# Solving a class of zero-sum stopping game with regime switching

arXiv: https://arxiv.org/abs/2303.15730 · HTML: https://mlsanity.com/paper/2303.15730/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Mar 2023.

## Built on by (most cited first, 1 of 1)

- [Entropy Regularized Reinforcement Learning for Zero-Sum Stochastic Differential Games in a Regime-Switching Jump-Diffusion Process](https://mlsanity.com/paper/2606.28669/) (2026)

## Abstract (arXiv)

This paper studies a class of zero-sum stopping game in a regime switching model. A verification theorem as a sufficient criterion for Nash equilibriums is established based on a set of variational inequalities (VIs). Under an appropriate regularity condition for solutions to the VIs, a suitable system of algebraic equations is derived via the so-called smooth-fit principle. Explicit Nash equilibrium stopping rules of threshold-type for the two players and the corresponding value function of the game in closed form are obtained. Numerical experiments are reported to demonstrate the dependence of the threshold levels on various model parameters. A reduction to the case with no regime switching is also presented as a comparison.