  We investigate critical properties of a spatial evolutionary game based on
the Prisoner's Dilemma. Simulations demonstrate a jump in the component
densities accompanied by drastic changes in average sizes of the component
clusters. We argue that the cluster boundary is a random fractal. Our
simulations are consistent with the fractal dimension of the boundary being
equal to 2, and the cluster boundaries are hence asymptotically space filling
as the system size increases.
