We study finite player stochastic differential games on possibly bounded spatial domains. The equilibrium problem is formulated through the dynamic programming principle, leading to a coupled Nash system of HJB equations and, in probabilistic form, to a corresponding Nash FBSDE with stopping at the first exit from the parabolic domain (covering both boundary and terminal conditions). The main focus of the talk is the analysis of a fictitious-play procedure applied at the level of FBSDEs. At each iteration, a player solves a best-response FBSDE against fixed opponent strategies, giving rise to a sequence of fictitious-play FBSDEs. We show that this sequence converges exponentially fast to the Nash FBSDE. In unbounded domains, this holds under a small-time assumption; in bounded domains, exponential convergence is obtained for arbitrary horizons under additional regularity conditions. For completeness, we also discuss how the fictitious-play FBSDE is approximated by a numerically tractable surrogate FBSDE, which itself converges exponentially to the fictitious-play equation. Since the surrogate FBSDE admits a standard time-discrete approximation of order 1/2, this provides a transparent overall error structure for the numerical approximation of the Nash FBSDE. We conclude with representative numerical illustrations of the full approximation scheme.