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A Microcomputer Workshop Exploring The Dynamics of Arms Races
David P. Kreutzer
Massachusetts Institute of Technology
ABSTRACT
This microcomputer workshop is being developed to encourage exploration,
testing, and discussion of the impact of alternative arms-building
policies. The model allows participants to adjust parameters that reflect
a number of psychological, technical, and political factors. For example,
participants can represent one country's tendency to overestimate the
strength of the other and underestimate its own strength. Before releasing
the model to the public, we are reviewing its conceptual soundness and its
educational effectiveness to be sure that it reflects empirically supported
technical, psychological, and political realities. The presentation of
this paper and the early versions of the workshop are part of this
preliminary review process.
INTRODUCTION
How can countries maintain an adequate national security while at the same
time avoiding a potentially destabilizing escalation in the numbers and
power of weapons? Increases in military capability improve a country's
sense of security while at the same time diminishing its adversary's
perceptions of security. If the adversary responds by increasing its
armaments, the consequent escalation of forces can create a dynamic
frequently called an "arms race."
“Exploring the Dynamics of Arms Races" is a microcomputer workshop being
developed to encourage participants to explore, test, and discuss the
impact of alternative arms-building policies. Participants adjust
competing countries' parameters, one at a time, on a simulation model to
reflect the most plausible and rational policies they think each country
could adopt. Each country's objective is to maintain a level of arms
consistent with its national security objectives relative to its perception
of the level of arms of the opposing country.
The model allows participants to adjust parameters that reflect a number of
psychological and political biases. For example, participants can
represent one country's tendency to overestimate the strength of the other
and underestimate its own strength. The model also incorporates realistic
delays for changing perceptions and closing gaps in the relative levels of
arms.
When participants adjust parameters for each country in isolation to
reflect policies that are most "rational" from that country's point of
view, the combined simulation for both countries will frequently show an
accelerating arms buildup. The workshop also shows that uncertainty and
fear about the adversary's total offensive capability can amplify a
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country's tendency to overestimate the numbers and destructiveness of
opposing arms and underestimate its own strength. These kinds of
psychological, political, and competitive forces can continue to drive arms
races even when negotiations lead countries to choose parities or even
build downs as their policy goals.
This project started as a result of a trip by Jay W. Forrester to Moscow in
October of 1983 for discussion of how system dynamics could be applied to
social problems. There was some interest shown in exploring the forces
underlying arms races (Forrester 1984). After his return, Professors Jay
W. Forrester, Peter M. Senge, John D. Sterman and David P. Kreutzer of the
System Dynamics Group; Professor Nazli Choucri of the Political Science
Department at M.I.T.; and Dr. Ron Heifetz and Bruce Allyn from the Kennedy
School of Government at Harvard met monthly to discuss how best to use
computers to increase public understanding of the arms race.
In the spring of 1984 Forrester created a simple model, with suggestions
from Sterman and Senge, to illustrate to the group what a system dynamics
model could contribute. Shortly thereafter, Sterman and I modified this
model into a workshop for our summer session. This model is similar to the
conceptual framework for studying NATO-Warsaw Pact force strength
competition proposed by C. White in 1981. The model has two goal seeking
loops competing over their relative force ratios as well as separate levels
for the actual and perceived levels of arms. This feedback representation
with economic constraints follows in the tradition of British meteorologist
Lewis Richardson who developed a mathematical model of arms races in 1919
that has become a standard way of analyzing arms races in political
science. (Schrodt 1982, p. 108.) There is some empirical research
supporting this kind of representation (Ward 1984, p. 196). The conceptual
soundness of the present model and its educational effectiveness needs much
more research and review before it is released to the public.
The purpose of this paper is to solicit advice on the technical and
psychological correctness of the model and workshop and to check to make
sure it does not convey unsupportable and biased viewpoints. For this same
reason we have been testing preliminary versions of the workshop with high
school and college students, teachers, political scientists, business
people, experts in arms control, visitors from the Soviet Union and members
of our own defense establishments. From these experiences we have modified
the software presentation style and model several times and anticipate
several more rounds of modifications prior to release.
