Traditionally, evolutionary game dynamics is described in terms of
deterministic differential equations. In the past years, evolutionary game
dynamics has benefitted from considering finite populations, which adds a
natural source of noise. The intensity of selection, which corresponds to an
inverse temperature, determines the interplay between selection and noise.
Weak selection allows numerous new results in stochastic evolutionary game
dynamics, but sometimes also strong selection allows analytical results.
Theoretical aspects of this development will be discussed and examples from
the evolution of cooperation and punishment will be given, where noise can
become crucial for the dynamics.