Model 3

Interpreting Results

Most of the research on this spatial version of the Prisoner's Dilemma has focused on the interesting patterns that can be produced by this model (Nowak and May, 1992. Evolutionary games and spatial chaos. Nature 359: 826-829. Nowak, Bonhoeffer, and May, 1994. Spatial games and the maintenance of cooperation. Proceedings of the National Academy of Sciences, USA 91: 4877-4881.), although even these patterns can provide some biological insights. For example with the following set of parameters (at range 1):


 Player 2
Player 1 
   Defect Cooperate
Defect  0  b
Cooperate  0  1

where 1.8 < b < 2.0, groups of cooperators can invade defectors, but groups of defectors can invade cooperators. This maintains a balance of cooperators and defectors, and tends to aggregate like types.

The tendency to aggregate like types in this model provides some insight into the differences between parameters run in the non-spatial Prisoner's Dilemma and the same parameters as run in this model. Even when an environment is say 50% of each type, that doesn't mean that each individual interacts with 50% of each type. For example, when a large clump of defectors is placed an environment of cooperators, the defectors in the center of the clump are experiencing a different environment than those on the edge. Defectors in the center are only interacting with other defectors which causes them to fare differently than those on the perimeter that interact with both defectors and cooperators. This can allow one type that does well with more of the same type to spread through the environment in a way that would not be possible if everyone interacted with everyone else.