Chaos and Complexity Courses for Spring 2006, UW-Madison

ECONOMICS 606,                                



Since I did not teach 606 last year and since the research frontier has
changed, this year's 606 will try to get you up to date on major new research
trends in economics. Besides trying to identify "cutting edge" research
topics in economics and trying to identify good PhD thesis topics, I try to
use 606 to teach basic tools that are hard to get elsewhere. Hence, if you
have had 606 before, and you would like to take this course for credit, even
though you may have "taken it before," I will sign the necessary paperwork
to do this for you.
On the first day of class I will sketch different potential areas of
teaching concentration listed in the syllabus below and hand out 3x5 cards
where each student is asked to identify areas of interest that they would like
me to teach. I will also ask students to tell me what courses they have taken
on these cards. I will then try to design the course to optimize a combination
reflected by the preferences and backgrounds revealed on these cards. I will
also try to link the teaching to research projects of faculty here.
I will list some recent and current UW PhD students who have gotten PhD
theses (or are currently working on PhD theses) out of the areas to be taught
below. You will want to talk to the ones who are currently here.
The topics below seem unrelated. I shall show how a few analytical
principles organize the lot. There will be some similarity between the
material of previous 606 courses but 606 Spring, 2006 will contain much more
work on "new" decision theory including different criteria for "optimization"
when underlying structure is partially known. This area is sometimes called
"Decision making under ambiguity." This area includes the following items and
ideas: Bayesian model averaging, maximin decision making, minimax regret
decision making, design limits, etc. Writers in the area include Larry
Epstein, Charles Manski, Lars Hansen, Thomas Sargent, Itzhak Gilboa, David
Schmeidler, and some faculty here. Key references to work outside UW are
located on the websites of Lars Hansen, Thomas Sargent, Larry Epstein, and
Charles Manski.
We shall also discuss recent econometric approaches to the analysis of
time series data and of panel data in an attempt to separate "spurious"
"spatial" and temporal dependencies from "true" dependencies that have some
notion of "multiplier." Documentation of existence of "multipliers" is
important for policy analysis because multipliers are associated with
externalities which policy may be able to correct.
There will also be more attention paid to the relationship between
dynamical systems phenomena such as bifurcations and jumps caused by presence
of "multipliers" to assist identification of such "endogenous interactions"
than recent work on identification of self selection effects and treatment
effects which was treated in years before. This will be a blending of
stochastic dynamical systems approaches with the review article,
"Interactions-Based Models," for the HANDBOOK OF ECONOMETRICS by Brock and
We will spend some time on very recent work in econometrics on "early
warning signals" of an impending bifurcation in settings where the time scales
can be separated. Rigorous treatment of the notion of "separation of time
scales" will be developed in the course.
Researchers such as N. Bockstael of University of Maryland and E. Irwin
of Ohio State (see the dramatic maps generated by simulated urban/suburban
interacting systems models compared with actual patterns on E. Irwin's website
at Ohio State) have recently taken interactive systems models towards exciting
empirical applications. We shall cover some of this new work.
The topics below have become very popular, not only because of their
intrinsic interest, but also because of the recent entry of
"establishment" figures. The popularity is projected to increase even more
due to recent empirical applications to issues of high political salience such
as the control of urban sprawl. At the risk of repeating, the purpose of this
course is to bring our students to the research frontier as well as to inform
our students of recent empirical applications as well as to suggest open
research problems.


This course is designed to help students locate and identify potential
thesis topics as well as to teach basic analytical tools. I believe that
students learn analytical tools and techniques much faster when applications
that lead to potential thesis topics are used as the main pedagogical
vehicles. Hence, I will base grades on a take home test and problem sets.
Students will be given a week to do the take home test. The problems on the
test and homeworks will be "toy" research problems that apply ideas taught in
the course. The take home test will be designed so that those students who
faithfully do their homework problem sets will almost surely do well on the
take home test. The key idea here is to help students adjust from the usual
type of course environment to the research environment.


