Complexity and the Economy

by W Brian Arthur

  involve interactions taking place in multilevel structures.

  A description of an approach to economics, however, is not a research pro-

  gram. To build a research program around a process-and-emergence perspec-

  tive, two things have to happen. First, concrete economic problems have to

  be identified for which the approach may provide new insights. A number of

  candidates are offered in this volume: artifact innovation (Lane and Maxfield), the evolution of trading networks (Ioannides, Kirman, and Tesfatsion), money

  (Shubik), the origin and spatial distribution of cities (Krugman), asset pricing (Arthur et al. and Brock), high inflation (Leijonhufvud), and persistent differences in income between different neighborhoods or countries (Durlauf).

  Second, cognitive and structural foundations for modeling these problems

  have to be constructed and methods developed for relating theories based on

  these foundations to observable phenomena (Manski). Here, while substan-

  tial progress has been made since 1987, the program is far from complete.

  The essays in this volume describe a series of parallel explorations of the

  central themes of process and emergence in an interactive world—of how to

  study systems capable of generating perpetual novelty. These explorations do

  not form a coherent whole. They are sometimes complementary, sometimes

  even partially contradictory. But what could be more appropriate to the Santa

  Fe perspective, with its emphasis on distributed processes, emergence, and

  self-organization? Here are our interpretations of the research directions that seem to be emerging from this process:

  COGNITION. The central cognitive issues raised in this volume are ones of

  interpretation. As Shubik puts it, “the interpretation of data is critical. It is not what the numbers are, but what they mean.” How do agents render their

  world comprehensible enough so that “information” has meaning? The two

  papers by Arthur, Holland, LeBaron, Palmer, and Tayler and by Darley and

  Kauffman consider this. They explore problems in which a group of agents

  take actions whose effects depend on what the other agents do. The agents

  base their actions on expectations they generate about how other agents will

  behave. Where do these expectations come from? Both papers reject common

  knowledge or common expectations as a starting point. Indeed, Arthur et al.

  Proce ss and emergence in t He economy [ 95 ]

  argue that common beliefs cannot be deduced. Because agents must derive their expectations from an imagined future that is the aggregate result of

  other agents’ expectations, there is a self-reference of expectations that leads to deductive indeterminacy. Rather, both papers suppose that each agent

  has access to a variety of “interpretative devices” that single out particular elements in the world as meaningful and suggest useful actions on the basis

  of the “information” these elements convey. Agents keep track of how use-

  ful these devices turn out to be, discarding ones that produce bad advice and

  tinkering to improve those that work. In this view, economic action arises

  from an evolving ecology of interpretive devices that interact with one

  another through the medium of the agents that use them to generate their

  expectations.

  Arthur et al. build a theory of asset pricing upon such a view. Agents—

  investors—act as market statisticians. They continually generate expectational models—interpretations of what moves prices in the market—and test these

  by trading. They discard and replace models if not successful. Expectations

  in the market therefore become endogenous—they continually change and

  adapt to a market that they create together. The Arthur et al. market settles

  into a rich psychology, in which speculative bubbles, technical trading, and

  persistence of volatility emerge. The homogeneous rational expectations of the standard literature become a special case—possible in theory but unlikely to

  emerge in practice. Brock presents a variant of this approach, allowing agents to switch between a limited number of expectational models. His model is

  simpler than that of Arthur et al., but he achieves analytical results, which he relates to a variety of stylized facts about financial times series, many of which have been uncovered through the application of nonlinear analysis over the

  past decade.

  In the world of Darley and Kauffman, agents are arrayed on a lattice, and

  they try to predict the behavior of their lattice neighbors. They generate their predictions via an autoregressive model, and they can individually tune the

  number of parameters in the model and the length of the time series they

  use to estimate model parameters. Agents can change parameter number or

  history length by steps of length 1 each period, if by doing so they would have generated better predictions in the previous period. This induces a coevolutionary “interpretative dynamics,” which does not settle down to a stable

  regime of precise, coordinated mutual expectations. In particular, when the

  system approaches a “stable rational-expectations state,” it tends to break

  down into a disordered state. They use their results to argue against conven-

  tional notions of rationality, with infinite foresight horizons and unlimited

  deductive capability.

  In his paper on high inflation, Leijonhufvud poses the same problem as

  Darley and Kauffman: Where should we locate agent cognition, between

  the extremes of “infinite-horizon optimization” and “myopic adaptation?”

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  Leijonhufvud argues that the answer to this question is context dependent. He claims that in situations of institutional break-down like high inflation, agent cognition shifts toward the “short memory/short foresight adaptive mode.”

