, to decrease accidents, the speed limits for vehicles on the highway could dynamically adjust based on various factors such as the volume of traffic, the kinds of vehicles present, current weather conditions, the road type, and the time of day, among others (Pentland and Mahari, Reference Pentland and Mahari2022). Alternatively, the speed limit could be changed every given month based on an assessment of its effectiveness in achieving a predefined, measurable goal (e.g. reducing car crashes or pollution). Either way, such adaptive regulations allow for real-time laws and standards rather than laws lagging behind or being ahead of technology. Building on the literature on epistemic game theory and social systems theory, real-time regulation effectively addresses ill-defined problems because it evolves based on effects that emerge from known and unknown parameters together (Lourenço and Turner, Reference Lourenço and Turner2019: 617).

Increasing returns

There are two fundamental questions in the field of economics. The first revolves around ‘allocation within the economy’, wherein the focus is on determining quantities of goods and services, as well as their respective prices, both within individual markets and across various market domains (Arthur, Reference Arthur2018b). The other pertains to ‘formation within the economy’, encompassing the genesis of an economy, its subsequent development, and the evolution of its structural characteristics with time (Arthur, Reference Arthur2018b). Although the ‘allocation problem is by now well understood and highly mathematicized, the formation question is less well understood’ (Arthur, Reference Arthur2018b). Arthur's work in complexity economics helps with the second question (Petit and Schrepel, Reference Petit and Schrepel2023). He seeks to answer, ‘[h]ow do economies come into being? How do they develop? How does innovation work? Where do institutions come from? How do institutions change things? What really is structural change, and how does it happen?’ (Arthur et al., Reference Arthur, Beinhocker and Stanger2020: 137).

To answer these questions, Arthur first slowed the economic selection processes ‘down and look[ed] at them step-by-step’ in order to identify how small events induce partial equilibrium (Arthur, Reference Arthur2018a). His approach contrasts with that of neoclassical economics. In ‘Complexity and the Economy’ (Arthur, Reference Arthur1999b: 107 & 108), Arthur observed that conventional economic theory opts not to investigate the dynamic development of patterns engendered by its agents. In short, neoclassical economic theory assumes that ‘individual behavior produces an outcome that doesn't give that behavior any incentive to change’ (Arthur et al., Reference Arthur, Beinhocker and Stanger2020: 134).Footnote ⁹ It does not ask how things of economic value are created but which strategy is consistent with the outcome that the things cause. This approach has substantial implications because ‘if everything is the same over time, time disappears and there's no history’ (Arthur et al., Reference Arthur, Beinhocker and Stanger2020: 126). By contrast, complexity asks how heterogeneous agents react to their created outcome. Complexity economics looks at changing behaviours.

Arthur's focus on the formation question led him to uncover several key mechanisms of today's fast-moving economy. He theorized them in publications initially rejected by the profession but are now widely celebrated across ideological lines. Complexity, evolutionary, and institutional economists are particularly fond of studying formation in recent literature (Brette and Chassagnon, Reference Brette and Chassagnon2021; Choi and Storr, Reference Choi and Storr2022; Van Bavel, Reference Van Bavel2020).

Inspired because of his background as an electrical engineer and his readings of Ilya Prigogine,Footnote ¹⁰ Arthur started working on the concept of positive feedback loops in 1983. Alfred Marshall previously explained that sectors of the economy can benefit from increasing returns – without naming them – but failed to derive all consequences from his observation. In ‘Competing Technologies, Increasing Returns, and Lock-in by Historical Events’ (Arthur, Reference Arthur1989) and ‘Positive Feedbacks in the Economy’ (Arthur, Reference Arthur1990a), Arthur popularizes the fact that economies with increasing returns (i.e. ‘the whole high-tech sector’, (Arthur, Reference Arthur2018a)) ‘magnif[y] the effect of small economic shifts’ (Arthur, Reference Arthur1989: 92). It follows that random events can decide market outcomes.Footnote ¹¹ These events can be rationalized ad hoc, but the multiplicity of small economic events makes prediction illusory. This, in short, is the main contribution Arthur made to the concept of increasing returns. He approached them as random (stochastic) processes with multiple possible outcomes.Footnote ¹²

