on all scales, large and small. Thus emerge periods of change triggering further change, periods of high volatility, followed by periods when little changes and little needs to be changed, periods of quiescence. This is GARCH behavior.
Let me now summarize. What we found in our artificial stock market is that,
providing our investors start near the rational-expectations academic solu-
tion, this solution prevails. But this is a small set of parameter space. Outside this, in the complex regime, self-reinforcing beliefs and self-reinforcing
avalanches of change emerge. A wider theory and a richer “solution” or set
of behaviors then appears, consonant with actual market behavior. The
rational-expectations theory becomes a special case.
In the standard view, which has come down from the Enlightenment, the
economy is an object. It is complicated but can be viewed mechanistically.
Subject and object—agents and the economy they perform in—can be neatly
separated. The view I am giving here is different. It says that the economy itself emerges from our subjective beliefs. These subjective beliefs, taken in aggregate, structure the micro economy. They give rise to the character of financial markets. They direct flows of capital and govern strategic behavior and negoti-ations. They are the DNA of the economy. These subjective beliefs are a-priori or deductively indeterminate in advance. They co-evolve, arise, decay, change, mutually reinforce, and mutually negate. Subject and object cannot be neatly
separated. And so the economy shows behavior that we can best describe as
organic, rather than mechanistic. It is not a well-ordered, gigantic machine. It is organic. At all levels it contains pockets of indeterminacy. It emerges from subjectivity and falls back into subjectivity.
t He end of certain t y in economics [ 181 ]
CHAPTER 12
Complexity and the Economy
W. BRIAN ARTHUR
This essay summarizes my thinking on complexity and the economy in 1999. It is a pre-cursor to (and heavily overlaps) the introductory chapter of this volume, but I include it here because it introduces the term “complexity economics” for the first time. The article appeared in Science, April 2, 1999, 244: 107–109.
Common to all studies on complexity are systems with multiple elements
adapting or reacting to the pattern these elements create. The elements
might be cells in a cellular automaton, ions in a spin glass, or cells in an
immune system, and they may react to neighboring cells’ states, or local mag-
netic moments, or concentrations of B and T cells. Elements and the patterns
they respond to vary from one context to another. But the elements adapt
to the world—the aggregate pattern—they co-create. Time enters naturally
here via the processes of adjustment and change: As the elements react, the
aggregate changes; as the aggregate changes, elements react anew. Barring the
reaching of some asymptotic state or equilibrium, complex systems are sys-
tems in process that constantly evolve and unfold over time.
Such systems arise naturally in the economy. Economic agents, be they
banks, consumers, firms, or investors, continually adjust their market moves,
buying decisions, prices, and forecasts to the situation these moves or deci-
sions or prices or forecasts together create. But unlike ions in a spin glass, which always react in a simple way to their local magnetic field, economic elements (human agents) react with strategy and foresight by considering out-
comes that might result as a consequence of behavior they might undertake.
This adds a layer of complication to economics that is not experienced in the
natural sciences.
Conventional economic theory chooses not to study the unfolding of the patterns its agents create but rather to simplify its questions in order to seek analytical solutions. Thus it asks what behavioral elements (actions, strategies, and expectations) are consistent with the aggregate patterns these
behavioral elements co-create? For example, general equilibrium theory asks
what prices and quantities of goods produced and consumed are consistent
with (would pose no incentives for change to) the overall pattern of prices
and quantities in the economy’s markets. Game theory asks what moves or
choices or allocations are consistent with (are optimal given) other agents’
moves or choices or allocations in a strategic situation. Rational expectations economics asks what forecasts (or expectations) are consistent with (are on
average validated by) the outcomes these forecasts and expectations together
create. Conventional economics thus studies consistent patterns: patterns
in behavioral equilibrium that would induce no further reaction. Economists
at the Santa Fe Institute, Stanford, MIT, Chicago, and other institutions are
now broadening this equilibrium approach by turning to the question of how
actions, strategies, or expectations might react in general to (might endog-
enously change with) the aggregate patterns these create ( 1, 2). The result—
complexity economics—is not an adjunct to standard economic theory but
theory at a more general, out-of-equilibrium level.
