Complexity and the Economy

by W Brian Arthur

  [ 88 ] Complexity and the Economy

  CHAPTER 5

  Process and Emergence in the Economy

  W. BRIAN ARTHUR, STEVEN N. DURL AUF,

  AND DAVID A. L ANE*

  This paper written in 1997 is as close as our Economics Program at the Santa Fe Institute came to a manifesto. It bears the unmistakable stamp of my two co-authors, Steven Durlauf and David Lane, both of whom have given considerable thought over the years to complexity and economics.

  We argue that the economy consists of heterogeneous agents acting in parallel and responding to the aggregate states they together co-create. In doing so they continually adapt to a perpetually changing world in which there is no global controller, a world in which human cognition, hierarchy, and interaction are important. The economy, we argue, shows all the hallmarks of complexity. The paper was an introduction to the volume The Economy as an Evolving Complex System II, W. B. Arthur, S. Durlauf, D. Lane (Eds.), SFI Studies in the Sciences of Complexity, Vol. XXVII, Addison-Wesley, 1–14, 1997. The papers in this 1997 volume give a good idea of the state of the complexity approach at that time.

  In September 1987, twenty people came together at the Santa Fe Institute to

  talk about “the economy as an evolving, complex system.” Ten were theoret-

  ical economists, invited by Kenneth J. Arrow, and ten were physicists, biolo-

  gists, and computer scientists, invited by Philip W. Anderson. The meeting was motivated by the hope that new ideas bubbling in the natural sciences, loosely tied together under the rubric of “the sciences of complexity,” might stimu-late new ways of thinking about economic problems. For ten days, economists

  * Arthur is Citibank Professor, Santa Fe Institute; Durlauf is with the Department of Economics, University of Wisconsin at Madison, and the Santa Fe Institute; and Lane is with the Department of Political Economy, University of Modena.

  and natural scientists took turns talking about their respective worlds and methodologies. While physicists grappled with general equilibrium analysis

  and noncooperative game theory, economists tried to make sense of spin glass

  models, Boolean networks, and genetic algorithms.

  The meeting left two legacies. The first was a volume of essays, The Economy as an Evolving Complex System, edited by Arrow, Anderson, and David Pines.

  The other was the founding, in 1988, of the Economics Program at the Santa

  Fe Institute, the Institute’s first resident research program. The Program’s

  mission was to encourage the understanding of economic phenomena from

  a complexity perspective, which involved the development of theory as well

  as tools for modeling and for empirical analysis. To this end, since 1988,

  the Program has brought researchers to Santa Fe, sponsored research proj-

  ects, held several workshops each year, and published several dozen working

  papers. And, since 1994, it has held an annual summer school for economics

  graduate students.

  This volume, The Economy as an Evolving Complex System II, repre-

  sents the proceedings of an August 1996 workshop sponsored by the SFI

  Economics Program. The intention of this workshop was to take stock,

  to ask: What has the complexity perspective contributed to economics

  in the past decade? In contrast to the 1987 workshop, almost all of the

  presentations addressed economic problems, and most participants were

  economists by training. In addition, while some of the work presented was

  conceived or carried out at the Institute, some of the participants had no

  previous relation with SFI—research related to the complexity perspective

  is under active development now in a number of different institutes and

  university departments.

  But just what is the complexity perspective in economics? That is not an easy question to answer. Its meaning is still very much under construction,

  and, in fact, the present volume is intended to contribute to that construc-

  tion process. Indeed, the authors of the essays in this volume by no means

  share a single, coherent vision of the meaning and significance of complexity

  in economics. What we will find instead is a family resemblance, based upon a

  set of interrelated themes that together constitute the current meaning of the complexity perspective in economics.

  Several of these themes, already active subjects of research by economists

  in the mid-1980s, are well described in the earlier The Economy as an Evolving Complex System: In particular, applications of nonlinear dynamics to economic theory and data analysis, surveyed in the 1987 meeting by Michele Boldrin

  and William Brock; and the theory of positive feedback and its associated phe-

  nomenology of path dependence and lock-in, discussed by W. Brian Arthur.

  Research related to both these themes has flourished since 1987, both in and

  outside the SFI Economics Program. While chaos has been displaced from its

  place in 1987 at center stage of the interest in nonlinear dynamics, in the

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  last decade economists have made substantial progress in identifying patterns of nonlinearity in financial time series and in proposing models that

  both offer explanations for these patterns and help to analyze and, to some

  extent, predict the series in which they are displayed. Brock surveys both

  these developments in his chapter in this volume, while positive feedback

  plays a central role in the models analyzed by Lane (on information conta-

  gion), Durlauf (on inequality) and Krugman (on economic geography), and

  lurk just under the surface of the phenomena described by North (develop-

  ment) and Leijonhufvud (high inflation).