Several editors first contested his work's scientific grounding. It took Arthur six years to publish his increasing returns paper (Arthur, Reference Arthur2018a). As he recollects, Arthur submitted his working paper to the American Economic Review, a publication he believed would be a suitable fit given the significance of the topic of increasing returns in economics. The editors answered that his article was not economics. Same with the Quarterly Journal of Economics and the Economic Journal in England (Arthur, Reference Arthur2018a). The paper was eventually published in the United Kingdom. It is now widely accepted in the literature (Ades and Glaeser, Reference Ades and Glaeser1999; Antweiler and Trefler, Reference Antweiler and Trefler2002; Schmitt-Grohé, Reference Schmitt-Grohé2000; Wang, Reference Wang2015).

The U.S. editors disapproved of the articles' main findings that economic theory can face a lack of predictability when there are increasing returns and that market processes do not necessarily lead to the most efficient outcome. As Arthur explained, increasing returns does not yield a state of equilibrium but rather engenders instability within a system. An initial advantage due to chance or astute strategic decisions could be amplified by increasing returns and result in a lock-in (Arthur, Reference Arthur1996). The lock-in is then typically intensified by path dependency, i.e. the ‘autocatalytic’ or self-reinforcing outcomes or structures under increasing returns (Arthur et al., Reference Arthur, Ermoliev and Kaniovski1987). ‘[H]istorical “small events” are not averaged away and “forgotten” by the dynamics – they may decide the outcome’ (Arthur, Reference Arthur1989: 116). Arthur describes that phenomenon as an expression of ‘non-ergodicity’ (North, Reference North1999).

Arthur's findings cannot be easily used to feed ideological preferences. As a New Yorker journalist recalls, the article's publication drew a predominantly negative reaction. Richard Zeckhauser, a Harvard economist, went as far as to object, ‘if you are right, capitalism can't work’. Several months later, when Arthur presented the same paper at a gathering in Moscow, an equally distinguished Russian economist vehemently declared, ‘your argument cannot be true!’ (Cassidy, Reference Cassidy1998) because it made the top–down control of the economy illusory (Arthur, Reference Arthur1996). Applied in practice, Arthur's theory was unsurprisingly used by both defendants and plaintiffs in the U.S. Microsoft antitrust case (Cassidy, Reference Cassidy1998).Footnote ¹³

Yet, Arthur's concepts are not recipes for the status quo. First, Arthur's work opens up space for legal enforcement to unfreeze markets stuck in inferior outcomes (Cassidy, Reference Cassidy1998). It gives legal institutions an important role to play, unlike the Chicagoans and Schumpeter's work, which does not.

In fact, Arthur's work informs what policymakers can do. Under constant and diminishing returns, the evolution of a market is primarily shaped by predetermined factors such as initial endowments, individual preferences, and available transformation possibilities. In such scenarios, minor events or perturbations hold little sway over the ultimate outcome. While this predictability may offer a sense of comfort, ‘it reduces history to the status of mere carrier – the deliverer of the inevitable’ (Arthur, Reference Arthur1989: 127). If they intervene to avoid the inevitable, policymakers must first choose ‘which technologies to bet on’ (Arthur, Reference Arthur1989: 127) and second, do more than inject a random event into the ecosystem. Arthur warns that ‘because a superior planning authority cannot know in advance which technology will turn out to be best, chance may lock in inferior technologies’ (Arthur, Reference Arthur2018a). The best policymakers can do is provide access to business opportunities for several competing technologies, e.g. by reducing legal barriers to entry or development. They can help enable entrepreneurship (Foster, Reference Foster2015: 41).

Under increasing returns, policies geared towards success in high-tech production and international trade take on a distinctive character (Arthur, Reference Arthur1989). Arthur's findings on increasing returns bear relevance to institutions in charge of innovation policy. Policymakers need not choose which technologies to bet on. Still, they must be prepared for unpredictable outcomes – to address the negative externalities generated by changes in the technical environment (Arthur, Reference Arthur2018b). Their interventions would require little interference if they act early or stronger remedies that unlock positive feedback loops if they intervene late.

