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

TL;DR

This paper provides an explicit solution to a two-player switching game using viscosity methods, characterizing switching regions and deriving thresholds for optimal switching in a stochastic setting.

Contribution

It introduces a novel explicit solution for a two-player switching game with non-positive costs, including a numerical procedure for value computation.

Findings

Explicit characterization of switching regions

Threshold-based switching strategy derived

Numerical simulations demonstrating the solution

Abstract

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.