  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 cocoercivity and
restricted strict monotonicity 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.