  Looking back over the developments in the past decade and the papers

  produced by the program, we believe that a coherent perspective—some-

  times called the “Santa Fe approach”—has emerged within economics. We

  will call this the complexity perspective, or Santa Fe perspective, or occasionally the process-and-emergence perspective. Before we describe this, we first

  sketch the two conceptions of the economy that underlie standard, neoclas-

  sical economics (and indeed most of the presentations by economic theorists

  at the earlier 1987 meeting). We can call these conceptions the “equilibrium”

  and “dynamical systems” approaches. In the equilibrium approach, the prob-

  lem of interest is to derive, from the rational choices of individual optimizers, aggregate-level “states of the economy” (prices in general equilibrium analysis, a set of strategy assignments in game theory with associated payoffs)

  that satisfy some aggregate-level consistency condition (market-clearing,

  Nash equilibrium), and to examine the properties of these aggregate-level

  states. In the dynamical systems approach, the state of the economy is repre-

  sented by a set of variables, and a system of difference equations or differential equations describes how these variables change over time. The problem is

  to examine the resulting trajectories, mapped over the state space. However,

  the equilibrium approach does not describe the mechanism whereby the state of the economy changes over time—nor indeed how an equilibrium comes

  into being.1 And the dynamical system approach generally fails to accommo-

  date the distinction between agent- and aggregate-levels (except by obscuring it through the device of “representative agents”). Neither accounts for the

  emergence of new kinds of relevant state variables, much less new entities,

  new patterns, new structures.2

  1. Since an a priori
intertemporal equilibrium hardly counts as a mechanism.

  2. Norman Packard’s contribution to the 1987 meeting addresses just this problem with respect to the dynamical systems approach. As he points out, “if the set of relevant variables changes with time, then the state space is itself changing with time, which is not commensurate with a conventional dynamical systems model.”

  Proce ss and emergence in t He economy [ 91 ]

  To describe the complexity approach, we begin by pointing out six features of the economy that together present difficulties for the traditional mathematics used in economics:3

  DISPERSED INTERACTION. What happens in the economy is determined by

  the interaction of many dispersed, possibly heterogeneous, agents acting in parallel. The action of any given agent depends upon the anticipated actions of a limited number of other agents and on the aggregate state these agents cocreate.

  NO GLOBAL CONTROLLER. No global entity controls interactions. Instead,

  controls are provided by mechanisms of competition and coordination among

  agents. Economic actions are mediated by legal institutions, assigned roles,

  and shifting associations. Nor is there a universal competitor—a single agent

  that can exploit all opportunities in the economy.

  CROSS-CUTTING HIERARCHICAL ORGANIZATION. The economy has many

  levels of organization and interaction. Units at any given level—behaviors,

  actions, strategies, products—typically serve as “building blocks” for con-

  structing units at the next higher level. The overall organization is more than hierarchical, with many sorts of tangled interactions (associations, channels

  of communication) across levels.

  CONTINUAL ADAPTATION. Behaviors, actions, strategies, and products are

  revised continually as the individual agents accumulate experience—the sys-

  tem constantly adapts.

  PERPETUAL NOVELTY. Niches are continually created by new markets, new

  technologies, new behaviors, new institutions. The very act of filling a niche may provide new niches. The result is ongoing, perpetual novelty.

  OUT-OF-EQUILIBRIUM DYNAMICS. Because new niches, new potentials,

  new possibilities, are continually created, the economy operates far from any

  optimum or global equilibrium. Improvements are always possible and indeed

  occur regularly.

  Systems with these properties have come to be called adaptive nonlinear

  networks (the term is John Holland’s5). There are many such in nature and society: nervous systems, immune systems, ecologies, as well as economies.

  An essential element of adaptive nonlinear networks is that they do not

  act simply in terms of stimulus and response. Instead they anticipate. In

  3. John Holland’s paper at the 1987 meeting beautifully—and presciently—frames these features. For an early description of the Santa Fe approach, see also the program’s March 1989 newsletter, “Emergent Structures.”

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  particular, economic agents form expectations—they build up models of the economy and act on the basis of predictions generated by these models. These

  anticipative models need neither be explicit, nor coherent, nor even mutually

  consistent.

  Because of the difficulties outlined above, the mathematical tools econo-

  mists customarily use, which exploit linearity, fixed points, and systems of

  differential equations, cannot provide a deep understanding of adaptive non-

  linear networks. Instead, what is needed are new classes of combinatorial

  mathematics and population-level stochastic processes, in conjunction with

  computer modeling. These mathematical and computational techniques are in

  their infancy. But they emphasize the discovery of structure and the processes through which structure emerges across different levels of organization.

