 In particular, we show that the existence of the solution and the game Nash equilibrium is connected with the solution of a system of non-linear reflected BSDE which remains an  problem.
<clarity>  In particular, we show that the existence of the solution and the game Nash equilibrium is connected with the solution of a system of non-linear reflected BSDE which remains an  problem.
 In particular, we show that the existence of the solution and the game Nash equilibrium is connected with the solution of a system of non-linear reflected BSDE which remains an open problem.