FRONTIERS OF ECONOMICS IN THE POST-NEOCLASSICAL ERA
J. Barkley Rosser, Jr.
James Madison University
rosserjb@jmu.edu
June, 2008
1
I. Introduction
The most important fact about 21st century economics is that it is the postneoclassical era in terms of the frontiers of economic research. One can still find
orthodox, neoclassical theory in most textbooks, especially those at the upper
undergraduate level. However, this no longer reflects the reality of how economists at
the cutting edge of economics are thinking, including those who are in the mainstream of
the profession. The intellectual orthodoxy of neoclassicism has died (Colander, 2000)
and the current thrust of research at the cutting edge of the frontier is the search for the
appropriate alternative to replace it.
It is useful at this point to distinguish between certain categories, following
Colander et al. (2004), notably “orthodoxy,” “mainstream,” and “heterodoxy.” In their
view, now gaining acceptance among many observers (Bateman, 2008), orthodoxy is an
intellectual category, an established structure of ideas or a paradigm, with the
neoclassical orthodoxy being characterized by the trinity of rationality, greed, and
equilibrium. Mainstream is a sociological category, the set of leading individuals in the
profession who control the leading universities, research institutions, journals, and other
centers of power and control. However, heterodoxy is both, with the heterodox both
opposing the dominant intellectual orthodoxy and also operating sociologically on the
fringes or margins of the profession, alienated from the mainstream leaders, sometimes
even to the point of persecution or suppression.1 The crucial point here is that during a
1
A fairly notorious recent example of such suppression has been the case of the well-known heterodox
economics department at Notre Dame University in the United States, where in 2003, the administration
took away the graduate program from the department and gave it to a newly created department openly
described as being “neoclassical.” A number of prominent mainstream economists protested this move
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period of upheaval when an established orthodoxy has died and is being replaced, the
mainstream can and will step aside from it and pursue this effort, not being tied to any
particular paradigm necessarily. During such periods, they may be open to drawing on
ideas from heterodox schools or approaches, if not always fully acknowledging doing so,
and the cutting edge or frontier of the profession may well be near the interface between
the mainstream and the heterodox.2
Now it must be recognized that many economists, quite possibly most
economists, do not recognize that neoclassical economics has died. However, I argue
that the case is easily made that it has for those at the cutting edge of the frontier, even if
no single new paradigm has clearly arisen to replace it. It is this latter fact that probably
serves most to continue the illusion for many that neoclassical economics has not died
(along with its persistence in lower level textbooks, where change is slow). Another
issue involves both when it died and how.
Colander (2000) pushes the date too far into the past for my taste, arguing in
effect that neoclassical economics was simply the marginalist economics that became
prominent in the German, French, and English language traditions starting in the 1870s
(with the Germans having been ahead of the others), and which culminated with the
publication of Samuelson’s (1947) Foundations of Economic Analysis. In this view, such
subsequent developments as Nash’s (1951) non-cooperative game theory and the closely
related Arrow-Debreu (1954) general equilibrium theory represented a move beyond
(along with many more heterodox ones, unsurprisingly), with Robert Solow being a prime example
(McCloskey, 2003).
2
It must be noted at this point that the heterodox have formed their own schools, of which there are many
quite well known and established ones, such as Marxism, Institutionalism, Post Keynesianism, and
Austrianism, among others. These schools can in turn create their own sub-orthodoxies, with their own
sub-mainstreams that may well enforce their orthodoxies through specialized journals and selected
universities or research entities where followers of these schools may predominate and enforce their views
on potential “heretics.”
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neoclassicism proper to something else. Certainly the case can be made for this view,
and it is arguably more consistent from a history of economics perspective.
However, for most economists the efforts carried out at such institutions as MIT
to marry this earlier marginalist Samuelsonianism with the later developments was
successful as epitomized by such widely used graduate textbooks as Varian (1992). In
this latter view, the highwater mark of neoclassical orthodoxy came in the 1970s and
early 1980s with the spread in macroeconomics of New Classical micro-founded models
assuming homogeneous (or at least representative) agents possessing rational
expectations. These models assumed Walrasian general equilibrium to hold,3 with the
macro-model simply reflected at large the micro-solution for this representative agent,
thereby overcoming the aggregation problems long posed by such observers as Keynes
(1936) with the well-known fallacy of composition.4 In this view it would be a series of
external shocks and events that would break this orthodoxy down, ranging from the
unexpected stock market crash of 1987 through the collapse of the Soviet Union and its
command socialist empire, through to a further series of financial crises in the late 1990s
and at the turn of the century, accompanied by a series of intellectual discoveries and
breakthroughs that would undermine this orthodoxy, including perhaps most importantly,
the repetition of results and findings in experimental economics that served to ultimately
3
Because of the emphasis on specifically Walrasian general equilibrium in these models, Colander (2006)
has argued for successor approaches in macroeconomics to be labeled “Post Walrasian.” Hoover (2006)
defends a Marshallian approach to the relationship between theory and empirics, with the Walrasian
approach being an “engineering” approach whereas the Marshallian is “archeological” and exemplified by
the econometric methods of Hendry and Krolzig (2001), with Colander (1995) also holding up Marshall as
exempt from many of the alleged sins of Walras. Hoover sees Milton Friedman as defending a Marshallian
methodology against the Walrasianism of Robert Lucas. It should also be noted that whereas “Post
Keynesian” refers to people who admire Keynes, “Post Walrasian” refers to critics of Walras.
4
Arguably the most serious criticisms based on aggregation problems came out of general equilibrium
theory itself, with Debreu (1974) contributing substantially to the analysis of the famous SonnenscheinMantel-Debreu results that showed serious limits to the theory in the aggregate. This would later culminate
in studies showing how even when there exists a representative agent, aggregate behavior may not
correspond to that of this representative agent (Kirman, 1992).
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undermine this all-knowing, rational individual agent, even if the difficult aggregation
problems could be overcome.
While many experiments would be done that would contribute to the undermining
of the orthodoxy of rationality, greed, and equilibrium (or at least the first two), arguably
the most stunning and influential was the ultimatum game experiment by Güth et al.
(1982). In this experiment, an agent has a sum of money to offer to divide with another
agent. The first agent suggests a division. If the second agent accepts it, they each get
the agreed-upon amounts. However, if the second agent rejects the (ultimatum) offer,
then neither gets anything. The Nash equilibrium is for the first agent to offer the
minimum possible amount, and for the second agent to accept the offer.5 In fact, it is
now well established that generally smaller offers are rejected, and that in the US the
median offers are around 40% of the total, with the modal offer being an even split, and
with most offers less than 20% being rejected, supposedly “irrationally.” Explaining this
result has been the foundation for an enormous amount of ongoing research that has
brought in other disciplines such as psychology into economics.
Another strand of economics that had been developing through the latter part of
the 20th century was complexity economics (Rosser, 1999), which also implied serious
limits to the ability of individuals to rationally assess the economic environment.6 The
combination of these results has led to the revival of an older idea of economics, bounded
More precisely, if the experiment is repeated it is Selten’s (1975) extension of the Nash equilibrium to the
repeated games case, sub-game perfect equilibrium, that is violated, with an irony being that it has been
reported by Ken Binmore (Colander, Holt, and Rosser, 2004, p. 53) that it was Selten himself who
suggested the ultimatum game experiment to Güth. There is evidence that repeating the game or putting it
into a two-stage form, offers and acceptances may become closer to the Nash equilibrium (Binmore et al.,
1985).