Arthur's findings on increasing returns also inform the work of institutions in charge of competition policy. In the short run, these institutions should see positive feedback loops as generating economic uncertainty (i.e. competition) because they change the business environment and thus force agents to ‘cognize’ (Arthur, Reference Arthur2009)Footnote ¹⁴ – rather than rationally devise – new strategies (Petit and Schrepel, Reference Petit and Schrepel2023). In the medium to long term, institutions in charge of competition policy should see that positive feedback loops have the potential to lead to lock-ins and path dependency, i.e. to a frozen ecosystem, especially when increasing returns are not bounded (Arthur, Reference Arthur1990b). The role of antitrust agencies becomes to ensure (or even encourage) the emergence of positive feedback loops in the short and long term.

To achieve this goal, Arthur's findings suggest that firms within a given industry should cooperate and pool resources through joint ventures. These joint ventures would facilitate the sharing of upfront costs, the creation of marketing networks, the exchange of technical expertise, and the standardization of compatibility conventions. Additionally, such policy may extend to the realm of strategic alliances, fostering cooperative endeavours among companies spanning multiple countries, particularly in situations where entering a complex industry proves insurmountable for any individual entity in isolation. Finally, Arthur's work on increasing returns suggests that competition agencies target anti-competitive practices that reduce the ability of third parties (i.e. competitors) to benefit from those returns. The theory of harm would be as follows: in industries with increasing returns, agencies would identify the source of those returns (e.g. users, computing power, etc.) and find harm when strategies are implemented to corner companies out of that source.

Overall, Arthur's work on increasing returns supports one of the central tenets of legal institutionalism: regulation can help create dynamic markets (Deakin et al., Reference Deakin, Gindis, Hodgson, Kainan and Pistor2017). However, regulation can only contribute to dynamism if two conditions are met. The first condition is for regulation to be adapted to the nature of the market. The presence of decreasing or increasing returns varies with the type and timing of the intervention required. The second condition derives from Arthur's views on complexity: policymakers should be concerned with how firms respond to these rules (Lourenço and Turner, Reference Lourenço and Turner2019; Schrepel, Reference Schrepel2022). As he points out, economic agents react to the context (legal, economic, etc.) in which they evolve. They adapt to it, which means that regulation can only bend inefficient monopolies if it adapts to how agents interpret the rules, play with the rules, and eventually bend the rules.

The nature of technology

Arthur's work on the nature of technology is foundational. Although Arthur describes his work on technology and complexity as separate topics, at the very least, they are interrelated: technologies evolve within the ecosystem of other technologies. Arthur's work on technology complements his work on complexity theory, which, as he notes, does not ‘tell us usually about the formation of tastes, or of technologies, or of structure’ (Arthur, Reference Arthur2006: 1554). Technology is also a driving economic force: ‘the economy [is] not so much a container for its technologies, as I had been implicitly taught. The economy arose from its technologies’ (Arthur, Reference Arthur2009: 3). Technologies play the role of ‘Lego pieces to build new organizational models’ (Arthur, Reference Arthur2017). Arthur's research in complexity economics naturally led him to focus on technology, its nature, evolution, and disappearance.

Departing from a strict Darwinian approach that ‘only’ explains how established technologies evolve, Arthur documented a different form of evolution. He published his findings in a book entitled ‘The Nature of Technology: What It Is and How It Evolves’ (Arthur, Reference Arthur2009), in which he derived some organizing principles for the emergence of new technologies. This book, which he began researching in 1997, builds on earlier lectures (Arthur, Reference Arthur2009: 4) and articles such as ‘The Evolution of Technology Within a Simple Computer Model’ (Arthur and Polak, Reference Arthur and Polak2006) and ‘The Structure of Invention’ (Arthur, Reference Arthur2007).

