In this paper we deal with the solutions of systems of PDEs with bilateral inter-connected obstacles of min-max and max-min types. These systems arise naturally in stochastic switching zero-sum game problems. We show that when the switching costs of one side are regular, the solutions of the min-max and max-min systems coincide. Furthermore, this solution is identified as the value function of a zero-sum switching game.
The paper is currently available on Arxiv at: arXiv:1408.4282