  Fictitious play (FP) is a canonical game-theoretic learning algorithm which
has been deployed extensively in decentralized control scenarios. However
standard treatments of FP, and of many other game-theoretic models, assume
rather idealistic conditions which rarely hold in realistic control scenarios.
This paper considers a broad class of best response learning algorithms, that
we refer to as FP-type algorithms. In such an algorithm, given some (possibly
limited) information about the history of actions, each individual forecasts
the future play and chooses a (myopic) best action given their forecast. We
provide a unifed analysis of the behavior of FP-type algorithms under an
important class of perturbations, thus demonstrating robustness to deviations
from the idealistic operating conditions that have been previously assumed.
This robustness result is then used to derive convergence results for two
control-relevant relaxations of standard game-theoretic applications:
distributed (network-based) implementation without full observability and
asynchronous deployment (including in continuous time). In each case the
results follow as a direct consequence of the main robustness result.