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Davidson (1996) and Rosser (2006) have debated the source of such limits, with Davidson arguing that it
is ontological and axiomatic, with complexity-based theories providing merely epistemological elements as
in the inability of people to compute. Rosser responds that while such factors enter in, complexity in fact
amounts more profoundly to an ontological explanation of its own for fundamental uncertainty.
5
5
rationality, first proposed by Herbert Simon (1957). This combination has also led to a
broader trend that has emerged strongly since the turn of the century, an ever-increasing
influence of other disciplines in economics, ranging from other social sciences such as
psychology and sociology to natural sciences such as physics and biology, as well as the
emerging computer sciences. All of this has led to a push for higher-order
transdisciplinary approaches.
The rest of this paper will focus on these three main themes with some subthemes in each section. First, we shall consider more seriously developments in
experimental and behavioral economics, with neuroeconomics being an especially recent
and promising area arising from these two. Second we shall look at various ideas
associated with the complexity movement, such as agent-based modeling, computational
economics, and econophysics. Implications for this for a successor to the New Classical
approach to macroeconomics will be examined. Then, we shall consider more
biologically based approaches drawing on evolution and ecology, suggesting a revival of
sorts of institutional economics, but in new forms as major areas of focus at the current
cutting edge of the frontiers of economics. Finally, there will be a brief consideration of
the role of the older schools of heterodox schools of thought in the newer developments.
II. Experimental and Behavioral Economic Research
A. Market Mechanisms and a Partial Defense of Orthodoxy
While we have already noted that there are many results coming out of economic
experiments that question the traditional vision of the neoclassical homo oeconomicus,
some strands of experimental economic research have produced results that can be argued
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to support the ability of properly structured free markets to reach reasonably efficient
equilibria despite these apparent findings about individuals. The key person arguing this
point has been the “father of experimental economics,” Vernon Smith ever since his
finding in 1962 that double auction markets converge very rapidly to equilibria, with this
result being reinforced and found to be efficient and robust by many later studies
(Friedman, 1974). Smith has since become a strongly pro-free market advocate and has
been involved in setting up many actual auction markets, and the double auction has
spread widely into many financial markets (Smith, 2008). Walrasian general equilibrium
may have serious problems, but individual markets, even ones linked with another market
or two, can be set up to function quite well in terms of equilibrating.
Even as Smith has argued this point for decades, he has not argued against the
findings of all sorts of irrationalities or peculiarities in individual behavior, nor has he
argued that all markets everywhere behave well or efficiently. Thus, he was one of the
first to show that speculative bubbles and crashes rather easily happen in experimental
markets, even if learning tends to reduce them (Smith et al. 1988). This result was found
to still hold even when experimental subjects had to provide their own money for the
market activity (Porter and Smith, 1995). Indeed, even though double auctions work
well, many real-world auctions are not easy to set up to follow them, and while Smith and
his allies have argued for simpler rules for large-scale auctions (Banks et al., 2003), many
have not followed this advice, such as in setting up the US power spectrum auctions.
This raises what has been an increasing concern for Smith and his coauthors over
time: how to reconcile this apparent irrationality of individual agents with their ability in
at least certain kinds of situations to act together in an apparently rational and efficient
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way. In this he has increasingly fallen back on arguments of Adam Smith and Friedrich
Hayek regarding markets as emergent spontaneous orders, and the idea that even though
people have bounded rationality, they are able to intuitively operate in market settings to
achieve efficient results, even as their conscious minds are not carrying out the necessary
calculations. People’s brains and minds have evolved to do these sorts of things, even if
unconsciously (Smith, 2008) as part of more generalized reciprocity, which is
evolutionarily advantageous.
In this regard, while arguing that boundedly rational people can achieve efficient
outcomes in the right institutional setups through intuition or rules of thumb, Smith and
his coauthors have directly confronted traditional game theory that posits high levels of
rationality to individual decisionmakers. Thus, Aumann (1995) has long argued for
assuming common knowledge, with its implication that people regularly use backward
induction to decide how to behave strategically when interacting with others. Such
backward induction depends on believing that others also are thinking ahead and
calculating the best possible responses of other agents into the distant future in response
to possible actions by oneself. As it is, the experimental evidence suggests that most
people do not think very far ahead in such situations (Stahl and Wilson, 1995; Camerer,
2003), and that backward induction is thus largely a purely theoretical construct.
The accumulation of this evidence has put game theory on the defensive. Major
developments coming out of this has been the emergence of both evolutionary game
theory (Binmore and Samuelson, 1999), with its greater emphasis on random forces
pushing agents into different basins of attraction over time and behavioral game theory
that recognizes that agents are not fully rational or perfectly informed (Camerer, 2003).
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B. Social Preferences and Other Complications
While there had been a long series of experiments documenting the ubiquity of
“anomalies” that undercut the standard model of the rational economic agent, particularly
the expected utility model of decisionmaking under risk (Strotz, 1955; Kahneman and
Tversky, 1979; Thaler, 1981), it was probably ultimately the ultimatum game
experiments mentioned above and the repeated verification of their findings that most
seriously drove the nail into the coffin of the greedily individualistic, rational economic
agent. People were regularly willing to bear costs to punish each other for violating
norms of fairness (Rabin, 1993). This argued for the serious introduction of
psychological and sociological ideas into economics, something which had been
regularly done before the middle of the 20th century, but which had fallen out of fashion
as it was thought that the rational agent model of economics offered the superior
paradigm for the social sciences more broadly. In particular Rabin and others argued that
people have a “taste for fairness” that must be accounted for by economists and which
goes against the standard model of simple greedy maximization.
Ironically this has set up a somewhat curious debate over how best to deal with this
matter. On the one hand is a group led by Rabin, more or less, that argues against the
conventional approach by asserting the reality of the taste for fairness, which may
somehow be viewed as a kind of selfless altruism.7 However, the approach taken by
Rabin is in another sense highly conventional; he assumes a conventional sort of utility
function that an individual maximizes subject to a budget constraint, with that utility
function simply having an additional argument: fairness, which then must be traded off
against other more standard such arguments in the utility maximization calculus. In this
7
Andreoni (1990) has labeled this purer altruism as the “warm-glow effect.”
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regard, Rabin in his interview in Colander et al. (2004, p. 151) expressed the side of his
views that believes in a more conventional approach.
“In fact, I have various fears about teaching psychological economics. One is of
attracting graduate students who are just hostile to economics. Another is all the people
who want to use evolution and other approaches to explain departures from classical
models rather than using evidence of departures to do better economics.”