Seeking to document and analyse how an economy forms out of technologies, Arthur first observes that ‘when we face the key question of how radically novel technologies originate – the equivalent of Darwin's question of how novel species originate in biology – we get stymied. Darwin's mechanism does not work’ (Arthur, Reference Arthur2009: 18).Footnote ¹⁵

His interest in the emergence of new technologies led him to question the process of invention – as truly innovative technologies result from invention (Arthur, Reference Arthur2018c). Arthur read historians of technology but found no satisfactory explanation for the ‘act of insight’ they only mentioned when describing the appearance of new inventions (Arthur, Reference Arthur2007). Instead of starting with a pen (or computer), Arthur started in the field. He went on to study ‘about 20 technologies’ with the goal of knowing ‘about a dozen extremely well’ (Arthur, Reference Arthur2009). More specifically, his engineering background led him to study aircraft, radar, spark radio, vacuum-tube radio, jet engines, the steam engine, railroads, computers, the cyclotron, the mass spectrograph, the polymerase chain reaction, penicillin, and others (Arthur, Reference Arthur2009). He did this for 12 years before finally putting his first word on paper (Arthur, Reference Arthur2009).

A pattern emerged: invention is problem-solving, and the problem is solved thanks to what he calls ‘combinatorial evolution’ (Beinhocker, Reference Beinhocker2007; Schumpeter, Reference Schumpeter1911; Silverberg and Verspagen, Reference Silverberg and Verspagen2005). As he summarizes it: ‘[n]ovel technologies must somehow arise by combination of existing technologies’ (Arthur, Reference Arthur2009: 19). Contrary to Darwinian evolution, which proceeds by variation and selection, radical innovation proceeds by combination and selection. W. Brian Arthur just developed a comprehensive theory of the emergence of new technology (Thurston, Reference Thurston1878),Footnote ¹⁶ which he calls ‘a vast system that creates itself out of itself constantly’ (Arthur, Reference Arthur2018c). That theory is now commonly cited in the literature published by complexity and institutional economists (Beinhocker, Reference Beinhocker2011; Kalthaus, Reference Kalthaus2020; Koppl et al., Reference Koppl, Gatti, Devereaux, Fath, Herriot, Hordijk, Kauffman, Ulanowicz and Valverde2023). It helps to further define the label ‘Arthurian’ as scholars who are not only interested in approaching economics from the perspective of complexity science but also focus on the key role that technological emergence and evolution play in driving these dynamics.

Echoing the views of Joel Mokyr (Mokyr, Reference Mokyr1992). Arthur further emphasizes that combinatorial evolution is increasingly the result of the accumulation of knowledge in a deep, systematic way (Arthur, Reference Arthur2009: 65). The production of modern inventions is thus in stark contrast to earlier technologies, which were often developed through empirical methods or common sense. This suggests a central role for institutions, both public and private, in making knowledge widely organized and accessible. Such accessibility can be facilitated through the development and promotion of open-source solutions and the creation of incentive programmes, digital libraries, and open-access repositories. As shown in the most recent literature, these initiatives significantly accelerate the emergence of new technologies, leading to what Arthur describes as combinatorial evolution (Wright et al., Reference Wright, Nagle and Greenstein2023).

Overall, Arthur's work on the nature of technology provides legal institutions (law enforcement agencies and policymakers) with several insights. For one thing, Arthur's work urges enforcers to think of new technologies as combinations of existing technologies. This means that the regulation of one component can affect (positively or negatively) all the others (Schrepel, Reference Schrepel2021b, Reference Schrepel2023b: 6). For example, regulating blockchain immutability affects all Web3 applications. The same is true for encryption (Department of Justice, 2023; Schrepel, Reference Schrepel2021a). This co-evolving ecosystem view leads to a preference for regulating use cases or individuals (e.g. users, developers, companies) rather than technical features (Schrepel, Reference Schrepel2021a).

Second, Arthur's suggestion to think of technology as Legos leads to the identification of critical pieces, i.e. technologies that are key to the development of others. Policymakers may want to (more) closely monitor the practices around these critical technologies, impose mandatory or fair, reasonable, and non-discriminatory (‘FRAND’) terms on licenses, etc.

