Phase Transition in Evolutionary Games

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.Comment: 12 pages + 3 figures, latex, submitted to Natur

A New Method Of Distinguishing Models For The High-Q2Q^2 Events At HERA

Many explanations for the excess high-Q^2 $e^+p \to e^+X$ events from H1 and ZEUS at HERA have been proposed each with criticisms. We propose a new method to distinguish different models by looking at a new distribution which is insensitive to parton distribution function but sensitive to new physics.Comment: 11 pages in revtex plus 3 figures in postscrip