Maximum principle via Malliavin calculus for regular-singular stochastic differential games

We consider non-zero-sum regular-singular stochastic differential games, where the informations available to the two players are asymmetry partial informations. The control strategy of each player consists of two components: regular control and singular control. Applying the Malliavin calculus approach, we establish a necessary maximum principle for the games, where the adjoint processes are explicitly represented by the parameters and the states of the system