Third, if one takes Arthur's reminder of the overall positive impact of technology on our modern world seriously, one needs to enact pro-innovation policies and regulations (Arthur, Reference Arthur2009).Footnote ¹⁷ He writes: ‘more than science, more than our legal system, more than philosophical or political ideas, it's technology that has created our modern world’ (Arthur, Reference Arthur2009). If indeed technology is a crucial institution shaping our modern life, regulation should first and foremost seek to ensure the survival of technology and a global environment conducive to the emergence of new technologies. To this end, regulation should not freeze the development of technology, favour specific characteristics, seek to ‘govern’ technology from above, remove incentives to combine existing technologies, create unnecessary barriers to entry, impose heavy regulatory burdens on open-source ecosystems, etc. Regular studies can and should be conducted to list and remove such regulations. To be clear, this does not mean that regulation should not address the problems created by technologies and consider banning the technologies that have only adverse effects, but it does mean that policymakers should be concerned with creating a thriving environment as a rule and that researchers could help keep track of that effort.

Realistic agent-based modelling

In addition to pioneering the use of agent-based modelling (‘ABM’) in economics, Arthur has developed a unique methodology for creating these models (Arthur et al., Reference Arthur, Beinhocker and Stanger2020: 124). This was years in the making. As early as 1988, Arthur discussed his desire to simulate a stock market with John Holland (Arthur, Reference Arthur2015b).Footnote ¹⁸ Holland had published a book entitled ‘Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence’ (Holland, Reference Holland1992), in which he deployed the process of adaptation by natural selection across the fields. Holland and Arthur relied on this pioneering approach to move from rule-based simulations to agent-based ones.

On the methodological side, W. Brian Arthur has published articles expressing his preference for inductive reasoning (Palmer et al., Reference Palmer, Arthur, Holland, LeBaron and Tayler1994). As he puts it, ‘[i]f you want to crack anything, first comes the idea, then comes the technique’ (Arthur, Reference Arthur2018a). In ‘On Learning and Adaptation in the Economy’ (Arthur, Reference Arthur1992), he emphasized that inductive reasoning revises hypotheses by importing new data (Arthur, Reference Arthur1994). Four years later, in ‘Inductive Reasoning, Bounded Rationality and the Bar Problem’ (Arthur, Reference Arthur1994), Arthur linked his preference for inductive reasoning to ABM. His simulation featured ‘many rules per agent’ (Arthur, Reference Arthur2018b), with ‘[a]gents [that] “learn” over time which of their hypotheses work’. He adds: ‘from time to time they may discard poorly performing hypotheses and generate new “ideas” to put in their place’ (Arthur, Reference Arthur1994). In other words, the rules that prove accurate are noticed and used by the agents, while the ones that are not ‘go down the chute’ (Arthur, Reference Arthur2018b).

Continuing his work in this area, Arthur and his co-authors developed the idea he first discussed with John Holland ten years earlier in ‘An Artificial Stock Market’ (Palmer et al., Reference Palmer, Arthur, Holland and LeBaron1999). Instead of creating a simulation in which ‘almost everything is decided at time zero’ and agents ‘work out how the whole future should be, and then the world just plays itself out’, Arthur's stock market ABM opposed neoclassical economics à la Samuelson and Debreu. His simulation featured dynamics, learning, and co-evolution (Palmer et al., Reference Palmer, Arthur, Holland, LeBaron and Tayler1994), with agents adapting to an ‘environment created by other agents’ hypotheses’ (Arthur, Reference Arthur1994).

Arthur followed Tom Sargent's suggestion to start with a neoclassical model and make the agents non-identical to increase realism (Arthur, Reference Arthur2018b). He and Holland did this using Robert Lucas' stock market model from 1978, in which agents could not differ. They added multiple small computer programs, each representing an agent that learned by trial and error. Their approach led to the creation of ABM in which problems are not well defined, i.e. situations where agents ignore what other agents are doing and thus cannot find an optimal equilibrium solution. Arthur's ABMs help understand systems that are alive. To quote John Holland, ‘[i]f it's in equilibrium, it must be dead’.Footnote ¹⁹

Arthur eventually published the results of his experiment in ‘Designing Economic Agents That Act like Human Agents’ (Arthur, Reference Arthur1991). As he recalls, he observed market crashes that mirrored the dynamics of real financial markets (Arthur, Reference Arthur2018b). His agents found what worked temporarily, leading to bubbles that Robert Lucas' simulation did not find.