This last sentence describes those taking the alternative view, which would include
Vernon Smith (2008) as well as some from the evolutionary game theoretic school such
as Binmore, as expressed in Colander et al., 2004. pp. 65-66, where he complains of
people assuming “exotic preferences” not defensible by evolutionary processes. While
Binmore tends to defend somewhat more conventional approaches, as with his
questioning of the robustness of the ultimatum game findings, Smith pushes a
methodologically more unconventional position, rejecting standard utility maximization
modeling, indeed of assuming a utility function at all. The evidence of people’s lack of
standard calculating and conscious optimization is too strong to be ignored. In the end,
this group argues for assuming an ultimate more selfish approach, that of some form of
reciprocity, even if it is distant and indirect. They argue that this is defensible as having
arisen from evolutionary processes, even if the mind makes the necessary calculations in
the sort of unconscious way described earlier above. It is an ultimately “selfish”
reciprocity motive that underlies ultimatum game results, not some vaguely selfish
altruism or inequity aversion.8
8
This view is also identified with the term reciprocal altruism introduced by the evolutionary biologist,
Robert Trivers (1971).
10
A response by those more willing to allow for such motives has spawned an
enormous amount of research, with Fehr and Schmidt (1999) and Bolton and Ockenfels
(2000) posing ways to distinguish reciprocity from inequity aversion in data. These
proposals have proven controversial and considerable debate has ensued regarding
whether these methods are accurate or not (Charness and Rabin, 2002; Engelmann and
Tyran, 2005). In any case, some of those supporting this approach see more generalized
forms of reciprocity, or strong reciprocity, as indeed being evolutionarily founded (Gintis
et al., 2004) and drawing on work of anthropologists as well as psychologists.9 Such
forms have come to be labeled social preferences.
C. Neuroeconomics and the Struggle of the Laboratory versus the Field
In laboratory experiments these debates have moved more deeply into the brain
itself as the use of magnetic resonance imaging (MRI) has come to be used in economic
experiments to see which parts of the brain are stimulated and how when agents are
engaging in various kinds of decisionmaking or actions (Zak, 2004; Camerer et al. 2005).
One of the first in economics was the study of McCabe et al. (2001) of cooperative
versus non-cooperative behavior in the prisoner’s dilemma. They found that very
different parts of the brain were stimulated when agents were engaging in one or the
other. Interestingly, whereas Nash originally posited that the selfishness of not
cooperating is “rational,” it is when agents are cooperating that they appear to be using
At a certain level this debate can be seen as another round of the old “Adam Smith problem,” how to
reconcile the Adam Smith of The Theory of Moral Sentiments (1759) with the apparently harder nosed
Adam Smith of The Wealth of Nations (1776) Vernon Smith (1998) draws on Hayek to say that it is a
matter of personal dealings within more closely knit groups where moral sympathy predominates versus
more arms-length dealings in larger society as in markets where reciprocity and ultimate selfishness
predominates.
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the pre-frontal cortex parts of their brains that are more usually identified with “higher”
or more “rational” thought by psychologists.
Given that such hard-wiring of the brain is almost certainly the result of deep
evolutionary processes, the debates over reciprocity and altruism have more recently
moved into the laboratories of the neuroeconomists. Thus, Fehr and Gächter (2002) and
Fehr et al. (2002) argue strongly that strong reciprocity involves a pleasure reward in the
brain associated with punishing those who violate social norms. Zak (2005) has
identified the development of trust as being associated with the chemical oxytocin, which
is released in the brain and provides a sensation of pleasure. Zak (2008) and his
associates have pushed this argument to say that oxytocin release and reinforcement of
socially virtuous behavior serves as the foundation of broader morality and social
cohesion within market economies..
Left unresolved here is the degree to which we can associate stimulation of
specific areas of the brain with particular psychological states or perceptions.
Furthermore, there also remains the issue of whether or not what is found in the
laboratory really reflects what goes on in reality, or “in the field.” This has led to deep
debates over the use of laboratory experiments versus so-called field experiments (Levitt
and List, 2007). Advocates of the former stress the ability to more scientifically pin
down circumstances and eliminate extra “noise,: even as advocates of the latter argue that
in laboratories important framing effects can arise from the influence of the
experimenters themselves that can influence and bias the results. A compromise would
seem to be that the two approaches are complementary, but this is a matter of ongoing
dispute, just as is the matter of the degree to which the results of neuroeconomics studies
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of which parts of the brain are associated with what kinds of decisions really carry over
into reality. In any case, all of those involved in experimental economics hope to achieve
a more truly scientific approach to the studying and understanding human behavior.
III. The Complex Implications of Economic Complexity
A. The Complexity Problem
While both the behavioralist and complexity approaches profoundly undermine
the fully rational and informed and selfish homo oeconomicus of neoclassical economics,
especially in its stricter Walrasian form, they have developed and operated largely
independently. However, they had a common link at the foundation of behavioral
economics with Herbert Simon, already mentioned as the inventor of the bounded
rationality hypothesis. He was also an early developer of complexity theory, especially
its hierarchical version (Simon, 1962). Simon saw the deep link between complexity and
behaviorialism through the role of complexity as a foundation for bounded rationality. It
should be kept in mind that Simon’s later innovative research efforts in pursuit of the
ideal of artificial intelligence was motivated deeply by his awareness of bounded
rationality and its foundation in the inevitable and unavoidable reality of complexity.
Rosser (2008a) poses three levels of thinking about the nature of complexity. At
the highest level is meta-complexity, the broadest conception, which allows for the 45
definitions of Seth Lloyd (Horgan, 1997, p. 303)10 as well as others. Next down is the
dynamic definition provided in Rosser (1999), taken from Day (1994). This “big tent”
definition is that a system is (dynamically) complex if it deterministically and
endogenously exhibits irregular dynamics that do not converge on a point, a limit cycle,
10
Horgan is a critic of the notion in most of its forms and coined the term chaoplexity partly to mock it.
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or a smooth growth or decline path (thus ruling out irregularities due to the exogenous
shock noise that drives real business cycle models). This “big tent” definition includes
“the four C’s” of cybernetics, catastrophe theory, chaos theory, and the “small tent”
complexity of heterogeneous interacting agent models. It is this last type that constitutes
our lowest level and is what most people think of when they think of “complexity
economics.” This last approach has often been associated with the Santa Fe Institute and
such computer simulation methods as cellular automata (Wolfram, 1984) and artificial
life programs (Langton, 1990; Tesfatsion, 2006).
Of the other definitions of complexity that one can find at the meta-complexity
level, probably the most important one in terms of current research are those based on
computability (Markose, 2005; Velupillai, 2005). There are a variety of these, most of
them ultimately drawing on the information theory of Shannon (1948) and its further
development by Kolmogorov (1965), Chaitin (1987), and others. Although there are
competing versions of these definitions and measures, such well-studied divisions as
between programs that are solvable in polynomial time versus in exponential time versus
those that cannot be solved at all in finite time due to halting problems (Blum et al.,
1998). All of these in some way or another end up being related to the minimum length
of the program required to compute a solution to a problem or system, and while there are
variations, these provide more specifically measurable degrees of complexity. It is this
latter fact (along with the increasing spread of computational economics in various
forms) that has added to the popularity more recently of this sort of definition. Although
this approach now has many followers, it was probably first applied in economics by
Albin (1982), with full discussion in Albin with Foley (1998).