USING SIMULATION MODELS FOR EDUCATION AND DISCUSSION
This workshop is part of a larger ongoing project to develop educational
software for use in homes, schools, and businesses to illustrate how
simulation models can improve understanding of complicated problems. One
purpose of the project is to show how a model can improve communication
between persons with opposing viewpoints by demonstrating the consequences
of differing underlying assumptions. We plan to create several companion
models that reflect other ideas about causes of arms races, such as
Professor Nazli Choucri's theory of lateral pressure as a cause of
international competition.
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In order to more adequately incorporate other viewpoints and increase the
use of models for educational discussion, the materials will become
available to the public on software disks.
The model
was originally
written in Micro-DYNAMO, however, in order to be able to provide the model
at a nominal cost with permission to copy and change material on the disks
we are developing our own software. Karl Buttner, an MIT undergraduate,
and Junko Vietze, a member of the System Dynamics Group staff, have been
working with me to create simulation software that is easier to use and has
more advanced interaction capabilities such as stories, help files, and
built in explanations. We hope the response to this permission to copy
will be that people will build their own models and modifications to more
accurately express their own viewpoints, analyze others viewpoints and send
us their new models and responses.
WORKSHOP FORMAT AND OVERVIEW OF MODEL STRUCTURE
In the workshops, I introduce the model by explaining that system dynamics
is a way of looking at problems at three levels: events, patterns of
I ask workshop participants to
think of examples of events in their lives related to arms races.
behavior and underlying causal structure.
Participants usually volunteer examples such as the bombing of Hiroshima,
newspaper headlines of debates over the MX missle, Strategic Defense
Initiative, Cuban missile crises, or Geneva peace talks.
on a chalkboard.
These are written
®
Nuclear Stockpiles
20,000
2? USA.
, 15,000 3 US.S.B.
s fe
: 3 an
Z i Fi
3 10,000-4 = :
3 g
z 2
= 50004 3
a & More than
2 adequate
= deterrent
L r
T T 1
1940 1960 1980 2000
Year
Land-based
Missile Silos
2,000-
1,800
1,600]
F1,400-4
2
2 1,200
2 1,000-4
2 800
2 600~
7 400-4
US.
2004 IRBM's
fo Cruise
Missiles
1950
TT T
1960 1970 1980
Year
1
1987
Figure 1. Examples of patterns of behavior
race (Weisner 1985, p. 9).
associated
with US-USSR arms
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I then ask them to think of patterns of behavior over time. The most
frequently suggested example volunteered is an exponential growth in
nuclear arms. I then show them examples of estimates of the real data by
Jerome Weisner shown’in Figure 1. Looking at the numbers of nuclear
warheads possesed by each side gives the impression that we are seeing
exponential growth.
I then ask participants to think of a cause and effect explanation or
structure that could produce such an escalation in arms. In all but one
workshop they have volunteered some version of the positive feedback loop
seen in Figure 2. Figure 3 is then presented as an elaboration of Figure
2. This format has turned out to be more effective than an earlier format
where I presented Figure 2 then Figure 3 in a lecture mode. In its current
form Figure 3 is very difficult for general audiences to understand. When
they see it merely as an elaboration of their own idea, it seems to be less
difficult. It is still much too complicated. In our software for the IBM
PC we do not have sufficient pixel resolution on the screen to be able to
present Figure 3. I am experimenting with a new intermediate diagram with
simple, intuitively obvious, icons. The intelligence sector in the lower
right hand corner is represented with a satellite. The evaluation of
domestic arms and the estimate of opposing arms is processed in the classic
five sided symbol of the Pentagon. The margin of superiority and effects
of economic constraints are in a picture of the Capitol building. The
rates and levels associated with the arms in production and stockpile are
replaced with pictures of workmen and missiles. This oversimplification
breaks with system dynamics symbol tradition but is necessary to
communicate to the general public.
By moving a cursor over the symbol of interest, a window on the screen
prompts you with your choices. If you are above the Capitol building for
example, the prompt would be "would you like to change your margin of
superiority?" If so, you do it by adjusting a thermometer like symbol that
"floats" through readings of 10%, 15%, 20%, etc. so that you do not have to
type in numbers. This more intuitive display and interaction style is
particularly valuable for adult groups who are usually far less familiar
with computers than high school students.
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COUNTRY X
ESTIMATION
OF OPPOSING
ARMS
x's ARMS
XA
oH)
YA
Y's ARMS
ESTIMATION
OF OPPOSING
ARMS
COUNTRY Y
= SOSA
Figure 2. A positive-feedback loop connecting countries X and Y can produc?
exponential growth. If country X attempts to raise its level of arms abov2
Y, and country Y attempts to keep its level of arms above X, arms spiral
upward.