Since much of the material that I have taught before in this course is
available elsewhere (Examples: Dynamic Programming is taught in first year
macroeconomics, Stochastic Calculus and Stochastic Optimal Control Theory is
taught in the Business School and the Math Department, Game Theory is taught
by other courses here) I keep revamping this course to teach material that
is not so easily available elsewhere on campus. I will teach newer
methods that have become popular in recent years. I list these methods and
topics below.
The emphasis in teaching the methods will be to isolate potential PhD
thesis topics. More will be said about this below.
Some major writers and/or sources are included in parentheses beneath
each topic. However, these will be very incomplete because, during the
course, I shall make up lists of current papers and their website locations in
order to build the good research habit of drawing up a list of high priority
websites and the habit of continuously monitoring these in order to keep up in
today's fast moving research environment.


This course will be accessible to students with preparation at the level
of "mature" first year graduate students in economics and business. Hence, I
am choosing a mathematical level to widen the accessibility of the course
compared to the past. I will also attempt to make the course accessible
(and relevant by using applications in the following areas if students in
those areas enroll in the course) to students in other disciplines such as
statistics, physics, biology, ecology, limnology, etc.
Since much of the material for the course consists of current working
papers as well as many published papers, I will make much use of websites and
other internet resources. I shall teach my own favorite internet search
methods for framing a research topic and projecting potential value-added of
the proposed topic before investing time on it. While this might seem banal,
it is surprising how many people fail to do this and end up re-inventing the
wheel. Students here have too many time committments to have their research
time wasted on projects that have already been done by someone else.
This course will represent a good hunting ground for potential thesis
topics because the new methods can be applied to many different areas of
economics, finance, and other areas including ecology. I shall try to outline
potential thesis topics during the lectures. For other students, the course
will give a tour of some interesting scenery on the research frontier of
economics and related areas such as ecology. The course is also designed to
be useful to advanced undergraduate students that are contemplating academic
research careers.
The unifying concepts and tools of the course will be: (i) stochastic
dynamical systems theory, (ii) decision theory in settings of partially known
or partially identified structures. Emphasis will be placed on
data-disciplined approaches. (iii) theories of self-organization, agent-based
modelling, scaling laws, evolutionary dynamics with many agent types,
including theories of the Santa Fe Institute variety, and some of the tools
being used by papers posted on websites that can be found by googling on
"CeNDEF" (Center for Nonlinear Dynamics, University of Amsterdam),
"econophysics," "the New England Complex Systems Institute," and the like.
(iv) econometric methods that stress heterogeneity and detection of regime
changes, e.g. bifurcations, caused by slow moving underlying variables.
I will also teach recent econometric and statistical methods of dealing
with separation of time scales, construction of early warning indicators of
impending bifurcations. Interesting material may be found by simply doing a
google search on the words "econophysics," "complex systems," "genetic
algorithms," "bifurcations", and other jargon words from "complexity theory."
The Santa Fe Institute website and CeNDEF website;

are good places to start looking at complex systems materials. We will use a
lot of materials on the CeNDEF website above.
I use applications heavily in my teaching of analytical tools and
techniques. For UW applications of complex adaptive systems ideas and related
ideas to ecological economics, see the following SSRI working papers:

W. D. Dechert and S. I. O'Donnell, 2005-19; S. Carpenter and W. Brock,
2005-18; W. Brock, S. Carpenter, and M. Scheffer, 2005-14; D. Ludwig, W.
Brock, and S.Carpenter 2005-15.

For some mathematical tools on bifurcation analysis, separation of time
scales, and their applications, see, Brock, W., "Some Mathematical Tools for
Analyzing Complex-Nonlinear Systems," SSRI W.P. 2020.
SSRI Working Papers are available on the Sixth Floor in the SSRI Office.
They are also available at the SSRI website where you can download them.


We will cover topics below in order of I,II,...Hence we may run out of
time before we cover all the topics listed here. But I will try to give you
at least a taste of all of them.

