An imitation game is a finite two person normal form game in which the two players have the
same set of pure strategies and the goal of the second player is to choose the same pure
strategy as the first player. We explain how, in two different settings, observations obtained
from imitation games complete a circle of ideas, showing that phenomena that had for many
years seemed to be distinct are actually superficially different manifestations of a single
structure. First, one can pass from a given two person finite game to an imitation game