  In stochastic Nash equilibrium problems (SNEPs), it is natural for players to
be uncertain about their complex environments and have multi-dimensional
unknown parameters in their models. Among various SNEPs, this paper focuses on
locally coupled network games where the objective of each rational player is
subject to the aggregate influence of its neighbors. We propose a distributed
learning algorithm based on the proximal-point iteration and ordinary
least-square estimator, where each player repeatedly updates the local
estimates of neighboring decisions, makes its augmented best-response decisions
given the current estimated parameters, receives the realized objective values,
and learns the unknown parameters. Leveraging the Robbins-Siegmund theorem and
the law of large deviations for M-estimators, we establish the almost sure
convergence of the proposed algorithm to solutions of SNEPs when the updating
step sizes decay at a proper rate.
