Comment on “Imitation processes with small mutations” [J. Econ. Theory 131 (2006) 251-262]

We give an alternative proof of a result of Fudenberg and Imhof (2006) on the embedded Markov chain of an imitation process with small mutations. Our proof also extends this result to more general imitation processes that, with rare mutations, have unique stationary distributions but are not necessarily irreducible.