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B. The Agent-Based Approach
This is one of the most productive and promising areas of current research at the
frontiers of economic research, although Tesfatsion and Judd (2006) provides broad and
in-depth coverage across many areas of economics and Delli Gatti et al. (2008) provide
excellent coverage for macroeconomics more particularly. Among the more useful of the
surveys in Tesfatsion and Judd are those on agent-based models in economics and
computational finance by Hommes (2006) and by LeBaron (2006) and also the one by
Duffy (2006), which examines links between the heterogeneous agent-based approaches
and the behavioral and experimental approaches we have discussed above. An early
approach that has been widely imitated for modeling broader societal development from
agent-based modeling is Epstein and Axtell (1996).
General theoretical modeling of interacting agent-based systems has been done by
Brock and Hommes (1997) and Brock and Durlauf (2001).11 These papers provided a
foundational approach based on mean-field dynamics drawn from statistical physics.
Central to the analysis of these nonlinear systems is consideration of the structure of
bifurcation sets and various forms of complex dynamics that arise as the system crosses
bifurcation. The complex dynamics extend well beyond just complex dynamics to
involve multiple basins of attraction and fractal basin boundaries of these basins.12 The
crucial control parameters determining the bifurcation structures in this set of models turn
out to be degree of interaction between the agents (willingness to herd) and their
willingness to change strategies, with more complex dynamics more likely as the values
11
Föllmer (1974) was the first to present a model of equilibrium of heterogeneous agents based on a
statistical mechanics approach, long before the establishment of the Santa Fe Institute or the development
of econophysics. Aoki and Yoshikawa (2006) show how the approach can be used in macroeconomics.
12
For a fuller analysis of systems with multiple basins of attraction with fractal boundaries and multidimensional chaotic dynamics using global analysis, see Agliari et al. (2002).
15
of these parameters increase. Brock et al. (2008) show how a model based on this
framework can be used to analyze the destabilization of financial markets as hedging
instruments increase, a result counter to that of standard financial economics theory.
Gallegati et al. (2008) also use a variation of this to study financial market dynamics with
the imposition of a Minsky (1972) type of financial constraint that allows for showing the
phenomenon of a “period of financial distress” between the peak and the crash of a
speculative bubble that is the most common pattern seen in historical bubbles
(Kindleberger, 2000, Appendix B), even though again such a pattern has not been
modeled by conventional economic theory. Föllmer et al. (2005) are able to get
somewhat similar results with a related agent-based model.
Agent-based models have also been used to model more specific market dynamics
not involving finance. So the evolving structures of loyalty in a market have been studied
by Kirman and Vriend (2001). How market structures relate to technological change has
also been a major area of study. Fagioli and Dosi (2003) have studied innovation
dynamics on a two-dimensional lattice with a variety of effects and processes. Silverberg
and Verspagen (2005) have looked at the diffusion process in more detailed in a variety
of technology spaces. Dawid and Reimann (2004) have used genetic algorithms to
examine innovation in relation to product life cycles.
A major thrust of many agent-based models has been to study learning dynamics.
This is an area where the agent-based complexity approach has intersected with the
experimental behavioral approach, with experiments increasingly involving subjects
interacting with computerized systems in repeated games or market interactions in which
learning takes place. Probably the first such in this line was Roth and Murnighan (1978)
16
who had subjects playing repeated Prisoners’ Dilemma games against computerized
opponents. Arifovic (1996) had experimental subjects using genetic algorithms to learn
about foreign exchange rate dynamics. She (2001) would later find that boundedly
rational agents could do better than fully rational agents in a complex context. Bullard
and Duffy (2001) studied how learning dynamics can lead to excess volatility, and
Brenner and Witt (2003) further studied game dynamics with learning. Nyarko and
Schotter (2002) saw how eliciting beliefs could enhance learning in laboratory subjects.
Perhaps the ultimate result involves zero-intelligence computerized agents that
nevertheless “learn” in a certain sense to move toward a double auction equilibrium
(Gode and Sunder, 1993). This result can be seen as underpinning the spread of
completely computerized exchanges without human actors, which fully make manifest
the prediction of Mirowski (2007) that markets simply are algorithms that evolve to
become what he labels markomata.
Finally, another area of current interest for studying agent-based models has been
in the emerging area of network analysis. This work, with close links to sociology
derives largely from the study of Watts and Strogatz (1998), but is now burgeoning
widely. Kirman and Vriend (2001), mentioned above, is an example in terms of
networks of market relations. Kranton and Minehart (2001) also study networks in
market relations. A general finding of this literature is that clusterings occur in patterns
that are neither completely random nor fully concentrated. The famous “small worlds”
phenomenon, sometimes described by the famous claim that no two people in the world
are separated by more than six degrees of separation.
B. Econophysics
17
A term coined by H. Eugene Stanley in the mid-1990s, econophysics has been
described by Mantegna and Stanley (2000, vii-ix) as the “multidisciplinary field…that
denotes the activities of physicists who are working on economic problems to test a
variety of new conceptual approaches deriving from the physical sciences.” This
sociologically oriented definition emphasizes who is doing it more than what it is. In
practice much emphasis has been on looking at data first and then trying to find models
that fit the data, in contrast with the usual economics approach of assuming that the
standard theory is generally correct and then applying it to data to see if it or the data can
be sufficiently tweaked to find a matchup. A major focus of much of the econophysics
research has been upon power law distributions that are linear in the mapping of logged
relationships between variables. In terms of returns in financial markets, such power
laws are associated with the presence of more extremal events than would be predicted if
the distribution were Gaussian normal, so that one observes kurtosis or “fat tails.” Many
of the models that the econophysicists bring to bear can be seen as variations on
heterogeneous agent models as many are drawn from statistical mechanics models of
interacting particles. They are thus linked to the broader “small tent” complexity
approach that emphasizes such interacting heterogeneous agent models. The most
fervent defenders of the approach (McCauley, 2004) argue for its superiority over
economic models because of their lack of invariance laws.
Prominent applications in financial models included Bouchaud and Cont (2002),
Farmer and Joshi (2002), and Sornette (2003). Wealth distributions have also been found
to have power law distributions (Levy and Solomon, 1997), although income
distributions appear to have such only at their upper ends (Drăgolescu and Yakovenko,
18
2001; Chatterjee et al. 2005).13 City size distributions have also been estimated by such
means (Gabaix, 1999) as have firm sizes (Axtell, 2001).
A curious aspect of this is that many of these ideas were first developed by
economists, whereas some of the more conventional ideas used by standard economic
theory originated from physicists, an old argument of Mirowski (1989). Thus the first to
suggest the use of power laws for studying income distribution was Pareto (1897).
Whereas the idea of normal distributions of financial returns was initiated by the
mathematician Bachelier (1900), this would become a standard idea in physics as
Brownian motion, and the physicist Osborne (1959) would later suggest its use in
financial economics, which then became standard. It was the mathematician Mandelbrot
(1963) who first suggested applying power laws to asset returns. It was a geographer
who would first suggest that city sizes might be distributed according to a power law
(Zipf, 1941), and Ijiri and Simon (1977) did so for firm sizes a quarter of a century before
Simon’s student Axtell (2001) would confirm this finding. Furthermore, the
mathematical economist Föllmer (1974) suggested applying statistical mechanics models
to studying markets well before the physicists did, and the economist, Duncan Foley
(1993) applied entropy theory to define statistical distributions of prices as a new concept
of equilibrium to replace the neoclassical one.
