On the role of the group composition for achieving optimality

We show the inability of any pure strategy imitation rule for leading a decision maker towards optimality for given and fixed population behaviour. The intuition is that a pure strategy state space is too small to deal with a large variety of environments. This result helps to understand the optimality result obtained by Schlag, where the population behaviour is let to evolve over time. The intuition is that the group composition provides an additional state space in which information about the environment can be accumulated.