In more recent years, Arthur has applied ABM outside of economics. In ‘The Evolution of Technology Within a Simple Computer Model’ (Arthur and Polak, Reference Arthur and Polak2006), he modelled the apparition of new technologies by constructing what he called an ‘artificial world within the computer’ (Arthur and Polak, Reference Arthur and Polak2006: 24).Footnote ²⁰ His conclusion rested on the premise that new technologies invariably emerge from the amalgamation of existing assemblies and components, with pre-existing technologies providing a foundational substrate or repository of building blocks for future technologies (Arthur and Polak, Reference Arthur and Polak2006: 30). In ‘All Systems will be Gamed: Exploitive Behavior in Economic and Social Systems’ (Arthur, Reference Arthur2015a), he used ABM to simulate the exploitation of social and economic systems. He showed that ‘exploitive behavior within the economy is by no means rare (…); [and] that policy studies can be readily extended to investigate the possibility of the policy's being “gamed”’ (Arthur, Reference Arthur2015a). In the end, Arthur's approach to ABM ‘is not that different from what really good playwrights have done (…) many very good writers don't have an idea how it's going to come out’ (Arthur, Reference Arthur2023c). Plays and ABMs unfold in unexpected ways.

Although Arthur's contribution to agent-based modelling is widely recognized in today's economic literature, it is also relevant when applied to the realm of legal institutions (Ahrweiler, Reference Ahrweiler2017; Bertani et al., Reference Bertani, Ponta, Raberto, Teglio and Cincotti2021; Haldane and Turrell, Reference Haldane and Turrell2019; Koppl et al., Reference Koppl, Gatti, Devereaux, Fath, Herriot, Hordijk, Kauffman, Ulanowicz and Valverde2023). Realistic ABM à la Arthur can indeed be used to (better) anticipate the effects of new rules, standards, policies, and enforcement actions. There are three reasons for this.

First, ABM can allow policymakers, regulators, and enforcers (i.e. legal institutions) to document the robustness of the problems they seek to regulate. In particular, ABMs, in which agents learn over time which of their hypotheses work in their (new) environment, help anticipate the evolving response of agents to new regulations and how their response, in turn, will change their environment. If an ABM leads to different outcomes each time it is run, the simulation indicates a fragile ecosystem that can be disrupted by regulation (i.e. a change in the institutional environment). If policymakers are still willing to intervene, regulation does not require significant changes in the environment to be effective. Conversely, if ABM leads to a consistent result each time it is run, the ecosystem's robustness indicates the need for a major change in the (regulatory) environment if policymakers want to address an issue effectively.

Second, Arthur's type of ABM, in which agents do not respond to tradeoffs in the same way, shows a path to more granularity than relying on the idea of the ‘average consumer’ or general concepts like ‘companies’, ‘businesses’, and so on. Realistic ABM could be used to document the different responses of all kinds of different agents and the dynamics that emerge from this vibrant ecosystem. For example, antitrust authorities could simulate how privacy-sensitive and quality-sensitive agents respond (differently) to the implementation of data protection regulation. In this sense, ABM informs the tradeoffs legal institutions have to settle.

Third, realistic ABM can help policymakers document something they often struggle with: the timing of regulation, especially the timing between different regulations. For example, the order in which privacy, competition, and financial regulations are introduced into an area can have a major impact on the state of the ecosystem. Taking a step back, ABM could also show the effect of introducing regulations before or after the emergence of certain market events (e.g. the emergence of new competitors). This means that ABM can help to optimize the timing of regulatory institutions as they introduce new rules and standards.