I. Bayesian Model Averaging, Robust Control, Design Limits in control theory,
Decision Making Under Ambiguity, and other methods of appraising and dealing
with decision making in contexts of partially identified structures. Several
UW students have gotten thesis topics out of this area, but I believe the
frontier is still wide open.
The articles on robust control and the book, ROBUST CONTROL AND MODEL
UNCERTAINTY IN MACROECONOMICS by Lars Peter Hansen and Thomas Sargent and
their coworkers (available on Sargent's website at NYU) has stimulated a lot
of recent interest. Get to Sargent's website at NYU by googling on "Thomas J.
Sargent." We shall cover the highlights of this work as well as related work
being done here.
Recent UW work in the area is in SSRI working papers by Brock and
Durlauf, Brock, Durlauf, and West. Some very recent UW theses in this area
include Oya Ardic (now at University of the Bosphorus), Chi Ming Tan (now at
Tufts), Andros Kourtellos (now at University of Cyprus), Sibel Sirakaya (now
at University of Washington, Seattle).
Mehmet Eris, Giacomo Rondina, and Ethan Cohen-Cole, are some current UW
PhD students working in this area.
For example the papers, "Policy Evaluation in Uncertain Economic
Environments, by Brock, Durlauf, and West (SSRI 2003-15), as well as "Growth
Economics and Reality" by Brock and Durlauf (available at the SSRI office and
website) review this area and applies it to growth econometrics and monetary
economics. The SSRI working paper, 2004-21, by Brock, "Profiling problems
under partially identified structures" discusses decision making under minimax
regret, maximin decision making and adaptive learning under these two
criteria. This paper can serve as an introduction to some economic
applications of general decision making and adaptive learning under ambiguity
where the ambiguity (i.e. the level of partial identification) is disciplined
by data. Key references are papers by Charles Manski which are located on
Charles Manski's website.
We will discuss some of these methods and potential applications for them
in the course.

II. Recent econometric and theoretical modelling of increasing
returns, threshold effects, interaction effects, and theories of endogenous
emergence of spatial patterns.

We will teach some of the latest work of this genre. Some illustrative
references are given below.

(W. Brock and A. Xepapadeas, "Optimal control and spatial heterogeneity:
Pattern formation in economic-ecological models," (SSRI 2005-11); The three
Santa Fe Institute Volumes by Anderson, Arrow, Pines, (1988), (Arthur,
Durlauf, and Lane) [Blume and Durlauf], THE ECONOMY AS AN EVOLVING COMPLEX
SYSTEM, (II), [III] Addison Wesley: Redwood City, CA. [Oxford University
Press]; Brock, W., (1993), "Pathways to Randomness in the Economy: Emergent
Nonlinearity and Chaos in Economics and Finance," SSRI Reprint 410; Brock,
W., (1991), "Understanding Macroeconomic Time Series using Complex Systems
Theory," SSRI Reprint 392. Manski, C., (1993), "Identification Problems
in the Social Sciences," SSRI Reprint 409. Manski, C., "Dynamic Choice in
Social Settings," SSRI Reprint 408.
Main sources of recent work that was stimulated by the economics
program at the Santa Fe Institute are the second and third SFI Volumes:
Arthur, Durlauf, and Lane, eds., (1997), [Blume and Durlauf (2005)] THE
CA. [Oxford University Press]. The review by Brock and Durlauf
"Interactions-Based Models," SSRI W.P. 9910 contains much material on
econometrics of social interactions.)

III. Neural Nets, Connectionist Networks, Bootstrapping, Surrogate Data
and their relationship to other received methods in econometrics such as
nonlinear least squares.

Some relevant references are below.

(Sullivan, A. Timmerman, and Halbert White, (1998), "Data-Snooping, Technical
Trading Rule Performance and the Bootstrap," Department of Economics, UCSD and
LSE Finance), Casdagli, M., Eubank, S., (1990), NONLINEAR MODELLING AND
FORECASTING, Addison-Welsey: Redwood City, CA. Work of Halbert White and his
students at UCSD on estimating neural nets using "Robbins-Monro" procedures
and nonlinear least squares. Similar methods are used in the adaptive
learning literature below.)

This year's 606 will also discuss the problem of controlling for
data-snooping in econometric methodology in general as well as in the
application of bootstrap-based specification tests (cf. Sullivan, Timmerman,
and White). See also the discussion below on how this material will be taught
and used this year.

IV. Self Organized Criticality Models

Some references are listed below.

(Bak, P., Chen, K., Scheinkman, J., Woodford, M., (1993), RICHERCHE
Attempt to explain the evidence for long dependence in economic and financial
data stressed by Mandelbrot and others. Recent articles on Self Organized
Criticality (SOC) that are mentioned in Per Bak's book, HOW NATURE WORKS,
Springer 1996 will also be covered. See also the ECONOPHYSICS website for
much material on SOC applied to economics. See especially the joint work of
Martin Shubik of Yale Economics with Per Bak of Physics.)

I will review some high points of this type of work posted on
ECONOPHYSICS websites as well as other related websites such as the Santa Fe
Institute. We will discuss how we might use this kind of material to advance
the frontiers of econometrics and theory in economics.