Given this tangled history it is not surprising that econophysics has engendered
controversy. Gallegati et al. (2006) criticized much work as not properly citing previous
work by economists, as using shoddy statistical methods, asserting universal laws where
13
It has long been argued that labor income tends to be distributed lognormally. To the extent that wealth
represents mostly accumulated capital income, and financial markets show power law distributions, then it
may be perfectly reasonable for the lower part of the income distribution to be lognormal, where labor
income is most important, while the upper end is power law where wealth and capital income predominate.
19
none apply, and lacking in theoretical models or explanations for findings. Rosser
(2008b) argues that most of these criticisms had some merit, but that they are being
overcome or can be by having economists and physicists work together, with Foley
(1993) providing an example of a theoretical model drawn from physics that is of
relevance for explaining economic phenomena. However, Lux (2009) warns that
physicists may get led astray if they work with economists whose ideas are too
conventional, with some econophysicists embarrassingly making incorrect public
forecasts based on inappropriate models drawn from economics.
C. Econobiology
In contrast to econophysics, econobiology is not a self-identified entity created by
its practitioners but rather a term of disapprobation assigned by critics such as McCauley
(2004, chap. 9), who sees biology lacking in invariance laws in the same way that
economics does and that therefore it cannot be a real science in the way that physics
is.(and econophysics might be). However, we can identify at least three sub-areas of
what might be called econobiology that have their own distinct and identities:
evolutionary economics, bioeconomics, and ecological economics.
Of these the first is certainly the oldest in terms of identity, with old institutional
economists taking up the term and the identity (Veblen, 1898) and economics and the
theory of evolution having a complicated interrelationship throughout much of the
nineteenth century as Malthus influenced Darwin, who in turn influenced both Marx and
Marshall (Rosser, 1991, chap. 12). As old institutionalism lost its struggle with
neoclassical economics (Veblen having coined the term, “neoclassical economics”), and
new institutional economics became more important, evolutionary economics fell from
20
favor and attention, although arguments relating to evolution continued to be made in
various parts of economics such as the theory of firms and how they change over time
and in the theory of technological change, although Schumpeter (1936) favored a more
discontinuous view of evolution that contrasted with Darwin and foreshadowed the
punctuated equilibrium theory of Stephen Jay Gould (2002).
However, evolutionary economics is experiencing a revival along two lines. One
is the already discussed area of evolutionary game theory, which has now become the
leading edge of game theory. The other is in work that seeks to overcome the divide
between the old and new institutionalist schools. This approach has been pushed by
Hodgson (2006) who sees in modern evolutionary theory as it has come to be after the
innovations of Gould and others a fresh paradigm for use in economics.
Arguably the latter two are simply variations on each other, although
bioeconomics is the older term, dating to its introduction by Colin W. Clark in 1976,
whereas ecological economics came into usage in the 1980s (Martinez-Alier, 1987).
Both can be viewed as transdisciplinary disciplines (indeed the ecological economists
specifically label themselves as such). Both seek to integrate fully models of biology or
ecology with those of economics. The former are more likely to more specifically model
population dynamics of biological populations in conjunction with the impact of
interactions with economic agents. Clark’s work on fisheries is the model here, and the
fact that supply curves for fish tend to bend backwards opens up the door to a variety of
possible nonlinear and complex dynamics in fisheries, including catastrophic collapses
(Rosser, 2001; Gunderson and Holling, 2002),which we have observed all too many
times in real life unfortunately.
21
Forestry has long been an area of study as well by bioeconomists and ecological
economists, using a variety of methods (Kant and Berry, 2005). The study of both
fisheries and forestry are seen as increasingly important given the role these sectors play
in developing countries and in the pressure that they are both perceived to be facing at the
global level. Similarly lake systems have been studied by joint teams of ecologists and
economists (Carpenter et al. 1999). For many of these systems problems of common
property resource management are the issue (Sethi and Somanathan, 1996), which bring
into relevance the issues studied by experimental and behavioral economists regarding
the ability of people to cooperate or not cooperate, along with the old debate about multilevel evolution (Henrich, 2004). These problems arguably come to ahead in the great
question of managing the global commons in the face of man-induced global warming
(Stern, 2008), which are from easy to resolve.
IV. Conclusion
It must be noted that we have barely scratched the surface of areas of current
research at the cutting edge of economics. However, most of what has been cited here in
terms of research since the turn of the century has moved beyond the orthodox
neoclassical approach, even if much of it has been done by mainstream economists,
although the econophysicists are clearly an exception to that. We have seen that although
they are mostly separate and parallel, our two main streams of experimental/behavioral
economics and complexity economics do have some common roots and also have
recently seemed to intersect and interpenetrate with each other more frequently.
Complexity and bounded rationality are deeply connected with each other.
22
A final question raises itself that we are not going to attempt to answer in any depth.
This involves the nature of the relationship between this newer research and the older
heterodox schools of thought. I shall only note here in conclusion that this period of
post-neoclassical upheaval opens many doors, and there are arguably chances for some
ideas from some of these schools to enter into the current discourse, just as there is also
the chance for some of these ideas to enter into and stimulate work in these schools.
Thus, I would note Chiarella et al. (2005) as an example of Post Keynesian work that has
been strongly influenced by the currents coming from research in nonlinear complex
dynamics, just as older Post Keynesian models were sources of inspiration for some of
the earlier complex dynamics models (Rosser, 2006). Also, certainly the ideas of Keynes
are clearly more in tune with the newer behavioral economics than with the idea of fully
rational and well-informed agents that have underpinned neoclassical economics.
Finally, just as one can find roots of modern approaches in Keynes, likewise
Hayek (1978) foresaw the complexity approach, and the Austrians have long disavowed
standard equilibrium analysis, emphasizing the distinctive nature of individual economic
agents, even as their interactions may bring about a spontaneous order. In this new
environment there may even be possibilities of cross-fertilization of ideas between these
older schools of heterodox thought as they open to providing and receiving influences
from the newer post-neoclassical approaches (Koppl and Rosser, 2002).
References
Agliari, Anna, Gian-Italo Bischi, and Laura Gardini. 2002. “Some Methods for the
Global Analysis of Dynamic Games Represented by Iterated Noninvertible Maps.” In
Tönu Puu and Irina Sushko, eds., Oligopoly Dynamics: Models and Tools. Heidelberg:
Springer, pp. 31-83.
23
Albin, Peter S. 1982. “The Metalogic of Economic Predictions, Calculations and
Propositions.” Mathematical Social Sciences 3, 329-358.
Albin, Peter S. with Duncan K. Foley. 1998. Barriers and Bounds to Rationality: Essays
on Economic Complexity and Dynamics in Interactive Systems. Princeton: Princeton
University Press.
Andreoni, James.1990. “Impure Altruism and Donations to Public Goods: A Theory of
Warm-Glow Giving.” Economic Journal 100, 464-477.
