that this broad tent view contains four successive approaches based on nonlinear
dynamics:7 cybernetics (Wiener, 1948), catastrophe theory (Thom, 1975), chaos theory
(Dechert, 1996), and “small tent” (or heterogeneous agent-based) complexity. This latter
is identified with approaches coming initially out of Brussels (Nicolis and Prigogine,
1977), Stuttgart (Haken, 1983), and the Santa Fe Institute, with Schelling (1971) being
another predecessor. This approach emphasizes dispersed and interacting, heterogeneous
agents (Arthur, Durlauf, and Lane, 1997; Hommes, 2006; Tesfatsion, 2006), and for
many economists this is what they mean when they refer to “complexity models.”
Arthur, Durlauf, and Lane (1997, pp. 3-4) provide a summary of this approach
through six characteristics: 1) dispersed interaction among heterogeneous agents,8 2) no
global controller in the economy, 3) cross-cutting hierarchies with tangled interactions, 4)
continual adaptation and learning by evolving agents, 5) perpetual novelty, and 6) out-of-
equilibrium dynamics with no presumption of optimality. This approach is seen as
implying bounded rationality, not rational expectations, as noted above.
Finally we come to our third definition, that of computational complexity. While
advocates of this approach emphasize its greater degree of precision, we shall also keep
this to a more general level, as there are many different varieties of this concept, with
7 It is generally argued that dynamically complex systems must be nonlinear, although not all nonlinear
systems are complex. However, Goodwin (1947) showed that coupled linear systems with lags could
exhibit what are described as complex dynamics, although the normalized equivalent of such a system is
nonlinear, and Turing (1952) used such systems to develop his idea of morphogenesis.
8 While it is generally argued that all this contradicts general equilibrium theory, Arrow has argued that
“One of the things that microeconomics teaches you is that individuals are not alike. There is heterogeneity,
and probably the most important heterogeneity here is heterogeneity of expectations. If we didn’t have
heterogeneity, there would be no trade. But developing an analytic model with heterogeneous agents is
difficult” (Colander, Holt, and Rosser, 2004a, p. 301) This reminds us that while current macroeconomists
like to describe their models as being “Walrasian,” their assumptions of representative agents with rational
expectations are far simpler than the assumptions in the Arrow-Debreu general equilibrium framework.
Curiously, some of the greatest criticisms of the Arrow-Debreu general equilibrium framework have come
from its own developers, as with the Sonnenschein-Mantel-Debreu Theorem (Debreu, 1974).