V. Econometric and Theoretical issues raised by the possible presence of
chaos and other forms of deep nonlinearity in economic and financial data.
The Problem of Detecting "Spurious" Nonlinearity in Data.

Some references are listed below.

ECONOMETRICS, December, 1992. Barnett, W., Gallant, A., Hinich, M.,
Jungeilges, J., Kaplan, D., Jensen, M., "A Single-Blind Controlled Competition
between Tests for Nonlinearity and Chaos," Washington University, St. Louis
working paper. See William Barnett's website at the University of Kansas,
Lawrence, Kansas, for many interesting papers and well as useful links. Some
interesting books are Benhabib J., ed., (1992), CYCLES AND CHAOS IN ECONOMIC
EQUILIBRIUM, Princeton University Press: Princeton, NJ. Brock, W., Hsieh, D.,
THEORY AND ECONOMIC EVIDENCE, MIT Press: Cambridge, MA. Granger, C.,
University Press: Oxford. De Grauwe, P., Dewachter, H., Embrechts, M.,
Blackwell: Oxford. A challenge to this literature is posed by Bickel and
Buhlmann, (1996) "What is a Linear Process?" PROC.NAT. ACAD. SCI. USA, Vol.
93, pp. 12128-12131, December. BB argue that the closure of the set of ARMA
processes "under a suitable metric" is "unexpectedly large" (Caution: This is
NOT the Wold representation). Further work on this problem should be at Peter
Bickel (Berkeley Statistics) and Peter Buhlmann's websites. The CeNDEF
website has lots of material on this topic. We will relate this type of work
to work by UW's Bruce Hansen on econometrics of nonlinear models, UW's Dennis
Kristensen on econometrics of diffusion processes, and other work at the UW.)

This area has grown rapidly. I shall pick highlights, teach the basics,
and show what still needs to be done. New work that has become available
recently will be covered. The emphasis will be to inform students on what
research problems are still open in this area and how it relates to the recent
surge of interest in modelling "bounded rationality" and "process approaches"
to economics rather than "equilibrium" approaches.

VI. Complex Systems Modelling and Scaling "Laws"

Some references are listed below.

Addison-Wesley: Redwood City, CA. Brock, W., "Scaling in Economics: A
Reader's Guide," SSRI Reprint. Blake LeBaron's website at Brandeis


LeBaron, B., 1999, "Volatility Persistence and Apparent Scaling Laws in
Finance," (available at LeBaron's website).

Browse the ECONOPHYSICS website (see especially the links to "minority

Here are examples of Scaling "Laws" in economics and finance: (i)
Gibrat's Law of firm size distribution, (ii) logistic "laws" of growth and
diffusion, (iii) Pareto's Law of income distribution, (iv) Mandelbrot's
"self similar" stochastic processes and "1/f" scaling in economics and
finance, (v) the stylized facts of finance such as autocorrelation
structure of returns, volatility measures, and volume measures across
individual stocks and indices, (vi) the stylized autocorrelation and
cross correlation structure of aggregative and less aggregated
macroeconomic time series. See Brock, W., and LeBaron, B., "A dynamic
structural model for stock return volatility and trading volume," REVIEW OF
ECONOMICS AND STATISTICS, 78(1), February, 1996, 94-110 for a list of these
stylized facts in finance and a discussion of theories to explain them.
An attempt will be made to show what useful insights can be learned from
locating scaling laws and how to correct for improper treatment of
heterogeneity. In particular we will stress how "spurious" "unconditional"
scaling "laws" can easily be produced from a system of individual stochastic
processes relaxing to different stochastic steady states (even though the
relaxation rate is the same for each process). This exercise will stress the
importance of correctly controlling for heterogeneity, i.e. correctly
controlling for mixing observations from different distributions. Scaling
laws appear also in ecology and we will teach some of this material and draw
lessons from it for econometric practice.

VII. Adaptive Learning, Partially Identified Structures, Evolutionary

There has been much recent interest in econometrics in settings where
point identification is replaced by partial identification. See Charles
Manski's website at Northwestern for key articles and books on this topic as
well as a good entry point into this topic. Standard decision theory is being
modified to deal with decision making under data disciplined but partially
identified structures. This movement creates an interesting interaction
between econometrics and decision theory. It creates new opportunities to
evaluate decision making criteria on the basis of how fast decision makers
learn partially identified features of structures. A good place to start
reading this literature is Charles Manski's website at Northwestern and Larry
Epstein's website at Rochester.