The type of systems I have described become especially interesting if they
contain nonlinearities in the form of positive feedbacks. In economics, posi-
tive feedbacks arise from increasing returns ( 3, 4). To ensure that a unique, predictable equilibrium is reached, standard economics usually assumes
diminishing returns. If one firm gets too far ahead in the market, it runs into higher costs or some other negative feedback, and the market is shared at a
predictable unique equilibrium. When we allow positive feedbacks, or increas-
ing returns, a different outcome arises. Consider the market for online ser-
vices of a few years back, in which three major companies competed: Prodigy,
Compuserve, and America Online. As each gained in membership base, it
could offer a wider menu of services, as well as more members to share spe-
cialized hobby and chat room interests with—that is, there were increasing
returns to expanding the membership base. Prodigy was first in the market,
but by chance and strategy America Online got far enough ahead to gain an
unassailable advantage. Today it dominates. Under different circumstances,
one of its rivals might have taken the market. Notice the properties here: a
multiplicity of potential solutions; the outcome actually reached is not pre-
dictable in advance; it tends to be locked in; it is not necessarily the most
efficient economically; it is subject to the historical path taken; and although the companies may start out equal, the outcome is asymmetrical. These properties have counterparts in nonlinear physics where similar positive feed-
backs are present. What economists call multiple equilibria, nonpredictability, lock-in, inefficiency, historical path dependence, and asymmetry, physicists
comPlexi t y and t He economy [ 183 ]
call multiple metastable states, unpredictability, phase or mode locking, high-energy ground states, non-ergodicity, and symmetry breaking ( 5).
Increasing returns problems have been discussed in economics for a long
time. A hundred years ago, Alfred Marshall ( 6) noted that if firms gain advantage as their market share increases, “whatever firm first gets a good start will obtain a monopoly.” But the conventional static equilibrium approach gets stymied by indeterminacy: If there is a multiplicity of equilibria, how might one be reached? The process-oriented complexity approach suggests a way to deal
&nb
sp; with this. In the actual economy, small random events happen; in the online
services case, events such as random interface improvements, new offerings,
and word-of-mouth recommendations. Over time, increasing returns magnify
the cumulation of such events to select the outcome randomly. Thus, increasing returns problems in economics are best seen as dynamic processes with random events and natural positive feedbacks—as nonlinear stochastic processes.
This shift from a static outlook into a process orientation is common to com-
plexity studies. Increasing returns problems are being studied intensively in
market allocation theory ( 4), international trade theory ( 7), the evolution of technology choice ( 8), economic geography ( 9), and the evolution of patterns of poverty and segregation ( 10). The common finding that economic structures can crystallize around small events and lock in is beginning to change policy in all of these areas toward an awareness that governments should avoid both extremes
of coercing a desired outcome and keeping strict hands off, and instead seek to push the system gently toward favored structures that can grow and emerge
naturally. Not a heavy hand, not an invisible hand, but a nudging hand.
Once we adopt the complexity outlook, with its emphasis on the formation
of structures rather than their given existence, problems involving prediction in the economy look different. The conventional approach asks what forecasting model (or expectations) in a particular problem, if given and shared by all agents, would be consistent with (would be on average validated by) the actual time series this forecasting model would in part generate. This “rational expectations” approach is valid. But it assumes that agents can somehow deduce
in advance what model will work and that everyone “knows” that everyone
knows to use this model (the common knowledge assumption.) What hap-
pens when forecasting models are not obvious and must be formed individu-
ally by agents who are not privy to the expectations of others?
Consider as an example my El Farol Bar Problem ( 11). One hundred people must decide independently each week whether to show up at their favorite
bar (El Farol in Santa Fe). The rule is that if a person predicts that more that 60 (say) will attend, he or she will avoid the crowds and stay home; if he predicts fewer than 60, he will go. Of interest are how the bar-goers each week
might predict the numbers of people showing up, and the resulting dynamics
of the numbers attending. Notice two features of this problem. Our agents
will quickly realize that predictions of how many will attend depend on others’
[ 184 ] Complexity and the Economy
predictions of how many will attend (because that determines their attendance). But others’ predictions in turn depend on their predictions of others’
predictions. Deductively there is an infinite regress. No “correct” expectational model can be assumed to be common knowledge, and from the agents’ viewpoint, the problem is ill defined. (This is true for most expectational problems, not just for this example.) Second, and diabolically, any commonalty of expectations gets broken up: If all use an expectational model that predicts few will go, all will go, invalidating that model. Similarly, if all believe most will go, nobody will go, invalidating that belief. Expectations will be forced to differ.
100
90
Numbers Attending
80
70
60
50
40
30
20
10
0
0
20
40
60
80
100
Time
Figure 1:
Bar attendance in the first 100 weeks.
In 1993, I modeled this situation by assuming that as the agents visit the
bar, they act inductively—they act as statisticians, each starting with a variety of subjectively chosen expectational models or forecasting hypotheses. Each
week they act on their currently most accurate model (call this their active
predictor). Thus agents’ beliefs or hypotheses compete for use in an “ecology”
these beliefs create.
