Self-organized criticality in spatial evolutionary game theory

Self!organized criticality is an important framework for understanding the emergence of scale!free natural phenomena [ Cellular automata provide simple interesting models in which to study self!organized criticality [ We consider the dynamics of a new class of cellular automata which are constructed as natural spatial extensions of evolutionary game theory [ This construction yields a discrete one!parameter family of cellular automata [ We show that there is a range of parameter values for which this system exhibits complex dynamics with long range correlations between states in both time and space [ In this region the dynamics evolve to a self!organized critical state in which structures exist on all time and length scales \ and the relevant statistical measures have power law behaviour