  Empirical Centroid Fictitious Play (ECFP) is a generalization of the
well-known Fictitious Play (FP) algorithm designed for implementation in
large-scale games. In ECFP, the set of players is subdivided into equivalence
classes with players in the same class possessing similar properties. Players
choose a next-stage action by tracking and responding to aggregate statistics
related to each equivalence class. This setup alleviates the difficult task of
tracking and responding to the statistical behavior of every individual player,
as is the case in traditional FP. Aside from ECFP, many useful modifications
have been proposed to classical FP, e.g., rules allowing for network-based
implementation, increased computational efficiency, and stronger forms of
learning. Such modifications tend to be of great practical value; however,
their effectiveness relies heavily on two fundamental properties of FP:
robustness to alterations in the empirical distribution step size process, and
robustness to best-response perturbations. The main contribution of the paper
is to show that similar robustness properties also hold for the ECFP algorithm.
This result serves as a first step in enabling practical modifications to ECFP,
similar to those already developed for FP.