  The causative relation between institutional and cognitive shifts becomes

  reciprocal. With the shrinking of foresight horizons, markets for long-term

  loans (where long-term can mean over 15 days) disappear. And as inflation

  accelerates, units of accounting lose meaning. Budgets cannot be drawn in

  meaningful ways, the executive arm of government becomes no longer fiscally

  accountable to parliament, and local governments become unaccountable to

  national governments. Mechanisms of social and economic control erode.

  Ministers lose control over their bureaucracies, shareholders over corporate

  management.

  The idea that “interpretative devices” such as explicit forecasting models

  and technical-trading rules play a central role in agent cognition fits with a more general set of ideas in cognitive science, summarized in Clark.2 This work rejects the notion that cognition is all “in the head.” Rather, interpretive aids such as autoregressive models, computers, languages, or even navigational

  tools (as in Hutchins6) and institutions provide a “scaffolding,” an external

  structure on which much of the task of interpreting the world is off-loaded.

  Clark2 argues that the distinctive hallmark of in-the-head cognition is “fast

  pattern completion,” which bears little relation to the neoclassical economist’s deductive rationality. In this volume, North takes up this theme, describing

  some of the ways in which institutions scaffold interpretations of what con-

  stitutes possible and appropriate action for economic agents.

  Lane and Maxfield consider the problem of interpretation from a differ-

  ent perspective. They are particularly inte
rested in what they call attributions of functionality: interpretations about what an artifact does. They argue that new attributions of functionality arise in the context of particular kinds of

  agent relationships, where agents can differ in their interpretations. As a consequence, cognition has an unavoidable social dimension. What interpreta-

  tions are possible depend on who interacts with whom, about what. They also

  argue that new functionality attributions cannot be foreseen outside the par-

  ticular generative relationships in which they arise. This unforeseeability has profound consequences for what constitutes “rational” action in situations of

  rapid change in the structure of agent-artifact space.

  All the papers mentioned so far take as fundamental the importance of

  cognition for economic theory. But the opposite point of view can also be

  legitimately defended from a process-and-emergence perspective. According

  to this argument, overrating cognition is just another error deriving from

  methodological individualism, the very bedrock of standard economic theory.

  How individual agents decide what to do may not matter very much. What

  happens as a result of their actions may depend much more on the interac-

  tion structure through which they act—who interacts with whom, according

  Proce ss and emergence in t He economy [ 97 ]

  to which rules. Blume makes this point in the introduction to his paper on population games, which, as he puts it, provide a class of models that shift

  attention “from the fine points of individual-level decision theory to dynam-

  ics of agent interaction.” Padgett makes a similar claim, though for a differ-

  ent reason. He is interested in formulating a theory of the firm as a locus of transformative “work,” and he argues that “work” may be represented by “an

  orchestrated sequence of actions and reactions, the sequence of which pro-

  duces some collective result (intended or not).” Hence, studying the structure of coordinated action-reaction sequences may provide insight into the organization of economic activity, without bringing “cognition” into the story at all.

  Padgett’s paper is inspired by recent work in chemistry and biology (by Eigen

  and Schuster3 and by Fontana and Buss,4 among others) that are considered

  exemplars of the complexity perspective in these fields.

  STRUCTURE. Most human interactions, even those taking place in “eco-

  nomic” contexts, have a primarily social character: talking with friends, asking advice from knowledgeable acquaintances, working together with colleagues,

  living next to neighbors. Recurring patterns of such social interactions bind

  agents together into networks.6 According to standard economic theory, what

  agents do depends on their values and available information. But standard

  theory typically ignores where values and information come from. It treats

  agents’ values and information as exogenous and autonomous. In reality,

  agents learn from each other, and their values may be influenced by oth-

  ers’ values and actions. These processes of learning and influencing happen

  through the social interaction networks in which agents are embedded, and

  they may have important economic consequences. For example, one of the

  models presented in Durlauf’s paper implies that value relationships among

  neighbors can induce persistent income inequalities between neighborhoods.

  Lane examines a model in which information flowing between agents in a

  network determines the market shares of two competing products. Kirman’s

  paper reviews a number of models that derive economic consequences from

  interaction networks.

