  We study stochastic Nash equilibrium problems with expected valued cost
functions whose pseudogradient satisfies restricted monotonicity properties
which hold only with respect to the solution. We propose a forward-backward
algorithm and prove its convergence under restricted strong monotonicity,
restricted strict monotonicity and restricted cocoercivity of the
pseudogradient mapping. To approximate the expected value, we use either a
finite number of samples and a vanishing step size or an increasing number of
samples with a constant step. Numerical simulations show that our proposed
algorithm might be faster than the available algorithms.
