  The evolution of cooperative behaviour is studied in the deterministic
version of the Prisoners' Dilemma on a two-dimensional lattice. The payoff
parameter is set at the critical region $1.8 < b < 2.0$ , where clusters of
cooperators are formed in all spatial sizes. Using the factorial moments
developed in particle and nuclear physics for the study of phase transition,
the distribution of cooperators is studied as a function of the bin size
covering varying numbers of lattice cells. From the scaling behaviour of the
moments a scaling exponent is determined and is found to lie in the range where
phase transitions are known to take place in physical systems. It is therefore
inferred that when the payoff parameter is increased through the critical
region the biological system of cooperators undergoes a phase transition to
defectors. The universality of the critical behaviour is thus extended to
include also this particular model of evolution dynamics.
