Existence of Saddle Points in Discrete Markov Games and Its Application in Numerical Methods for Stochastic Differential Games

摘要

This work establishes sufficient conditions for existence of saddle points indiscrete Markov games. The result reveals the relation between dynamic gamesand static games using dynamic programming equations. This result enables us toprove existence of saddle points of non-separable stochastic differential gamesof regime-switching diffusions under appropriate conditions.