In the paper the Dynkin zero sum stopping game is considered. The players observe a discrete time Markov process. At each moment n the players decide separately if they accept or reject the realization of the process. One of the player is choosing at most two states, the second one is choosing at most one state. It means that Player 1 has pairs of stopping time as strategy and Player 2 is using the stopping time as his strategy. The payoff function depends on all choosing states. If it happens that more than one player has selected the same moment n to accept the state, then a lottery decides which player gets the right (priority) of acceptance. A formal model of the game and construction of the solution for the finite horizon game is given. The example related to the secretary problem is solved. The model is generalization of the two person games considered by Szajowski (1994) and N person game with fixed priority scheme solved by Enns and Ferenstein (1987).