We present the results of analytical and numerical studies of a one-dimensional nonlocal and nonlinear diffusion equation, which describes non-equilibrium processes ranging from aggregation phenomena to cooperation of individuals (game theory).  On tuning the initial conditions, a dynamical transition with a universal scaling behaviour is observed between two different asymptotic (in time) solutions, corresponding to states with full cooperation and full defection in the language of game theory. On temporally evolving the diffusion equation subject to a mirror symmetry transformation, the observed scaling regime of the solutions at the transition point is reached in a self-organized manner, independently of the initial conditions.

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