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TIME
Giana. DESIRED
DESIRED MARGIN OF
MARGIN OF SUPERIORITY
SUPERIORITY XDMSI
XTOMS ;
DESIRED
TIME TC
AUTHORIZE \ i MARGIN OF
ARMS N SUPERIORITY
XDMS2
XTAA >
FP DESIRED _-7
¢ ARMS
vf =_
ae SENSITIVITY
he TO OPPOSING
~~ N ARMS
™~ \ PRODUCTION
‘\ xsoap
ESTIMATED Nn 2
XAUD
ARMS UNDER
DEVELOPMENT
OOMESTIC
ARMS
ESTIMATED
- OPPOSING
—< “7 ARMS
XBEDA / ra
BIAS IN / xBEOA
ESTIMATING 1 Bias IN
OMe 7 ESTIMATING a ‘
/ OPPOSING Ze \
>” ARMS \
| XA 7 \
i elie DELAY. om DELAY
te / ¢ x 7 Ly
XAPD “oe ye J NV \
AVERAGE
PROCUREMENT aot x XTPOA |
DELAY XALA TIME TO PERCEIVE |
AVERAGE 72 OPPOSING ARMS ;
LIFE OF if
ARMS /
/
x
se oat ay".
1 wa z
boars snes: Cee =z
va 7 | YAUD } 3
' v's arms! ARMS UNDER 3
| | | DEVELOPMENT |
Figure 3. A flow-diagram of country X's arms planning. Country X's
intelligence system estimates country Y's arms.
After taking into account
its desired margin of superiority (or inferiority), X determines its own
desired level of arms.
spending on new weapons.
usable arms. Country Y
X then evaluates its own capability and authorizes
After a procurement delay, X has a new level of
has a similar structure. Also shown are the policy
levers that allow testing of alternatives.
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USING THE SIMULATIONS
After this brief presentation of the structure we proceed through a series
of simulations. The strategy here is to demonstrate that the model is a
way of extending, testing, and exploring their own assuptions. Rather than
presenting my opinions, we use partial model testing and purposefully set
the original parameters to neutral or even incorrect values. A guided
series of exercises requires the participant to correct parameter values or
choose values they think are more plausible.
This seems to be effective for three reasons. First, it is more fun to
learn about the model by playing with it than by having a longer lecture on
the structure. Second, many people assume that arms races are caused by
evil or misguided generals and politicians. By producing arms races from
participants' own chosen policies, the model provokes a rethinking of prior
assumptions and illustrates the importance of structure in producing
behavior. It also introduces the concept of bounded rationality. Third,
it emphasizes that this is a hypothetical logical excercise, the purpose of
which is to stimulate thinking and not a policy recommendation based on the
analysis of the real system.
SUMMARY OF SIMULATIONS
DPK843: This model simulation shows an “equilibrium" with all policies in a
neutral condition. Both countries start with 100 units of arms, accurately
perceive the other side's level of arms, and desire only parity.
DPK844: Before using a model you should always "test-drive" it. Here we
see country X's response to a 10% exogenous increase in arms at country Y
starting from equilibrium. X's response is too slow. How could you speed
it up?
DPK845: Shortening X's time to adjust arms, XTAA, from 5 to 2 gives a more
plausible response time. Country Y is still held constant for test
purposes.
DPK846: A 10% bias in estimating opposing arms is added to the conditions
in DPK845. Country Y is still held constant.
DPK847: Country Y is now allowed to respond. Country X is able to
unilaterally drive an arms race even though both countries desire only
parity. Country X's bias is equivalent to a desired margin of superiority.
DPK848: In addition to the 10% bias shown in Figure 9, Country X desires a
10% margin of superiority. This increases the rate of growth of the arms
race.
DPK849: At year 30, Country Y changes its definition of security and is now
willing to accept a margin of arms 25% less than Country X. This is
sufficient to offset the growth pressure caused by X's desired margin and
bias thereby producing a slow decline in arms.
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DPK850: When more realistic policies are added to the rest of Country X,
however, the same strategy which ended the arms race in Figure 11 now is
overwhelmed and no longer works.
DPK851: When more realistic values are added for Y as well, the rate of
growth is even faster.
