Computational Modelling in Philosophy
and the Social Sciences
This web site contains links to some evolutionary game theoretic models
written in Java. The models are known to work in Internet Explorer, version 5
and up, and the most recent version of Mozilla.
You need to have the most recent Java plug-in installed. To get that, go
to the download page at Sun's web site and follow the instructions.
The installation is very easy, although it will take some time if you have a
slow network connection. You only need to do this once.
If you aren't using Windows, Java support is a bit hit-and-miss. Mac OS
X, so I am told, comes with support for Java 1.3 preinstalled. If true,
this means that these models
should work under OS X. If you are using Linux, you can find
the Linux plug-in here.
You should probably have a reasonably fast computer to use these models.
Clicking on a link below will take you to the specified model. The
model may take some time to load as the necessary JAR files are
transferred to your computer. If you are using a slow network connection
(i.e., any telephone dial-up), the models will take some time to load. On some machines, users have reported an
unnaturally long delay before the models are useable. If you suspect that
things are taking longer than they should, hit the "Reload" button on
your browser. That usually solves the problem.
The models were designed for a minimum screen resolution of
800x600. If your display does not support that, you may find them somewhat
awkward to use since they will not fit entirely on screen.
Some useful tips:
- You need to press <Enter> after typing information into a text box
for it to be recognized.
- Left-clicking and dragging in the lattice will pan the view.
Right-clicking and dragging in the lattice will zoom in or out. If you
right-click and drag to the right, you zoom in; if you right-click and drag
to the left, you zoom out. Zooming in and out can be done as the model
runs. If you want to return to the original view, click on the "Recenter
The prisoner's dilemma
- The spatial
prisoner's dilemma. This model is based on the one found in Martin
A. Nowak and Robert M. May, "The Spatial Dilemmas of Evolution," International
Journal of Bifurcation and Chaos, Vol. 3, No. 1 (1993) pp. 35-78.
- The asynchronous spatial prisoner's
dilemma. This model is based on the one discussed in Bernardo A.
Huberman and Natalie S. Glance, "Evolutionary games and computer
simulations," Proc. Natl. Acad. Sci., Vol. 90 (August 1993) pp.
7716-7718. That paper isn't entirely clear about how the dynamics were
implemented, so some reading between the
lines was involved in putting this model together. Regardless,
Huberman and Glance's main claim - that the general qualitative behaviour of
asynchronous models can differ greatly from that of the synchronous version
- is reproduced.
The stag hunt
- The stag hunt on a lattice. The stag hunt
is a much-understudied model of cooperation.
- The stag hunt on an arbitrary network (a
minimal model). This model seeks to lift the sometimes unnatural
topological assumptions imposed by lattice models. It is in the very
early stages, so you can't draw many (if any)
conclusions from it.
The Nash bargaining game
- The spatial Nash bargaining game. This model is
essentially the one discussed by myself and Brian Skyrms in
"Bargaining with Neighbors: Is Justice Contagious?" The Journal
of Philosophy, Vol. 96, No. 11 (November 1999) pp. 588-598; analyzed at
greater length in "Evolutionary Explanations of Distributive
Justice," Philosophy of Science, 67 (September 2000) pp.
- The asynchronous spatial Nash bargaining game.
This model uses the exact same algorithm for the dynamics as that of the
asynchronous spatial prisoner's dilemma above. Note that Huberman and
Glance's claim fails to hold for the Nash bargaining game. The
equilibrium where everyone follows the strategy of fair division is a
sufficiently strong attractor that, even when asynchronous dynamics are
used, we still get uniform convergence to fair division.
The ultimatum game
- The spatial ultimatum game. This model is
essentially the one I developed in "Artificial Justice," Artificial
Life VII: Proceedings of the Seventh International Conference, edited by
Mark A. Bedau, John S. McCaskill, Norman H. Packard, and Steen Rasmussen,
MIT Press, 2000. It currently lacks the ability to introduce new
strategies by mutation and to have the population employ a variety of
- The asynchronous ultimatum game. This
model uses the exact same dynamics as the asynchronous Nash bargaining game
and the asynchronous prisoner's dilemma. Interestingly enough, we once
again witness that the use of asynchronous dynamics seems to make little
difference for this game.
These models use the Jazz
toolkit for constructing zoomable user interfaces developed by Ben Bederson at
the University of Maryland and the ptplot
package developed at UC Berkeley. Source code available upon request.
J. McKenzie Alexander
Department of Philosophy, Logic and Scientific Method
London School of Economics and Political Science