  Evolutionary dynamics in finite populations is known to fixate eventually in
the absence of mutation. We here show that a similar phenomenon can be found in
stochastic game dynamical batch learning, and investigate fixation in learning
processes in a simple 2x2 game, for two-player games with cyclic interaction,
and in the context of the best-shot network game. The analogues of finite
populations in evolution are here finite batches of observations between
strategy updates. We study when and how such fixation can occur, and present
results on the average time-to-fixation from numerical simulations. Simple
cases are also amenable to analytical approaches and we provide estimates of
the behaviour of so-called escape times as a function of the batch size. The
differences and similarities with escape and fixation in evolutionary dynamics
are discussed.