DPK852: Both countries now have more realistic policies. Y no longer
accepts a 25% margin of inferiority at time 30. This rate of growth is
closer to, but still slower than, the real growth rates in the U.S.
arsenal.
DPK853: If both countries agree to set their desired arms to 15% below what
the other side has there is still an arms race. The biases and
inaccuracies in evaluating domestic and foreign arms are sufficient to
produce an arms race even when both countries have a goal of a build down.
DPK854: A build down is theoretically possible if the commitment is
sufficiently aggressive to offset the growth pressures from the biases and
inaccuracies. These simulations are not an analysis or proposal, but
merely a logical exercise for studying the interaction of selected
policies.
D-3689-1
K8432 EQUILIBRIUM
eect ~~ — CONTRY Ys ARMS (80., 180.)
100, meee a2 ao omnes = X=Y ARMS RATIO OB 1,4)
14
140,
12
0 10, ry E 40, 30. 60.
TIME
K845: FASTER ADJUSTMENT TIME
a = = COUNTRY Ye AS BO. 100.)
Se as ey. ARMS RATIO ©, 1. 4)
140,
1.2
THe
ACTIVATE COUNTRY Y
K847s
COUNTRY Xe ARMS @., 400.)
ee 2 = = = COUNTRY Ye ARG ., 400.)
400, mm X-Y ANS RATIO (81.4
14
300,
1.2;
at Cd a eee en Se ee
lL
100, Coeds aie
i)
)
rT ar’ ya
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K844: RESPONSE TO EXOGENOUS 10% INCREASE
wm wm — COUNTRY Ve ARMS BD, 160.)
10D, ee me XY ARNS RATIO GG, 1. 4)
140,
1.2
K846: 10% BIAS IN ESTIMATE
COUNTRY Xs ARKS GBO.. 180.)
tm COUNTRY Yo RNB GB... 160.)
sso, X-V_ARHS RATIO G6, 1. 4)
140,
1.2)
ed /\W ~~ “~~ ~ :
100, | §
8
TIME
K848: X DESIRES 10% SUPERIORITY
COUNTRY Xs ARHS (0, . 400.)
ee —— = COUNTRY Yo ARKS 0, 400.)
40D, ene on wo men = = X-Y ARMS RATIO (6, 1. 4?
rey
300.
2
fo PSweters -- -4 4
200, |
rs
en
et ee
fon |
Figure 5. Selected simulation runs from workshop.
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K849; Y ACCEPTS -252 MARGIN AT YEAR 30
—————— Cor ARS, son.
wn---- == COUNTRY Yo ARMB @D.,, 400, )
00, ar en ARMB RATIO CG, 1.4)
2 ~*~
A
100. extasa=F =] eden eked
“Ss
fe
/
«0 10. a 3a. a, Ly oo
TIE
K853: BOTH X AND Y ACCEPT -15% MARGINS
COUNTRY Xs AS 00... 400.)
tam = COUNTRY Ve ARMS ©, 400.)
OS aes eer Sekt ARMS RATIO C& 1.4
Phe)
00.
2
wm! |
Boe — i -
100, _
ht
0
K850: MORE REALISTIC POLICIES FOR X
COUNTRY Xe AWS (0. 400.)
won 222TH Yo ARMS ., 400.)
00, ww mm HY AE RATIO C81.
?
rN Hy
00, / ee
1.2 a
'
t a
= PT el
. >I at
o- an
-
wal Ae
4
“oo me OB OS 8S
Te
K852: MORE REALISTIC POLICIES FOR BOTH
eee em = CON fh ARS oO. 400, )
OL, ms a es = X-Y ARKS RATIO 68, 1.4)
14
t
Vi;
300,
12 ve
10 Nan ofl nw heen op meee bo ened
=m, (>
% WA
a
wo |
3
1)
coi a 8S BO
a ey Ye @., 400.)
08 eo ee oY ARMS RATIO C6, 1. 4)
300.
1.2
Figure 6. Selected simulation runs from workshop (continued).
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ISSUES AND COMMENTS RAISED IN TRIAL TESTING
With the advent of new generations of weapons technologies and the
continued instability in certain sectors of the international there is
growing public concern and discussion of arms races. While most people
seem to view themselves as patriotic citizens and support the need for
their countries to be secure against attack or manipulation by adversaries,
there is little agreement on how to best achieve such security.