  This conception of the economy as an adaptive nonlinear network—as an

  evolving, complex system—has profound implications for the foundations of

  economic theory and for the way in which theoretical problems are cast and

  solved. We interpret these implications as follows:

  COGNITIVE FOUNDATIONS. Neoclassical economic theory has a unitary

  cognitive foundation: economic agents are rational optimizers. This means

  that (in the usual interpretation) agents evaluate uncertainty probabilisti-

  cally, revise their evaluations in the light of new information via Bayesian

  updating, and choose the course of action that maximizes their expected util-

  ity. As glosses on this unitary foundation, agents are generally assumed to

  have common knowledge about each other and rational expectations about

  the world they inhabit (and of course cocreate). In contrast, the Santa Fe viewpoint is pluralistic. Following modern cognitive theory, we posit no single,

  dominant mode of cognitive processing. Rather, we see agents as having to

  cognitively structure the problems they face—as having to “make sense” of

  their problems—as much as solve them. And they have to do this with cogni-

  tive resources that are limited. To “make sense,” to learn, and to adapt, agents use variety of distributed cognitive processes. The very categories agents use to convert information about the world into action emerge from experience,

  and these categories or cognitive props need not fit together coherently in

  order to generate effective actions. Agents therefore inhabit a world that

  they must cognitively interpret—one that is complicated by the presence and

  actions of other agents and that is ever changing. It follows that agents generally do not optimize in the standard sense, not because they are constrained

  by finite memory or processing capability, but because the very concept of

  an optimal course of action often cannot be defined. It further follows that

  the deductive rationality of neoclassical economic agents occupies at best

  a marginal position in guiding effective action in the world. And it follows

  that any “common knowledge” agents might have about one another must be

  attained from concrete, specified cognitive processes operating on experiences Proce ss and emergence in t He economy [ 93 ]

  obtained through concrete interactions. Common knowledge cannot simply be assumed into existence.

  STRUCTURAL FOUNDATIONS. In general equilibrium analysis, agents do

  not interact with one another directly, but only through impersonal markets.

  By contrast, in game theory all players interact with all other players, with

  outcomes specified by the game’s payoff matrix. So interaction structures are

  simple and often extreme—one-with-all or all-with-all. Moreover, the inter-

  nal structure of the agents themselves is abstracted away.4 In contrast, from

  a complexity perspective, structure matters. First, network-based structures

  become important. All economic action involves interactions among agents,

  so economic functionality is both constrained and carried by networks defined

  by recurring patterns of interaction among agents. These network structures

  are characterized by relatively sparse ties. Second, economic action is struc-

  tured by emergent social roles and by socially supported procedures—that is,

  by institutions. Third, economic entities have a recursive structure: they are themselves comprised of entities. The resulting “level” structure of entities

  and their associated action processes is not strictly hierarchical, in that component entities may be part of more than one higher-level entity, and enti-

  ties at multiple l
evels of organization may interact. Thus, reciprocal causation operates between different levels of organization—while action processes at

  a given level of organization may sometimes by viewed as autonomous, they

  are nonetheless constrained by action patterns and entity structures at other

  levels. And they may even give rise to new patterns and entities at both higher and lower levels. From the Santa Fe perspective, the fundamental principle of

  organization is the idea that units at one level combine to produce units at the next higher level.5

  PROCESS AND EMERGENCE. It should be clear by now that exclusively pos-

  ing economic problems as multiagent optimization exercises makes little

  sense from the viewpoint we are outlining—a viewpoint that puts empha-

  sis on process, not just outcome. In particular, it asks how new “things”

  arise in the world—cognitive things, like “internal models;” physical things,

  like “new technologies;” social things, like new kinds of economic “units.”

  And it is clear that if we posit a world of perpetual novelty, then outcomes

  cannot correspond to steady-state equilibria, whether Walrasian, Nash,

  or dynamic-systems-theoretical. The only descriptions that can matter in

  such a world are about transient phenomena—about process and about

  emergent structures. What then can we know about the economy from a

  4. Except in principal-agent theory or transaction-costs economics, where a simple hierarchical structure is supposed to obtain.

  5. We need not commit ourselves to what constitutes economic “units” and “levels.”

  This will vary from problem context to problem context.

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  process-and-emergence viewpoint, and how can we come to know it? Studying process and emergence in the economy has spawned a growth industry in the

  production of what are now generally called “agent-based models.” And what

  counts as a solution in an agent-based model is currently under negotiation.

  Many of the papers in this volume—including those by Arthur et al., Darley

  and Kauffman, Shubik, Lindgren, Kollman et al., Kirman, and Tesfatsion—

  address this issue, explicitly or implicitly. We can characterize these as seeking emergent structures arising in interaction processes, in which the interacting entities anticipate the future through cognitive procedures that themselves