Physics – Nuclear Physics – Nuclear Theory
Scientific paper
1995-09-28
Int.J.Mod.Phys. A14 (1999) 1551-1560
Physics
Nuclear Physics
Nuclear Theory
12 pages + 3 figures, latex, submitted to Nature
Scientific paper
10.1142/S0217751X99000786
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.
Cao Zhen
Hwa Rudolph C.
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