Aoki, Masanao and Hiroshi Yoshikawa. 2006. Restructuring Macroeconomics: A
Perspective from Statistical Physics and Combinatorial Stochastic Processes.
Cambridge: Cambridge University Press.
Arifovic, Jasmina. 1996. “The Behavior of the Exchange Rate in the Genetic Algorithm
and Experimental Economies.” Journal of Political Economy 104, 510-541.
Arifovic, Jasmina. 2001. “Performance of Rational and Boundedly Rational Agents in a
Model with Persistent Exchange Rate Volatility.” Macroeconomic Dynamics 5, 204-234.
Arrow, Kenneth J. and Gérard Debreu. 1954. “Existence of an Equilibrium for a
Competitive Economy.” Econometrica 22, 265-290.
Aumann, Robert. 1995. “Backward Induction and Common Knowledge of Rationality.”
Games and Economic Behavior 8, 6-19.
Axtell, Robert. 2001. “Zipf Distribution of U.S. Firm Sizes.” Science 293, 1818-1820.
Bachelier, Louis. 1900. “Théorie de la Spéculation.” Annales Scientifique de l’École
Supérieure III-I, 21-86.
Banks, Jeffrey M., Mark Olson, David Porter, Stephen Rassenti, and Vernon Smith.
2003. “Theory, Experiment and the Federal Communications Commission Spectrum
Auctions.” Journal of Economic Behavior and Organization 51, 303-350.
Bateman, Bradley W. 2008. “2007 HES Presidential Address: Reflections on the
Secularization of American Economics,” Journal of the History of Economic Thought 30,
1-20.
Binmore, Ken and Larry Samuelson. 1999. “Equilibrium Selection and Evolutionary
Drift.” Review of Economic Studies 66, 393-394.
Binmore, Ken, Avner Shaked, and John Sutton. 1985. “Testing Non-Cooperative Game
Theory: A Preliminary Study.” American Economic Review. 75, 1178-1180.
24
Blum, Lenore, Felipe Cucker, Michael Shub, and Steve Smale. 1998. Complexity and
Real Computation. New York: Springer.
Bolton, Gary E. and Axel Ockenfels. 2000. “ERC: A Theory of Equity, Reciprocity, and
Competition.” American Economic Review 90, 166-193.
Bouchaud, Jean-Philippe and R. Cont. 2002. “ A Langevin Approach to Stock Market
Fluctuations and Crashes.” European Physical Journal B 6, 543-550.
Brenner, Thomas and Ulrich Witt. 2003. “Melioration Learning in Games with Constant
and Frequency-Dependent Payoffs.” Journal of Economic Behavior and Organization 50,
429-448.
Brock, William A. and Steven N. Durlauf. 2001. “Discrete Choice with Social
Interactions.” Review of Economic Studies 68, 235-260.
Brock, William A. and Cars H. Hommes. 1997. “A Rational Route to Randomness.”
Econometrica 65, 1059-1095.
Brock, William A., Cars H. Hommes, and Florian Wagener. 2008. “More Hedging
Instruments may Destabilize Markets.” Mimeo, SSRI University of Wisconsin-Madison,
CeNDEF, University of Amsterdam.
Bullard, James and John Duffy. 2001. “Learning and Excess Volatility.” Macroeconomic
Dynamics 5, 272-302.
Camerer, Colin F. 2003. Behavioral Game Theory: Experiments on Strategic Interaction.
Princeton: Princeton University Press.
Camerer, Colin F., George Lowenstein, and Drazen Prelec. 2005. “Neuroeconomics:
How Neuroeconomics Can Inform Economics.” Journal of Economic Literature 48, 964.
Carpenter, Stephen R., Donald Ludwig, and William A. Brock. 1999. “Management of
Eutrophication for Lakes Subject to Potentially Reversible Change.” Ecological
Applications 9, 751-771.
Chaitin, Gregory J. 1987. Algorithmic Information Theory. Cambridge: Cambridge
University Press.
Charness, Gary and Matthew Rabin. 2002. “Understanding Social Preferences with
Simple Tests.” Quarterly Journal of Economics 117, 817-869.
Chatterjee, Arnab, Sudhakar Yarlagadda, and Bikas K. Chakrabarti, eds. 2005.
Econophysics of Wealth Distributions. Milan: Springer.
25
Chiarella, Carl, Peter Flaschel, and Reiner Franke. 2005. Foundations for a
Disequilibrium Theory of the Business Cycle. Cambridge: Cambridge University Press.
Clark, Colin W. 1976. Mathematical Bioeconomics. New York: Wiley-Interscience (2nd
edition, 1990).
Colander, David. 1995. “Marshallian General Equilibrium Analysis.” Eastern Economic
Journal 21, 281-293.
Colander, David. 2000. “The Death of Neoclassical Economics.” Journal of the History
of Economic Thought 22, 127-143.
Colander, David, ed. 2006. Post Walrasian Macroeconomics: Beyond the Dynamic
Stochastic General Equilibrium Model. New York: Cambridge University Press.
Colander, David, Richard P.F. Holt, and J. Barkley Rosser, Jr. 2004. The Changing Face
of Economics: Conversations with Cutting Edge Economists. Ann Arbor: University of
Michigan Press.
Davidson, Paul. 1996. “Reality and Economic Theory.” Journal of Post Keynesian
Economics 18, 479-508.
Dawid, Herbert and M. Reimann. 2004. “Evaluating Market Attractiveness: Individual
Incentives vs. Industrial Profitability.” Computational Economics 24, 321-355.
Day, Richard H. 1994. Complex Economic Dynamics, Volume I: An Introduction to
Dynamical Systems and Market Mechanisms. Cambridge: MIT Press.
Debreu, Gérard. 1974. “Excess Demand Functions.” Journal of Mathematical Economics
1, 15-23.
Delli Gatti, Domenico, Edoardo Gaffeo, Mauro Gallegati, Gianfranco Giulioni, and
Antonio Palestrini. 2008. Emergent Macroeconomics: An Agent-Based Approach to
Business Fluctuations. Milan: Springer.
Drăgulescu, A.A. and Victor Yakovenko. 2001. “Exponential and Power-Law Probability
Distributions of Wealth and Income in the United Kingdom and the United States.
Physica A 299, 213-231.
Duffy, John. 2006. “Agent-Based Models and Human Subject Experiments.” In
Tesfatsion and Judd, eds., pp. 950-1011.
Engelmann, Dirk and Jean-Robert Tyran. 2005. “To Buy or Not to Buy? An
Experimental Study of Consumer Boycotts in Retail Markets.” Economica 72, 1-16.
26
Epstein, Joshua and Robert Axtell. 1996. Growing Artificial Societies: Social Science
from the Bottom Up. Cambridge: MIT Press.
Fagioli, Giorgio and Giovanni Dosi. 2003. “Exploitation, Exploration and Innovation in a
Model of Endogenous Growth with Locally Interacting Agents.” Structural Change and
Economic Dynamics 14, 237-273.
Farmer, J. Doyne and S. Joshi. 2002. “The Price Dynamics of Common Trading
Strategies.” Journal of Economic Behavior and Organization 49, 149-171.