The phrase "arms race" connotes a wide range of images to different people.
For some, it brings to mind an exponential escalation of weapons that could
potentially lead to disaster. To others, the arms race is an unfortunate
necessity forced upon us by hostile and agressive adversaries. There are
some who have expressed the notion that arms races are innocuous and
perhaps even a beneficial stimulant to the economy and to the advancement
of science and technology. There are also political components across the
range of perspectives. Although greatly oversimplified, those who regard
themselves as liberal seem to be more likely to see the primary issue of
the arms race as the threat of nuclear war and the destruction of
civilization. On the other hand, people who describe themselves as more
conservative seem to place more emphasis on the threat of domination or
manipulation by foriegn adversaries (Marks 1985).
It has been interesting to notice how these differences in starting
assumptions affect what you see in the model. Liberals tend to notice that
even if both countries are building arms very quickly, but at the same
rate, neither country is any more or less secure. On the other hand, one
defense contractor noticed that because the model represented depreciation
and obsolesence of the arsenal, a country needs a constant stream of
replacement orders just to stay even. He said this is something "freeze
people" often don't realize. Many of the weapons, such as the MX missile
and the B1 bomber, that many think of as an escalation of arms, he views
merely as replacements for aging outdated weapons such as the Trident and
B52. He has raised issues which could show how a dynamic model could add a
great deal of precision to the "freeze" debate. If a freeze is thought of
in terms of freezing the investment rate, and that is higher the rate of
obsolesence, the level of arms will still increase. There would be very
different implication depending on whether a freeze were to be proposed in
terms of expenditures, expenditures as a fraction of GNP, absolute numbers
of weapons, or the total technological destructiveness of the weapons.
Again, it is important to note that the model is not a proposal, but merely
and examination of the relationship between structure and behavior.
For me, the experience of showing the model to dozens of groups has been
interesting and educational and has lead me to change my opinion about what
is the best way of using a simulation model for stimulating public debate.
One striking feature of almost everyone I've talked to is that no matter
where they stood on the issue from the most radical or most conservative,
they almost always view their own position on the issue as the most
reasonable. They view the other positions on the political spectrum as
often naive, suspicious, demented, misinformed, etc. but seldom more
correct than their own.
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There have been many interesting comments. One older man said, "it
disturbs me to see so many bright, well intentioned young people wasting
their time and energy over an issue that they really can't have much
influence on." He accepts Wiesner's assertion that above a certain
threshold of overkill, additional weapons don't really add to security.
But, "so what, arms races don't matter. Give the generals what they want.
At a time when there is unemployment and excess capacity in the economy it
would irresponsible to cut back on military expenditures."
One expert expressed concern that the model might be misused to mislead the
public to support a particular political position. Another suggested that
using country X and country Y rather than the US-USSR was naive and
unnecessary. Another interesting comment was that there may be occasions
in negotiations and debate where a better, clearer, more explicit
representation of each parties viewpoint is not useful and may even be
counter-productive.
These are the kinds of reactions we need to analize and think about over
the next year as we work on turning the model into a tool of stimulating
thinking, discussion, and debate about national security and arms races.
CONCLUSIONS AND NEXT STEPS
The conceptual soundness of the present models and their educational
effectiveness need to be reviewed by a variety of evaluators before
releasing the model to the public. We must be sure that it is correct both
technically and psychologically. It must not convey unsupportable and
biased viewpoints.
I have added a single economic sector to illustrate the "guns versus butter
trade-offs" and also the long-term versus short-term trade-offs possible
with higher fractions of a nation's output devoted to military
expenditures. Some evidence indicates that military investments are not as
efficient as capital investments. To the extent that increases in military
expenditures come from domestic capital investment rather than consumption
there is a danger that the military will get a larger fraction of a smaller
GNP. This idea needs much more research and review before preliminary
testing in the workshop model. It is just one example of a potentially
sensitive issue where a cautious approach is called for.
There is still much work to be done on the software adding error checking
and a more facile and intuitive interaction. One important change in our
thinking arising from the workshop tests is that it will be more difficult
than we thought to design the software to be entirely self-explanatory,
thereby replacing the need for a workshop leader and making possible wide
distribution. The reaction so far is that a highly valuable part of the
workshop are the stories, interpretations, and answers to questions,
provided by the workshop leader. Although we have a limited number of
stories and data stored in interactive menus within the software the
messages and purpose is not sufficiently clear to adequately replace 4
workshop leader.