Computer simulation (Figure 1) showed that the mean attendance quickly
converges to 60. In fact, the predictors self-organize into an equilibrium ecology in which, of the active predictors, 40% on average are forecasting above
60 and 60% below 60. This emergent ecology is organic in nature, because
although the population of active predictors splits into this 60/40 aver-
age ratio, it keeps changing in membership forever. Why do the predictors
self-organize so that 60 emerges as average attendance and forecasts split
into a 60/40 ratio? Well, suppose 70% of predictors forecasted above 60 for a
longish time, then on average only 30 people would show up. But this would
validate predictors that forecasted close to 30, restoring the ecological bal-
ance among predictions. The 40%/60% “natural” combination becomes an
comPlexi t y and t He economy [ 185 ]
emergent structure. The Bar Problem is a miniature expectational economy with complex dynamics ( 12).
One important application of these ideas is in financial markets. Standard
theories of financial markets assume rational expectations—that agents
adopt uniform forecasting models that are on average validated by the
prices these forecast ( 13). The theory works well to first order. But it doesn’t account for actual market anomalies such as unexpected price bubbles and
crashes, random periods of high and low volatility (price variation), and the
heavy use of technical trading (trades based on the recent history of price
patterns). Holland, LeBaron, Palmer, Tayler, and I ( 14) have created a model that relaxes rational expectations by assuming, as in the Bar Problem, that
investors cannot assume or deduce expectations but must discover them.
Our agents continually create and use multiple market hypotheses—indi-
vidual, subjective, expectational models—of future prices and dividends
within an artificial stock market on the computer. These “investors” are
individual, artificially intelligent computer programs that can generate and
discard expectational hypotheses and make bids or offers based on their
currently most accurate hypothesis. The stock price forms from their bids
and offers and thus ultimately from agents’ expectations. So this market-in-
the-machine is its own self-contained, artificial financial world. Like the bar, it is a mini-ecology in which expectations compete in a world those expectations create.
Within this computerized market, we found two phases or regimes. If
parameters are set so that our artificial agents update their hypotheses slowly, the diversity of expectations collapses quickly into homogeneous rational
ones. The reason is that if a majority of investors believes something close to the rational expectations forecast, then resulting prices will validate it, and deviant or mutant predictions that arise in the population of expectational
models will be rendered inaccurate. Standard finance theory, under these
special circumstances, is upheld. But if the rate of updating of hypotheses is increased, the market undergoes a phase transition into a complex regime and
displays several of the anomalies observed in real markets. It develops a rich psychology of divergent beliefs that don’t converge over time. Expectational
rules such as “if the market is trending up, predict a 1% price rise” that appear randomly in the population of hypotheses can become mutually reinforcing: If enough investors act
on these, the price will indeed go up. Thus sub-
populations of mutually reinforcing expectations arise, agents bet on these
(therefore technical trading emerges), and this causes occasional bubbles and
crashes. Our artificial market also shows periods of high volatility in prices, followed randomly by periods of low volatility. This is because if some investors discover new profitable hypotheses, they change the market slightly,
causing other investors to also change their expectations. Changes in beliefs
therefore ripple through the market in avalanches of all sizes, causing periods
[ 186 ] Complexity and the Economy
of high and low volatility. We conjecture that actual financial markets, which show exactly these phenomena, lie in this complex regime.
After two centuries of studying equilibria—static patterns that call for no
further behavioral adjustments—economists are beginning to study the gen-
eral emergence of structures and the unfolding of patterns in the economy.
Complexity economics is not a temporary adjunct to static economic theory
but theory at a more general, out-of-equilibrium level. The approach is making itself felt in every area of economics: game theory ( 15), the theory of money and finance ( 16), learning in the economy ( 17), economic history ( 18), the evolution of trading networks ( 19), the stability of the economy ( 20), and political economy ( 21). It is helping us understand phenomena such as market instability, the emergence of monopolies, and the persistence of poverty
in ways that will help us deal with these. And it is bringing an awareness that policies succeed better by influencing the natural processes of formation of
economic structures than by forcing static outcomes.
When viewed in out-of-equilibrium formation, economic patterns some-
times fall into the simple homogeneous equilibria of standard economics.
More often, they are ever changing, showing perpetually novel behavior and
emergent phenomena. Complexity therefore portrays the economy not as
deterministic, predictable, and mechanistic but as process dependent, organic, and always evolving ( 22).
Complexity and the Economy Page 33