The prisoner's dilemma (PD) involves contests between two players and may n
aturally be played on a spatial grid using voter model rules, In the model
of spatial PD discussed here, the sites of a two-dimensional lattice are oc
cupied by strategies. At each time step, a site is chosen to play a PD game
with one of its neighbors. The strategy of the chosen site then invades it
s neighbor with a probability that is proportional to the payoff from the g
ame. Using results from the analysis of voter models, it is shown that with
simple linear strategies, this scenario results in the long-term survival
of only one strategy, If three nonlinear strategies have a cyclic dominance
relation between one another, then it is possible for relatively cooperati
ve strategies to persist indefinitely With the voter model dynamics, howeve
r, the average level of cooperation decreases with time if mutation of the
strategies is included, Spatial effects are not in themselves sufficient to
lead to the maintenance of cooperation.