More references are listed below.

(T. Sargent, (1993), BOUNDED RATIONALITY IN MACROECONOMICS, Oxford University
Press. Chen, X., White, H., (1994), "Nonparametric Adaptive Learning with
Feedback," UCSD Working Paper. Holland, J., (1992), ADAPTATION IN NATURAL AND
ARTIFICIAL SYSTEMS, MIT Press: Cambridge, MA. CeNDEF experiments on
expectation formation as well as other CeNDEF research on bounded rationality.
Fudenberg/Levine's book, THE THEORY OF LEARNING IN GAMES (1998), Larry
Samuelson's book on evolutionary games, Peyton Young's book on evolution of
conventions in games, ECONOPHYSICS website (see especially the links to
"minority games"), R. Selten's lab on strategy experiments in oligopoly
theory, CeNDEF work on strategy experiments in other types of games.)

The basic first year courses say little about dynamics and adaptive
learning towards a notion of "equilibrium." For example, Selten's lab at Bonn
has recently shown that optimization appears to play no role at all in
repeated oligopoly games (i.e. finite horizon supergames) with small numbers
of players. Rather something somewhat like Axelrod's TIT-FOR-TAT strategy
emerges as players evolve "ideal points" and induce play towards them by
"measure for measure".
First year courses say even less about any kind of socially interactive
learning on any kind of network or Selten-like behavior of players trying
to "train" each other towards a more cooperative outcome.
Since much of economics is based on equilibrium concepts which impose
restrictions on data which can be tested and since introduction of
"disequilibrium" concepts such as adaptive learning introduces extra "free
parameters," this imposes an even higher priority to discipline theorizing by
data than usual.
Researchers here, at the Santa Fe Institute, and other research centers
are trying to carry out this kind of research program consistent with observed
"scaling laws" and observed estimated conditional distributions in economics
and finance. We shall cover the basic methods and highlights of this new
literature. We shall also review experimental results. For example CeNDEF
has been using strategy experiments (originating from Selten's work) to
produce a set of stylized regularities about the expectations formation
process which is separated from other aspects of the game (such as strategy
involved via sharing a market as in oligopoly games) via a special design of
the experiment to "control-out" all other expects of the game except for the
expectation formation process itself.
Research on the "El Farol" problem (called the "minority game" by
physicists) has documented a "phase transition" and a "scaling law" (cf. work
on the ECONOPHYSICS website by Robert Savit of the University of Michigan and
many others). The parameters are "s" the "size of brain" of each player
(measured by the size of the strategy set available to each player), the "size
of the universal brain" (measured by the size of the universal set Omega(m) of
potential strategies that could be played) and memory "m" (measured by the
number of lagged observations allowed to be in each prediction function which
describes each forecasting strategy). The focus of the CeNDEF group is on the
dynamic evolution of adaptive forecasting systems whereas the focus of Savit
et al. is on uncovering "scaling" relationships and evidence of "phase
transitions" via computational experiments. There is also analytical work
reported on the ECONOPHYSICS website.
We shall spend some time comparing and contrasting these different
approaches to the modelling of adaptive learning as well as learning what we
can from results reported from laboratory experiments around the world. The
emphasis of this part of the course will be to develop model systems that
replicate experimental results, but at the same time develop analytical
methods for general use in this area.
Development of methods from natural science in searching for useful
"order parameters" to uncover "phase transitions" and "scaling laws" and
relating these to "scaling laws" from sampling theory in statistics (such as
central limit theorems, Edgeworth expansions, large deviations "scaling"
relations, breakdowns of central limit theorems due to series of cross
correlations diverging) will be stressed.
We will stress the incentive differences inherent in "small numbers"
adaptive (or other) "learning" situations of repeated play in contrast to
"large numbers" situations of repeated play. Selten's lab stressed the
inherent incentives of repeated "small numbers" play to "train" each other to
reach a cooperative outcome. Such incentives will get smaller as the number
of players increases because each player will be increasingly unable to
capture the benefits of her own "training efforts" onto the other players.
This relates to work on "evolution of norms and conventions" in Peyton Young's
As one varies the number of players, the memory allowed in their
strategies, the size of their individual strategy sets and the size of the
size of all potential strategies of fixed memory as well as other quantifiable
aspects of the game the "order parameter" approach suggests looking for key
"order parameters" such that when an order parameter increases, the system
goes through an abrupt change in dynamical behavior (a "phase transition"
and/or a "bifurcation"). Analysis of continuous state space dynamical systems
of increasing size creates a demand for analytic results on eigenvalues of
dynamical systems of increasing size. Alan Edelman's website at MIT Math
contains very nice papers on this problem (e.g. "circular laws") which we
shall discuss.
Since we will be on new ground here, this should be an exciting part of
the course.

