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<p>In this paper we use a viscosity solutions approach to solve a differential switching game problem. The game involves two players and the time horizon is infinite. We first reduce the switching problem from one of finding the optimal sequence of stopping times into that of finding a finite number of threshold values in state process that would trigger switchings. To this end, we characterize the switching regions by relying on the system of quasi-variational inequalities associated to the game. We then derive an explicit solution to the problem when the state process is a one-dimensional Itô diffusion together with possibly non-positive switching costs. We also suggest a numerical procedure to compute the value function in case we know the qualitative structure of the switching regions and we illustrate our results by numerical simulations.</p>

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Explicit Solution to an Optimal Two-player Switching Game in Infinite Horizon

  • 期刊论文

  • 发表日期：

    2026年4月25日

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  • El Asri Brahim,
  • Magnoudéwa Paka

摘要

In this paper we use a viscosity solutions approach to solve a differential switching game problem. The game involves two players and the time horizon is infinite. We first reduce the switching problem from one of finding the optimal sequence of stopping times into that of finding a finite number of threshold values in state process that would trigger switchings. To this end, we characterize the switching regions by relying on the system of quasi-variational inequalities associated to the game. We then derive an explicit solution to the problem when the state process is a one-dimensional Itô diffusion together with possibly non-positive switching costs. We also suggest a numerical procedure to compute the value function in case we know the qualitative structure of the switching regions and we illustrate our results by numerical simulations.