  In this paper we study iterative procedures for stationary equilibria in
games with large number of players. Most of learning algorithms for games with
continuous action spaces are limited to strict contraction best reply maps in
which the Banach-Picard iteration converges with geometrical convergence rate.
When the best reply map is not a contraction, Ishikawa-based learning is
proposed. The algorithm is shown to behave well for Lipschitz continuous and
pseudo-contractive maps. However, the convergence rate is still unsatisfactory.
Several acceleration techniques are presented. We explain how cognitive users
can improve the convergence rate based only on few number of measurements. The
methodology provides nice properties in mean field games where the payoff
function depends only on own-action and the mean of the mean-field (first
moment mean-field games). A learning framework that exploits the structure of
such games, called, mean-field learning, is proposed. The proposed mean-field
learning framework is suitable not only for games but also for non-convex
global optimization problems. Then, we introduce mean-field learning without
feedback and examine the convergence to equilibria in beauty contest games,
which have interesting applications in financial markets. Finally, we provide a
fully distributed mean-field learning and its speedup versions for satisfactory
solution in wireless networks. We illustrate the convergence rate improvement
with numerical examples.