Fehr, Ernst, Urs Fischbacher, and Simon Gächter. 2002. “Strong Reciprocity, Human
Cooperation and the Enforcement of Social Norms.” Human Nature 13, 1-25.
Fehr, Ernst and Simon Gächter. 2002. “Altruistic Punishment in Humans.” Nature 415,
137-140.
Fehr, Ernst and Klaus M. Schmidt. 1999. “A Theory of Fairness, Competition, and
Cooperation.” Quarterly Journal of Economics 114, 817-868.
Föllmer, Hans. 1974. Random Economies with Many Interacting Agents.” Journal of
Mathematical Economics 1, 51-62.
Föllmer, Hans, Ulrich Horst, and Alan P. Kirman. 2005. “Equilibria in Financial Markets
with Heterogeneous Agents: A Probability Perspective.” Journal of Mathematical
Economics 41, 123-155.
Friedman, Daniel. 1974. “On the Efficiency of Double Auction Markets.” American
Economic Review 74, 60-72.
Gabaix, Xavier. 1999. “Zipf’s Law for Cities: An Explanation.” Quarterly Journal of
Economics 114, 739-767.
Gallegati, Mauro, Steve Keen, Thomas Lux, and Paul Ormerod. 2006. “Worrying Trends
in Econophysics.” Physica A 370, 1-6.
Gallegati, Mauro, Antonio Palestrina, and J. Barkley Rosser, Jr. 2008. “The Period of
Financial Distress in Speculative Markets: Interacting Heterogeneous Agents and
Financial Constraints.” Mimeo, Polytechnic University of the Marches, University of
Teramo, and James Madison University, available at http://cob.jmu.edu/rosserjb.
Gintis, Herbert, Samuel Bowles, Robert Boyd, and Ernst Fehr. 2004. Moral Sentiments
and Material Interests: On the Foundations of Cooperation in Economic Life.
Cambridge: MIT Press.
27
Gode, D.K. and Shyam Sunder. 1993. “Allocative Efficiency of Markets with ZeroIntelligence Traders: Markets as a Partial Substitute for Individual Rationality.” Journal
of Political Economy 101, 119-137.
Gould, Stephen Jay. 2002. The Structure of Evolutionary Theory. Cambridge: Belknap
Press of Harvard University.
Gunderson, Lance H. and C.S. Holling, eds. 2002.Panarchy: Understanding
Transformations in Human and Natural Systems. Washington: Island Press.
Güth, Werner, Rolf Schmittberger, and Bemd Schwarze. 1982. “An Experimental
Analysis of Ultimatum Bargaining.” Journal of Economic Behavior and Organization 3,
367-388.
Hayek, Friedrich A. 1967. “The Theory of Complex Phenomena.” In Friedrich A. Hayek,
Studies in Philosophy, Politics, and Economics.London: Routledge & Kegan Paul, pp.
22-42.
Hendry, D.F. and H.M. Krolzig. 2001. Automatic Econometric Model Selection Using
PcGets 1.0. London: Timberlake Consultants.
Henrich, Joseph. 2004. “Cultural Group Selection, Coevolutionary Processes, and LargeScale Cooperation.” Journal of Economic Behavior and Organization 53, 3-35.
Hodgson, Geoffrey M. 2006. Economics in the Shadow of Darwin and Marx: Essays on
Institutional and Evolutionary Themes. Cheltenham: Edward Elgar.
Hommes, Cars H. “Heterogeneous Agent Models in Economics and Finance.” In
Tesfatsion and Judd, eds., pp. 1109-1186.
Hoover, Kevin D. 2006. “The Past as the Future: The Marshallian Approach to Post
Walrasian Econometrics.” In Colander, ed., (2006), pp. 239-257.
Horgan, John. 1997. The End of Science: Facing the Limits of Knowledge in the Twilight
of the Scientific Age. New York: Broadway Books (paperback).
Ijiri, Y. and Herbert A. Simon. 1977. Skew Distributions and the Sizes of Business Firms.
Amsterdam: North-Holland.
Kahneman, Daniel and Amos Tversky. 1979. “Prospect Theory: An Analysis of Decision
under Risk.” Econometrica 47, 263-291.
Kant, Shashi and R. Albert Berry, eds. 2005. Sustainability, Economics, and Natural
Resources: Economics of Sustainable Forest Management. Dordrecht: Springer.
28
Keynes, John Maynard. 1936. The General Theory of Employment, Interest and Money.
London: Macmillan.
Kindleberger, Charles P. 2000. Manias, Panics, and Crashes: A History of Financial
Crises, 4th edn. New York: Wiley and Sons.
Kirman, Alan P. 1992. “Whom or What Does the Representative Individual Represent?”
Journal of Economic Perspectives 6(2), 117-136.
Kirman, Alan P. and Nicolaas J. Vriend. 2001. “Evolving Market Structure: An ACE
Model of Price Dispersion and Loyalty.” Journal of Economic Dynamics and Control 25,
459-502.
Kolmogorov, Andrei N. 1965. “Three Approaches to the Quantification of the Definition
of Information.” Problems of Information Transmission 1, 4-7.
Koppl, Roger and J. Barkley Rosser, Jr. 2002. “All that I have to Say has Already
Crossed Your Mind.” Metroeconomica 53, 339-360.
Rachel Kranton and D. Minehart. 2001. “A Theory of Buyer-Seller Networks.” American
Economic Review 91, 485-508.
Langton, Christoper G. 1990. “Computation at the Edge of Chaos: Phase Transitions and
Emergent Computation.” Physiica D 42, 12-37.
LeBaron, Blake. 2006. “Agent-Based Computational Finance.” In Tesfatsion and Judd,
eds., pp. 1187-1233.
Levitt, Steven D. and John A. List. 2007. “What Do Laboratory Experiments Measuring
Social Preferences Reveal about the Real World?” Journal of Economic Perspectives 21,
153-174.
Levy, M. and Sorin Solomon. 1997. “New Evidence for the Power-Law Distribution of
Wealth.” Physica A 242, 90-94.
Lux, Thomas. 2009. “Applications of Statistical Physics in Finance and Economics.” In J.
Barkley Rosser, Jr., ed., Handbook of Complexity Research. Cheltenham: Edward Elgar,
in press.
Mandelbrot, Benoit B. 1963. “The Variation of Certain Speculative Prices.” Journal of
Business 36, 394-419.
Mantegna, Rosario N. and H. Eugene Stanley. 2000. An Introduction to Econophysics:
Correlations and Complexity in Finance. Cambridge: Cambridge University Press.
29
Markose, Sheri M. 2005. “Computability and Evolutionary Complexity: Markets as
Complex Adaptive Systems.” Economic Journal 115: F159-F192.
Martinez-Alier, J. 1987. Ecological Economics: Energy, Environment and Society.
Oxford: Blackwell.
McCabe, Kevin, Daniel Houser, Lee Ryan, Vernon. Smith, and Theodore Trouard. 2001.
“A Functional Imaging Study of Cooperation in Two-Person Reciprocal Exchange.”
Proceedings of the [US] National Academy of the Sciences 98, 11832-11835.