  Ioannides, Kirman, and Tesfatsion consider the problems of how networks

  emerge from initially random patterns of dyadic interaction and what kinds

  of structure the resulting networks exhibit. Ioannides studies mathematical

  models based on controlled random fields, while Tesfatsion works in the con-

  text of a particular agent-based model, in which the “agents” are strategies

  that play Prisoner’s Dilemma with one another. Ioannides and Tesfatsion are

  6. There is a voluminous sociological literature on interaction networks. Recent entry points include Noria and Eccles,7 particularly the essay by Granovetter entitled

  “Problems of Explanation in Economic Sociology,” and the methodological survey of Wasserman and Faust.8

  [ 98 ] Complexity and the Economy

  both primarily interested in networks involving explicitly economic interactions, in particular trade. Their motivating idea, long recognized among soci-

  ologists (for example, Baker1), is that markets actually function by means of

  networks of traders, and what happens in markets may reflect the structure

  of these networks, which in turn may depend on how the networks emerge.

  Local interactions can give rise to large-scale spatial structures. This phe-

  nomenon is investigated by several of the papers in this volume. Lindgren’s

  contribution is particularly interesting in this regard. Like Tesfatsion, he

  works with an agent-based model in which the agents code strategies for play-

  ing two-person games. In both Lindgren’s and Tesfatsion’s models, agents

  adapt their strategies over time in response to their past success in playing

  against other agents. Unlike Tesfatsion’s agents, who meet randomly and

  decide whether or not to interact, Lindgren’s agents only interact with neigh-

  bors in a prespecified interaction network. Lindgren studies the emergence of

  spatiotemporal structure in agent space—metastable ecologies of strategies

  that maintain themselves for many agent-generations against “invasion” by

  new strategy types or “competing” ecologies at their spatial borders. In particular, he compares the structures that arise in a lattice network, in which each agent interacts with only a few other agents, with those that arise in a fully connected network, in which each agent interacts with all other agents. He

  finds that the former “give rise to a stable coexistence between strategies that would otherwise be outcompeted. These spatiotemporal structures may take

  the form of spiral waves, irregular waves, spatiotemporal chaos, frozen patchy patterns, and various geometrical configurations.” Though Lindgren’s model

  is not explicitly economic, the contrast he draws between an agent space in

  which interactions are structured by (relatively sparse) social networks and

  an agent space in which all interactions are possible (as is the case, at least in principle, with the impersonal markets featured in general equilibrium analysis) is suggestive. Padgett’s paper offers a similar contrast, in a quite different context.

  Both Durlauf and Krugman explore the emergence of geographical segrega-

  tion. In their models, agents may change location—that is, change their posi-

  tion in a social structure defined by neighbor ties. In these models (especially Durlauf’s), there are many types of agents, and the question is under what

  circumstances, and through what mechanisms, do aggregate-level “neighbor-

  hoods” arise, each consisting predominantly (or even exclusively) of one agent type. Thus, agents’ choices, conditioned by current network structure (the

  agent’s neighbors and the neighbors at the sites to which the agent can move), change that structure; over time, from the changing local network structure,

  an aggregate-level pattern of segregated neighborhoods emerges.

  Kollman, Miller, and Page explore a related theme in their
work on

  political platforms and institutions in multiple jurisdictions. In their

  agent-based model, agents may relocate between jurisdictions. They show

  Proce ss and emergence in t He economy [ 99 ]

  that when there are more than three jurisdictions, two-party competition outperforms democratic referenda. The opposite is the case when there

  is only one jurisdiction and, hence, no agent mobility. They also find that

  two-party competition results in more agent moves than does democratic

  referenda.

  Manski reminds us that while theory is all very well, understanding of real

  phenomena is just as important. He distinguishes between three kinds of

  causal explanation for the often observed empirical fact that “persons belong-

  ing to the same group tend to behave similarly.” One is the one we have been

  describing above: the behavioral similarities may arise through network inter-

  action effects. But there are two other possible explanations: contextual, in which the behavior may depend on exogenous characteristics of the group (like

  socioeconomic composition); or correlated effects, in which the behavior may be due to similar individual characteristics of members of the group. Manski shows, among other results, that a researcher who uses the popular linear-in-means model to analyze his data and “observes equilibrium outcomes and the

  composition of reference groups cannot empirically distinguish” endogenous

  interactions from these alternative explanations. One moral is that nonlinear

  effects require nonlinear inferential techniques.

  In the essays of North, Shubik, and Leijonhufvud, the focus shifts to another

  kind of social structure, the institution. North’s essay focuses on institutions and economic growth, Shubik’s on financial institutions, and Leijonhufvud’s

  on high-inflation phenomenology. All three authors agree in defining institu-

  tions as “the rules of the game,” without which economic action is unthink-

  able. They use the word “institution” in at least three senses: as the “rules”

  themselves (for example, bankruptcy laws); as the entities endowed with the