From The Economy as an Evolving Complex System II
Edited by W. Brian Arthur, Steven Durlauf and David Lane,
Addison-Wesley, Reading, Mass., 1997
Introduction: Process and Emergence in the Economy
by W. Brian Arthur, Steven Durlauf and David A. Lane.
In September 1987 twenty people came together at the Santa Fe Institute
to talk about "the economy as a evolving, complex system." Ten were theoretical
economists, invited by Kenneth J. Arrow, and ten were physicists, biologists
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 stimulate
new ways of thinking about economic problems. For ten days, economists 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 projects, 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, represents
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
a 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 presenters 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 construction
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
an interrelated set of 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 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 phenomenology
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 1987 place at
center stage of the interest in nonlinear dynamics, in the 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 even 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 contagion), Durlauf (on inequality)
and Krugman (on economic geography), and lurk not far under the surface of
the phenomena described by North (development) and Leijonhufvud (high inflation).
Looking back over the developments in the past decade, and of the papers
produced by the program, we believe that a coherent perspective--sometimes
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, neoclassical
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 problem
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 represented
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 accommodate
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]
To describe the complexity approach, we begin by pointing out six features
of an 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
co-create No Global Controller No global entity controls interactions.
Instead, controls are provided by mechanisms of competition and coordination
between 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 constructing units at the next higher level. The overall organization
is more than hierarchical, with many sorts of tangling interactions (associations,
channels of communication) across levels Continual Adaptation Behaviors,
actions, strategies, and products are revised continually as the individual
agents accumulate experience--the system 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's, 1987.) 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 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 mutually consistent.
Because of the difficulties outlined above, the mathematical tools economists
customarily use, which exploit linearity, fixed points, and systems of differential
equations, cannot provide a deep understanding of adaptive nonlinear networks.
Instead, what is needed is 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--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 probabilistically,
revise their evaluations in the light of new information via Bayesian updating,
and choose the course of action that maximizes their expected utility. 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 co-create). 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 cognitive 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 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
internal 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 structured
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 entities
at multiple levels 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 of that units at one level combine to produce
units at the next higher level.[5]
What counts as a problem and as a solution It should be clear by
now that exclusively posing economic problems as multi-agent optimization
exercises makes little sense from the viewpoint we are outlining--a viewpoint
that puts emphasis 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 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 involve interactions
taking place in multi-level structures.
* * *
A description of an approach to economics, however, is not a research
program. To build a research program around a process-and-emergence perspective,
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., Brock), high inflation (Leijonhuvfud), 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 substantial 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. 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 useful 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 together create. 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
conventional 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"? 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 (1996).
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 Hutchins, 1995) and institutions provide a
"scaffolding," an external structure on which much of task of interpreting
the world is off-loaded. Clark (1996) 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 constitutes possible and appropriate action
for economic agents.
Lane and Maxfield consider the problem of interpretation from a different
perspective. They are particularly interested 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 interpretations
are possible depend on who interacts with whom, about what. They also argue
that new functionality attributions cannot be foreseen outside the particular
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 interaction structure
through which they act--who interacts with whom, according 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 dynamics of agent
interaction." Padgett makes a similar claim, though for a different 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 produces 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 Schuster and by Fontana
and Buss, among others) that are considered exemplars of the complexity perspective
in these fields.
Structure Most human interactions, even those taking place in "economic"
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 others' 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 context
of a particular agent-based model, in which the "agents" are strategies that
play Prisoner's Dilemma with one another. Ioannides and Tesfatsion are both
primarily interested in networks involving explicitly economic interactions,
in particular trade. Their motivating idea, long recognized among sociologists
(for example, Baker, 1984), 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 phenomenon 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 playing 2-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 neighbors
in a prespecified interaction network. Lindgren studies the emergence of
spatio-temporal 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, and 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 spatio-temporal
structures may take the form of spiral waves, irregular waves, spatio-temporal
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 segregation.
In their models, agents may change location--that is, change their position
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 "neighborhoods"
arise, each consisting predominantly (or even exclusively) of one agent type.
Thus, agent's choices, conditioned by current network structure (the agent's
neighbors and the neighbors at the sites to which the agent can move), changes
that structure; over time, from the changing local network structure, an
aggregate-level pattern of segregated neighborhoods emerges.
No Global Controller No
global entity controls interactions. Instead, controls are provided by mechanisms
of competition and coordination between 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 constructing units at the next higher level. The overall organization
is more than hierarchical, with many sorts of tangling interactions (associations,
channels of communication) across levels Continual Adaptation Behaviors,
actions, strategies, and products are revised continually as the individual
agents accumulate experience--the system 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's, 1987.) 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 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 mutually consistent.
Because
of the difficulties outlined above, the mathematical tools economists customarily
use, which exploit linearity, fixed points, and systems of differential equations,
cannot provide a deep understanding of adaptive nonlinear networks. Instead,
what is needed is 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--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 probabilistically, revise their evaluations
in the light of new information via Bayesian updating, and choose the course
of action that maximizes their expected utility. 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
co-create). 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 cognitive 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 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 internal 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 structured 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 entities at multiple levels 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 of that units at one
level combine to produce units at the next higher level.[5]
What counts as a problem and as a solution
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."
3.
John Holland's outline at the 1987 meeting beautifully--and presciently--frames
these features. For an early description of the Santa Fe approach, see also
the program's 1989 newsletter, "Emergent Structures." 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. 6. There
is a voluminous sociological literature on interaction networks. Recent entry
points include Noria and Eccles (1992), particularly the essay by Granovetter
entitled "Problems of Explanation in Economic Sociology", and the methodological
survey of Wasserman and Faust (1994).
Last Modified: Monday, December 17, 2001
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