McCauley, Joseph L. 2004. Dynamics of Markets: Econophysics and Finance.
Cambridge: Cambridge University Press.
McCloskey, Deirdre N. 2003. “Notre Dame Loses.” Eastern Economic Journal 29, 309315.
Minsky, Hyman P. 1972. “Financial Instability Revisited: The Economics of Disaster.”
Reappraisal of the Federal Reserve Discount Mechanism 3, 97-136.
Mirowski, Philip. 1989. More Heat than Light: Economics as Social Physics, Physics as
Nature’s Economics. Cambridge: Cambridge University Press.
Mirowski, Philip. 2007. “Markets Come to Bits: Evolution, Computation and Markomata
in Economic Science.” Journal of Economic Behavior and Organization 63, 209-242.
Nash, John F., Jr. 1951. “Non-Cooperative Games.” Annals of Mathematics 54, 286-295.
Nyarko, Yaw and Andrew Schotter. 2002. “An Experimental Study of Belief Learning
using Elicited Beliefs.” Econometrica 70, 971-1005.
Osborne, M.F.M. 1959. “Brownian Motion in Stock Markets.” Operations Research 7,
145-173.
Porter, David P. and Vernon L. Smith. 1995. “Futures Contracting and Dividend
Uncertainty.” Journal of Business 68, 509-541.
Rabin, Matthew. 1993. “Incorporating Fairness into Game Theory and Economics.”
American Economic Review 83, 1281-1302.
Rosser, J. Barkley, Jr. 1991. From Catastrophe to Chaos: A General Theory of Economic
Discontinuities. Boston: Kluwer.
Rosser, J. Barkley, Jr. 1999. “On the Complexities of Complex Economic Dynamics.”
Journal of Economic Perspectives 13(4), 169-192.
30
Rosser, J. Barkley, Jr. 2001. “Complex Ecologic-Economic Dynamics and Environmental
Policy.” Ecological Economics 37, 23-37.
Rosser, J. Barkley, Jr. 2006. “Complex Dynamics and Post Keynesian Economics.” In
Mark Setterfield, ed., Complexity, Endogenous Money and Macroeconomics: Essays in
Honour of Basil J. Moore. Cheltenham: Edward Elgar, pp. 74-98.
Rosser, J. Barkley, Jr. 2008a. “Is a Transdisciplinary Perspective on Economic
Complexity Possible?” Mimeo, Department of Economics, James Madison University,
available at http://cob.jmu.edu/rosserjb.
Rosser, J. Barkley, Jr. 2008b. “Debating the Role of Econophysics.” Nonlinear
Dynamics, Psychology, and Life Sciences, in press.
Roth, Alvin E. and J.K. Murnighan. 1978. “Equilibrium Behavior and Repeated Play of
the Prisoner’s Dilemma.” Journal of Mathematical Psychology 17, 189-198.
Samuelson, Paul A. 1947. Foundations of Economic Analysis. Cambridge: Harvard
University Press, enlarged edition, 1983.
Schumpeter, Joseph A. 1936. The Theory of Economic Development. Cambridge:
Harvard University Press.
Selten, Reinhard. 1975. “Reexamination of the Perfectness Concept for Points in
Extensive Games.” International Journal of Game Theory 4, 25-55.
Sethi, Rajiv and Eswaran Somanathan. 1996. “The Evolution of Social Norms in
Common Property Resource Use.” American Economic Review 86, 766-788.
Shannon, Claude E. 1948. “A Mathematical Theory of Communication.” Bell Systems
Technical Journal 27, 379-423, 623-656.
Silverberg, Gerald and Bart Verspagen. 2005. “A Percolation Model of Innovation in
Complex Technology Space.” Journal of Economic Dynamics and Control 29, 225-244.
Simon, Herbert A. 1957. Models of Man. New York: Wiley.
Simon, Herbert A. 1962. “The Architecture of Complexity.” Proceedings of the
American Philosophical Society 106, 467-482.
Smith, Adam. 1759. The Theory of Moral Sentiments. Reprinted 1976, Indianapolis:
Liberty Press.
Smith, Adam. 1776. An Inquiry into the Nature and the Causes of the Wealth of Nations.
London: Strahan and Cadell.
31
Smith, Vernon L. 1962. “An Experimental Study of Competitive Market Behavior.”
Journal of Political Economy 70, 111-137.
Smith, Vernon L. 1998. “The Two Faces of Adam Smith.” Southern Economic Journal
65, 1-19.
Smith, Vernon L. 2008. Rationality in Economics: Constructivist and Ecological Forms.
New York: Cambridge University Press.
Smith, Vernon L., Gerry L. Suchanek, and Arlington W. Williams. 1988. “Bubbles,
Crashes, and Endogenous Expectations.” Econometrica 56, 1119-1131.
Sornette, Didier. 2003. Why Stock Markets Crash: Critical Points in Complex Financial
Systems. Princeton: Princeton University Press.
Stahl, Dale and Paul Wilson. 1995. “On Players’ Models of Other Players: Theory and
Experimental Evidence.” Games and Economic Behavior 10, 218-254.
Stern, Nicholas. 2008. “The Economics of Climate Change.” American Economic
Review, Papers and Proceedings 98, 1-37.
Strotz, Robert H. 1955. “Myopia and Inconsistency in Dynamic Utility Maximization.”
Review of Economic Studies 23, 165-180.
Tesfatsion, Leigh. 2006. “Agent-Based Computational Economics: A Constructive
Approach to Economic Theory.” In Tesfatsion and Judd, pp. 831-880.
Tesfatsion, Leigh. and Kenneth L. Judd, eds. 2006. Handbook of Computational
Economics, Volume 2: Agent-Based Computational Economics. Amsterdam: NorthHolland.
Thaler, Richard. 1981. “Some Empirical Evidence on Dynamic Inconsistency.”
Economics Letters 8, 201-207.
Trivers, Robert L. 1971. “The Evolution of Reciprocal Altruism.” Quarterly Review of
Biology 46, 35-57.
Varian, Hal R. 1992. Microeconomic Analysis, 3rd edition. New York: W.W. Norton.
Veblen, Thorstein. 1898. “Why is Economics not an Evolutionary Science?” Quarterly
Journal of Economics 12, 373-397.
Velupillai, K. Vela, ed. 2005. Computability, Complexity and Constructivity in Economic
Analysis. Victoria: Blackwell.
32
Watts, Duncan and Steven H. Strogatz. 1998. “Collective Dynamics of ‘Small-World’
Networks.” Nature 393, 440-442.
Wolfram, Stephen. 1984. “Uncertainty and Complexity in Cellular Automata.” Physica D
10, 1-35.
Zak, Paul J. 2004. “Neuroeconomics.” Philosophical Transactions of the Royal Society
359, 1737-1748.
Zak, Paul J. 2005. “Trust: A Temporary Human Attachment Facilitated by Oxytocin.”
Behavioral and Brain Sciences 228, 336-368.
Zak, Paul J., ed. 2008. Moral Markets: The Critical Role of Values in the Economy.
Princeton: Princeton University Press.
Zipf, George K. 1941. National Unity and Disunity. Bloomington: Principia Press.
33