In this article, a modelling framework for the information transmission between agents in an evolutionary game setting is proposed. Agents observe traits which reflect past and present behaviour and success of other agents. If agents imitate more successful agents based on these traits, the resulting dynamics are a multivariate stochastic process. An example for such a process is simulated. The results resemble the replicator dynamics to a remarkable degree. If traits moderately depend on the past, this accelerates convergence of the dynamics towards a stable state. If the dependence is strong, the stable state is not reached.