  Motivated by applications to data networks where fast convergence is
essential, we analyze the problem of learning in generic N-person games that
admit a Nash equilibrium in pure strategies. Specifically, we consider a
scenario where players interact repeatedly and try to learn from past
experience by small adjustments based on local - and possibly imperfect -
payoff information. For concreteness, we focus on the so-called "hedge" variant
of the exponential weights algorithm where players select an action with
probability proportional to the exponential of the action's cumulative payoff
over time. When players have perfect information on their mixed payoffs, the
algorithm converges locally to a strict equilibrium and the rate of convergence
is exponentially fast - of the order of
$\mathcal{O}(\exp(-a\sum_{j=1}^{t}\gamma_{j}))$ where $a>0$ is a constant and
$\gamma_{j}$ is the algorithm's step-size. In the presence of uncertainty,
convergence requires a more conservative step-size policy, but with high
probability, the algorithm remains locally convergent and achieves an
exponential convergence rate.