VIII. Cellular Automata, Ising Models, Spin Glass Models

Some references to this area are listed below.

(Mezard, M., Parisi, G., Virasoro, (1987), SPIN GLASS THEORY AND BEYOND, World
Scientific. Durlauf, S. (1993), REVIEW OF ECONOMIC STUDIES and various
working papers. Mitchell, M., Crutchfield, J., Hraber, P., (1994), "Evolving
Cellular Automata to Perform Computations: Mechanisms and Impediments,"
PHYSICA D, 75, 361-391. Doyon, B., Cessac, B., Quoy, M., Samuelides, M.,
(1993), "Control of the Transition to Chaos in Neural Networks with Random
279-291. Material on eigenvalues of large systems from Alan Edelman's website
at MIT Math. See material from Jim Crutchfield, Melanie Mitchell, and others
available by linking from the Santa Fe Institute's website.)

This material will give math modules from which we can build models of
adaptive interaction and parse out the components due to socially interactive
learning from "plain vanilla" adaptive expectations formation and other kinds
of "individualistic" adaptation. However, our posture will be somewhat
different than the large recent theory literature on networks and games. It
will be guided by a desire to formulate useful econometric frameworks where
tools like the Efficient Method of Moments (cf. George Tauchen's website at
Duke) and Computational Bayes (cf. John Geweke's website at Iowa, and his
paper, "Computational Experiments and Reality" available at his website at
University of Iowa, Iowa City, along with software available there) can be
used to measure the "statistical significance" of the "extra free parameters"
brought by adaptive learning theory. Emphasis will also be placed upon
econometrically separating interactive effects from empirically similar
looking effects due to correlated unobservables and other phenomena.

IX. Information Contagion, Polya Processes, Cascades, Self Reinforcing
Mechanisms, Magnification Mechanisms of Income and Wealth.

Some references are listed below.

(Arthur, W., (1988), "Self Reinforcing Mechanisms in Economics," in Arrow,
Anderson, Pines, op.cit. Bikhchandani, S., Hirshleifer, D., Welch, I.,
(1992), "A Theory of Fads, Fashion, Custom, and Cultural Change as
Informational Cascades," JOURNAL OF POLITICAL ECONOMY, 100 (5): 992-1026. De
Vany, A., and Walls, W., (1994), "Information, Adaptive Contracting, and
Distributional Dynamics: Bose-Einstein Statistics and the Movies," University
of California, Irvine, Working Paper, recently appeared in ECONOMIC JOURNAL.
Rosen, S., "The Economics of Superstars," AMERICAN ECONOMIC REVIEW, 71:

This material relates naturally to the above discussions in the sense
that it lays out a variety of channels through which interaction may operate
in a dynamically evolving social system as an economy. Emphasis will be
placed on econometric identification of the different "observable empirical
signatures" produced by each of these very different mechanisms of interaction
that may look the same to an econometric exercise if it is not carefully
formulated. Formulation of econometric exercises to differentiate different
channels of interaction including "social learning," "informational cascades,"
"positional reward structures" (e.g. "tournament" payoff structures), and
other related channels of possible interaction will take a very high priority
in this year's 606.

X. "Process vs. Equilibrium"

A common theme thoughout the above materials is moving thinking about the
economy away from "equilibrium" (even that of the stochastic process Real
Business Cycle type modelling) towards a view more like Artificial Life and
John Holland's Complex Adaptive Systems (cf. Leigh Tesfatsion's website, Tom
Ray's TIERRA, The Santa Fe Artificial Stock Market, "Sugarscape," and other
Artificial Life frameworks) where the system never settles down. This kind of
approach to economics can be viewed as a modern form of Austrianism. We shall
try to develop some analytics (rather like large system limits over a
hierarchy of "spatial" and temporal scales) to complement the exciting
computational work in this area.