Neveu's martingale conditions and closedness in dynkin stopping problem with a finite constraint

The Dynkin stopping problem with a constraint that the game must always terminate after some finite number of observations is considered. We give the equivalent conditions for the closedness of the game, one of which is of martingale form. We also find [set membership, variant]-saddle points and prove that this 0-saddle point is a certain kind of minimal one.optimal stopping problem Dynkin's game finite constraint martingale condition saddle point