Science from the outside world

Arthur's approach to science is unique in (at least) three ways. First, one of Arthur's notable strengths is his ability to derive research ideas from personal experience rather than relying solely on the literature.Footnote ²¹ He advised that ‘it's a good idea at the start of a research project to ignore everything that's been written and simply think for yourself’ (Arthur, Reference Arthur2017). For instance, he drew inspiration for his well-known El Farol article (Arthur, Reference Arthur1994) from a real-life experience at a Santa Fe bar named… El Farol. The bar featured Irish music on Thursday nights. The enjoyment of the evening depended on the bar's crowd size. It was pleasant when not too crowded but less enjoyable when overly crowded. Arthur realized that if everyone anticipated a large crowd on a particular night, they might decide not to go, thus invalidating that prediction. Conversely, if everyone expected a small crowd, they might decide to attend, again rendering that prediction inaccurate (Arthur, Reference Arthur2015b).

This approach to research allowed Arthur to avoid researching problems that others had preconceived. This led him to big questions such as what is technology, which technology will succeed (Arthur, Reference Arthur1999a: 108; Arthur and Polak, Reference Arthur and Polak2006), how do economic systems evolve (Arthur, Reference Arthur1990a), are economic agents rational (Arthur and Polak, Reference Arthur and Polak2006: 30), is the information revolution dead (Arthur, Reference Arthur2002: 65), how to simulate markets with computers (Palmer et al., Reference Palmer, Arthur, Holland, LeBaron and Tayler1994), and how inventions come about (Arthur, Reference Arthur2007).

Second, Arthur's training as an engineer made a strong impression on his later work. Most of his publications are informed by his technical understanding of the subjects he studies – Arthur often refers to the example of light-water reactors versus gas-cooled reactors (Arthur, Reference Arthur1989: 126; Reference Arthur1990a). As a result, W. Brian Arthur's work is technically deep and relevant across the political spectrum.Footnote ²² His writings are used by the public and private sectors, corporations and governments, sometimes in the same cases. To that technical side, Arthur adds social science approaches by considering bounded rationality, influences and dynamics among agents on the market, etc. (Arthur, Reference Arthur2018a).Footnote ²³ These concepts allow Arthur to get even closer to the reality of the markets and escape what he calls ‘economics using stick figures’ (Arthur, Reference Arthur2023c). In short, Arthur combines the technical analysis of non-conscious entities such as technology with that of living beings, resulting in a unique blend in the field of economics.

Third, Arthur shows interest in the scientific instruments made available outside of his own field of research. As he explains, ‘[s]cience proceeds as much by its instruments – its technologies – as it does by human thought’ (Arthur, Reference Arthur2023b: 638). Arthur identifies three major shifts in the language of science: the emergence of geometry, then algebra, and now algorithms (i.e. computation). He describes computation as the language of biology, emphasizing that algorithmic expression is crucial in understanding how variables and events lead to new ones; in other words, algorithms help address ill-defined problems (Arthur et al., Reference Arthur, Beinhocker and Stanger2020: 124).Footnote ²⁴ He also stresses that computation is not as limited as algebra, which can only express balanced quantities (the left part of the equation must equal the right part of the equation) and is limited by the human ability to keep track of complicated formulas. Arthur suggests using computational thinking to approach complexity because with ‘algorithms or computation, you can model agents acting, (…) you can directly use verbs: agents can buy, sell, change their minds, throw things out, create new things’ (Arthur, Reference Arthur1999a). Algorithms enable the understanding of processes. In other words, Arthur links what he observes in economics to a new scientific method. This method does not necessarily require the use of computers (Arthur, Reference Arthur2006) but a new approach that integrates processes and actions. Computation emerges as a central concept in complexity economics. In fact, complexity economics would not be possible without computation, which is why complexity economics was formalized in the late 1980s after computational power was democratized.

