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This paper studies a class of zero-sum stopping game in a regime switchingmodel. A verification theorem as a sufficient criterion for Nash equilibriumsis established based on a set of variational inequalities (VIs). Under anappropriate regularity condition for solutions to the VIs, a suitable system ofalgebraic equations is derived via the so-called smooth-fit principle. ExplicitNash equilibrium stopping rules of threshold-type for the two players and thecorresponding value function of the game in closed form are obtained. Numericalexperiments are reported to demonstrate the dependence of the threshold levelson various model parameters. A reduction to the case with no regime switchingis also presented as a comparison.

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