The spatial version of the Prisoner's Dilemma is the latest approach to this problem. This idea was introduced by Martin Nowak and Robert May (Nowak and May, 1992. Evolutionary games and spatial chaos. Nature 359: 826-829). Their studies of this problem have concentrated on one set of payoff values that conforms to the following parameters (at range 1):
where b is between 1.0 and 2.5. Parameters in this range can produce a diversity of interesting pictures. Be sure to run each set of parameters multiple times if you are starting from the initial random configuration. You should also try loading some of the prepared pictures, especially those that are one or a few defectors with the rest cooperators.
There are other parameters that lead to interesting comparisons with Model 1, the non-spatial version of the Prisoner's Dilemma. For example, take the following set of payoffs (again at range 1):
Run this set of parameters in Model 1, and then in this model. Then try slowly increasing the mutual cooperation payoff, while keeping it less than 4. Each time you try a new value be sure to restart from a random initial condition. Towards the higher end of the range try using some of the prepared images. Can a single defector invade an environment of cooperators? How many are necessary to do this? How about the reverse situation with cooperators invading defectors? Does the shape of the initial clump matter? Choose a value for mutual cooperation at which cooperation can just take hold in the environment. Now try increasing the range of interaction. What effect does this have?
For those that are more adventurous, another set of parameters to try is:
Again, try these parameters in Model 1. This time, you should be sure to run Model 1 multiple times observing which type wins. Now try it in the spatial version. Does the same species win every time in the non-spatial version? the spatial version? In the spatial version can a single cooperator invade an environment of defectors? How many does it take to invade?