  The paper is concerned with distributed learning in large-scale games. The
well-known fictitious play (FP) algorithm is addressed, which, despite
theoretical convergence results, might be impractical to implement in
large-scale settings due to intense computation and communication requirements.
An adaptation of the FP algorithm, designated as the empirical centroid
fictitious play (ECFP), is presented. In ECFP players respond to the centroid
of all players' actions rather than track and respond to the individual actions
of every player. Convergence of the ECFP algorithm in terms of average
empirical frequency (a notion made precise in the paper) to a subset of the
Nash equilibria is proven under the assumption that the game is a potential
game with permutation invariant potential function. A more general formulation
of ECFP is then given (which subsumes FP as a special case) and convergence
results are given for the class of potential games. Furthermore, a distributed
formulation of the ECFP algorithm is presented, in which, players endowed with
a (possibly sparse) preassigned communication graph, engage in local,
non-strategic information exchange to eventually agree on a common equilibrium.
Convergence results are proven for the distributed ECFP algorithm.