The number of weapons has escalated continuously for the last forty years
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despite a number of administrations and treaties. This suggests that there
must be deeper underlying forces that can propel an arms race. The study
of these underlying political and psychological forces and the structure of
the information channels of the relationship between both countries, with
interactive feedback simulation models, represents important areas of
research and public education. Considering these system properties when
proposing solutions will probably increase the likelyhood of success.
System dynamicists often assert that when dealing with people of different
languages, viewpoints, geographical, and organizational contexts, an
explicit simulation model represented in graphic and intuitive terms can
aid communication by providing a vivid picture of what each party is
thinking. The model can be a conversation piece, a map of your current
understanding. When your logic goes amiss you have, a way of testing for
inconsistencies in your thinking. The explicity history of your
assumptions allows you or others to go back to your wrong turn and start
anew. The future research and design of this workshop exploring the
dynamics of arms races should be interesting test case for these
assertions. Perhaps we will learn how to broaden the discussion from
national security to international or global security. With the rapidly
changing technology of weapons we may not be able to have one without the
other.
REFERENCES
Choucri, N. and M. Bousfield. "Alternative Futures: An Exercise in
Forecasting." Chapter 21 in N. Choucri and T. W. Robinson (eds.),
Forecasting in International Relations: Theory, Methods, Problems,
Prospects (San Francisco, W. H. Freeman and Co., 1978)., pp. 308-326.
Choucri, N. and R. C. North. Nations in Conflict: National Growth and
International Violence (San Francisco, W. H. Freeman and Co., 1975).
Clark, T. D. "The United States Arms Transfer Process and Policy: A Systems
Dynamics Approach," Proceedings of the 1981 System Dynamics Research
Conference, Institute on Man and Science, Rensselaerville, New York,
October 14-17, 1981, pp. 236-237.
Cusack, T. R. and M. D. Ward. "Military Spending in the United States,
Soviet Union, and the People's Republic of China, Journal of Conflict
Resolution, Volume 25, Number 3, September 1981, pp. 429-469.
Forrester, J. W. "Dynamic Modeling of the Arms Race," Cambridge, MA:
Massachusetts Institute of Technology, System Dynamics Group Memo D-3684-3,
1985.
Forrester, J. W. "System Dynamics Modeling of the Arms Race," Cambridge,
MA: Massachusetts Institute of Technology, System Dynamics Group Memo
D-3561, 1984.
Kreutzer, D.P. "A Personal Computer Workshop Exploring the Dynamics of the
Arms Race," Cambridge, MA: Massachusetts Institute of Technology, System
Dynamics Group Memo D~3732, 1985.
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Kreutzer, D.P. "Documentation of Arms Race Model and Simulation Runs,"
Cambridge, MA: Massachusetts Institute of Technology, System dynamics Group
Memo D-3747, 1985.
Kreutzer, D. P. “Corporate and Economic Policy Design with Microcomputers:
A System Dynamics Approach," Cambridge, MA: Massachusetts Institute of
Technology, System Dynamics Group Memo D-3585, 1984.
Marks, J. Whither: Search for Common Ground. Brochure available from the
author, Suite 1126, 1346 Connecticut Ave., Washington, DC 20036, 1985.
Richardson, L. F. "Arms Races." Chapter 2 in L. F. Richardson, Arms and
Insecurity. (Chicago: Quadrangle, 1960).
Schrodt, P. A. "Microcomputers in the Study of Politics: Predicting Wars
with the Richardson Arms-Race Model," BYTE, July 1982, pp. 108-134.
Sterman, J. D., "A Simple Model of the Arms Race," Cambridge, MA:
Massachusetts Institute of Technology, System Dynamics Group Memo D-3713,
1985.
Ward, M. D. "Modeling the USA-USSR Arms Race," Simulation, Volume 43,
Number 4, October 1984, pp. 196-203.
Wiesner, J. B. "A Perilous Sense of Security," Reprinted from the Boston
Globe Magazine, October 7, 1984.
White, C. "Elements of Control in Alliance Force Development," Proceedings
of the 1981 System Dynamics Research Conference, Institute
on Man and Science, Rensselaerville, NY, October 14-17, 1981, pp. 94-95.
