Nash Equilibrium for Multi-Player Regime Switching Stochastic Differential Games

In this study, we consider multi-player stochastic differential games with regime switching in the player dynamics modeled by a Markov chain with a finite state space. We study the associated Nash system, which comprise a system of coupled nonlinear partial differential equations. We prove the existence and uniqueness of solutions to the Nash system, thereby establishing the existence of a unique Nash equilibrium.