Existence of Saddle Points in Discrete Markov Games and Its Application   in Numerical Methods for Stochastic Differential Games
  This work establishes sufficient conditions for existence of saddle points in discrete Markov games. The result reveals the relation between dynamic games and static games using dynamic programming equations. This result enables us to prove existence of saddle points of non-separable stochastic differential games of regime-switching diffusions under appropriate conditions. 
Q. S. Song, G. Yin