Zero-sum stochastic differential games of mean-field type and BSDEs

In this paper, we deal with zero-sum stochastic game problems for stochastic differential equations (SDEs) of mean-field type, in which the coefficients depend on the law of some functional as well as the state of the process. Moreover, the cost functional is also of mean-field type. For the bounded case, applying the theory of backward stochastic differential equations, we obtain the existence of a saddle point under the Isaacs' condition.