Applied to legal issues and institutions, Arthur's reality-based approach calls for research to begin with the ‘outside world’, that is, with what happens outside the legal system. To be sure, this does not mean that doctrinal research focused on legal sources (e.g. court decisions, policies, academic publications, etc.) is not important. Legal scholars can contribute to society by increasing the relevance of legal sources. But, Arthur's work suggests that research questions should come from outside the legal system itself. Legal scholarship does little to advance the common good by studying sources for their own sake. As Arthur suggests, a good rule of thumb for anticipating the impact of legal scholarship on society is to formulate research questions based on experiences (i.e. lived experiences such as his El Farol moment and learned experiences such as reading interviews with regulated agents, etc.) rather than legal sources.

Arthur suggests that a deep technical understanding of the subject is more than just a nice feature to have when answering research questions related to technical fields. It is a necessity. When addressing digital issues, this means having a (self-made) background in computational thinking. More specifically, when it comes to AI-related challenges, it means having a technical background in machine learning to, at the very least, be able to understand, communicate, and collaborate effectively with computer scientists. Indirectly, Arthur's work also suggests exploring legal subjects with computational tools. These tools, as he shows in economics, allow scientists not only to understand better the subject they study but also to change the substance of the subject itself. Lawyers who study computational law should rejoice at their ability to influence the nature of new rules and norms (Schrepel, Reference Schrepel2021c, Reference Schrepel2023b).

Entrepreneurship

Two of Arthur's character traits have persisted throughout his career. First, Arthur is a risk-taker.Footnote ²⁵ Despite being the youngest person to hold an endowed chair at Stanford University at the age of 37, despite being a colleague of Ken Arrow and other great names in the field, Arthur decided to leave Stanford because, I quote, he was ‘bored’.Footnote ²⁶ He took a full-time position at the newly formed, and at that time not yet prestigious, Santa Fe Institute. There, Arthur decided to work on complexity economics, nonlinearity, disequilibrium, etc. With his research agenda, Arthur made a conscious decision to forgo publishing in the top five economics journals that were not open to theories other than neoclassical, despite having strong credentials in both mathematics and economics.Footnote ²⁷

Second, Arthur is an academic-entrepreneur. I have discussed his contribution to science through the many concepts he has developed. But more than that, Arthur also contributed to the emergence of the Santa Fe Institute (founded in 1984) as a leading academic institution (Waldrop, Reference Waldrop1992). At Kenneth Arrow's invitation, Arthur travelled to New Mexico in 1987 to participate in a meeting Kenneth had convened with Philip Anderson. As Arthur recalls, the gathering included a contingent of 10 theoretical economists (including Tom Sargent and Larry Summers) brought by Arrow and an additional group of 10 physicists and mathematicians (including John Farmer and John Holland) brought by Anderson. A year later, Arthur became the head of the Santa Fe Institute's economic programme. His group was funded by John Reed, the chairman of Citibank, with a single mandate: ‘[d]o anything you like, providing it is at the foundations of economics, and is not conventional’ (Arthur, Reference Arthur2023a). Arthur hired 25 people that first year. He then developed a unique research programme. As he recalls, ‘there were no orthodox departments, no orthodox people, and so unconventional ideas could thrive and conventional ones could be held up to the light and examined for what they were. This was a different world’ (Arthur, Reference Arthur2018a). For the rest, ‘Complexity Economics: Proceedings of the Santa Fe Institute's 2019 Fall Symposium’ nicely relates how the Santa Fe Institute came to be (Arthur et al., Reference Arthur, Beinhocker and Stanger2020). Today, the SFI's economics programme is one of the most prestigious in the world.

As Arthur's professional life illustrates, being a risk-taker means pursuing one's own interests regardless of what universities, (funding) institutions, and group pressures may want to see. It means pursuing what excites scholars most, regardless of trends and calculated moves. It means taking a bottom-up, emergent, and flexible approach to research rather than following a top-down, long-term agenda. This approach is compatible with professorships, as many have proven. The only drawback, in Arthur's words, is that this approach ‘ignores other things like how much money is in [your] bank’ (Arthur, Reference Arthur2023c). Being an entrepreneur means creating research projects, groups, institutes, taking part in young, nascent initiatives in which one can play a decisive role rather than always preferring well-established, initially more prestigious groups.