Volume 8, Issue 3, 1994
Teaching and Learning
Economics using Cellular Automata in Asymmetrix Toolbook.
- Kevin Macken and Ken Randall
- Staffordshire University
Having been given one of the least visually tractable topics in the first
year Economics curriculum, Privatisation and Nationalisation, to turn into
interactive Computer Aided Learning material, our first draft of the
module was on the dull side. This module is one of over twenty comprising
the TLTP Economics Consortium's main product, WinEcon and looked likely to
be the dullest. It would have stayed that way but for a chance remark
from a friend on the interest he has in Genetic Algorithms. This led to an
idea for simulating a marketplace in Toolbook where competition could take
place. After an evening spent with ten empty fields on an otherwise blank
Toolbook screen and a short, messy script (i.e. program) the idea seemed
workable. The outcome is described below, along with ways the idea could
be developed further.
To see it, the simulation consists of differently coloured squares
contained within a large rectangular area. These represent competing
entities (typically firms) in a market where the size of the square
corresponds to the size of the firm. They are called 'Cellular Automata'
because each operates independently of the others in a robot-like way,
whilst all obey similar or identical rules of behaviour. In action, the
squares move and frequently collide with consequences for both parties to
the collision. This process continues in real time. Figure 1 shows how
this is introduced to the user.
To model the different types of market, (oligopoly, perfect competition,
monopolistic competition and monopoly) it was only necessary to specify
different outcomes to collisions. For instance, if competing in a
monopolistic market, larger firms tend to grow in size whilst smaller
firms are forced or kept out of the market, culminating in one dominating
firm. Therefore in the simulation, the instructions programmed for a
monopolistic market were.
- after a collision, make the smaller square smaller
- after a collision, make the bigger square bigger
- create no new squares
In a similar way, if the market was of the perfect competition type, the
following rules were programmed.
- after a collision, make the smaller square bigger
- after a collision, make the bigger square smaller
- create new squares at intervals to restore original complement
Figure 1: Click to see the full-size image
In the four types of market, different sets of rules were programmed to
ensure the simulation simulated in a valid manner. (One very keen drawback
of this was that it involved staring at moving coloured squares for hours
on end - there was no way of speeding the process up except running it on
a faster PC - so if the reader is tempted to develop independently minded
little beasties like these, bear this in mind!)
The Uses of the Simulation in the WinEcon Module: Privatisation and
To justify the work involved in getting the simulation working, it now
needed to enhance the module and be made as interactive as possible. It
was therefore decided to use it repeatedly to illustrate points, but in a
way which avoided repetition, and to develop a highly interactive screen
around it. The fact that it really belongs to another WinEcon module on
competition meant it had to be focused on teaching privatisation and
In figure 2 the simulation is used to enliven a point - that industries
can be nationalised using the argument of economies of scale. To
de-emphasize the simulation (because it was being used to illustrate a
rather obvious point) it was made smaller. This being the first time it is
used in the module it's presence and simplicity served to introduce the
user to it. Figure 3 In figure 3 the simulation is again de-emphasized,
as it is being used to support a point developed more fully in another
module. However, it does something more interesting now by having two
modes corresponding to a cartel being in effect or not. This shows the
user in a dynamic way the point made in the text and therefore reinforces
the learning taking place. Much further development of the model could
occur here. (See below.)
Figure 2 Click to see the full-size image
Figure 3 Click to see the full-size image
Figure4 Click to see the full-size image
Figure 4 shows the last time the simulation is used and it forms the basis
of the entire screen; hence it fills the screen. The user is invited to
set different conditions either by resetting the model or interrupting it.
These conditions are to specify one of the four types of market, and/or
specify whether a privatisation or nationalisation policy has been
enacted. The learning takes place by showing dynamically situations which
the user already has read about elsewhere or wishes to investigate. e.g.
- What happens if the firms in a market in perfect competition are nationalised?
- What happens if the firms in an oligopoly are privatised and broken up?
Hopefully the user realises that regulation can be simulated by changing
the type of market in effect, whilst the simulation is running.
In all of this the user is a long way from a text book on a screen which
the module would otherwise have tended to. And, a single simulation has
been reused in several parts of the same courseware without diminishing
As the reader may already have appreciated, this simulation could be used
to teach and learn about competition itself, regulation etc. It could be
developed much further. The theory behind oligopoly includes Game Theory
where separate entities have several strategies to pursue in a similar
way. The simulation above could be developed by making the Cellular
Automata of different kinds, so that for instance, cartels could be
simulated with cheating and colluding squares/automata - where the
parameters governing their choice of strategy can be varied by the user.
This would lead to a truer simulation of cartels where the
cartel-breaker initially benefits greatly but conditions soon favour the
rebuilding of the cartel. All this would proceed in real time. Similarly,
the squares could be made more purposeful, searching for some kinds of
squares and the colliding with them - the reader may know of an
application for this idea in economic theory.
As Game theory is one of the main tools of analysis in mathematical
economics, enhanced versions of this simulation should have many uses in
teaching and learning economics.
Module 21 has benefited greatly from the above simulation. The module now
has a third way that a user can approach it; the first is from the module
menu, analogous to a table of contents; the second is via questions posed
in various screens, corresponding to a problem-solving approach; the third
is via the highly interactive simulation described above. All three ways
point the user to the raw materials that form topics within the module.
This increase in the ways of approaching the material boosts the teaching
and learning efficacy of the software by catering for different types of
user and user need.
Kevin Macken and Ken Randall
Computers in Economics Unit
The Business School
(1) von Neumann,
J., Morgenstern, O. (1944), Theory
Games and Economic Behaviour
(2) Parkin, M., King, D. (1992), Economics.
Addison-Wesley Publishers Ltd.