Explicit solution to an optimal two-player switching game in infinite horizon

In this paper we use viscosity approach to provide an explicit solution to the problem of a two - player switching game. We characterize the switching regions which reduce the switching problem into one of finding a finite number of threshold values in state process that would trigger switchings and then derive an explicit solution to this problem. The state process is a one dimensional It\^o diffusion process and switching costs are allowed to be non-positive. We also suggest a numerical procedure to compute the value function in case we know the qualitative structure of switching regions and we illustrate our results by numerical simulations.