<p>Typically, randomness in evolutionary games is included by equipping the discrete deterministic replicator dynamics with Moran noise processes. Here, we extend this approach to obtain, from first principles, continuous evolution equations subject to white noise excitation. The modeling of these stochastic replicator dynamics will follow the approach applied in biological systems subject to system-internal random fluctuations. Our focus of study is evolutionary games with three pure strategies as they can be found by playing rock-scissor-paper or, in nature, by the territorial dynamics of the side-blotched lizards <i>Uta stansburiana</i>. Simulations of the stochastic game dynamics in its phase space together with discussions of the evolutionary stability of the equilibria will round up the presentation.</p>