In this work we introduce the new approach of Dynamical Game Theory (DGT). In this approach, individuals perceive their payoffs differently as a function of their previous gain history and intrinsic characteristics. We present the dynamical donation game as a first case in this framework and analyze its corresponding dynamics through analytical and numerical approximations. We find that a high level of cooperation can be achieved and maintained when the dynamical donation game is played. The introduction of dynamical games opens new horizons in the explanation of the evolution of cooperation in social environments.