  It is known that learning of players who interact in a repeated game can be
interpreted as an evolutionary process in a population of ideas. These
analogies have so far mostly been established in deterministic models, and
memory loss in learning has been seen to act similarly to mutation in
evolution. We here propose a representation of reinforcement learning as a
stochastic process in finite "populations of ideas". The resulting birth-death
dynamics has absorbing states and allows for the extinction or fixation of
ideas, marking a key difference to mutation-selection processes in finite
populations. We characterize the outcome of evolution in populations of ideas
for several classes of symmetric and asymmetric games.
