On a discrete-time non-zero-sum Dynkin problem with monotonicity

We consider a monotone case of the non-zero-sum stopping game with discrete time parameter which is called the Dynkin problem. Marner (1987) has investigated a stopping game with general monotone reward structures, but his monotonicity is too strong to apply our problem. We establish that there exists an explicit equilibrium point in our monotone case. We also give a simple example applicable to a duopolistic exit game.