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

2024/07/30 by Brahim El Asri, Asri, Brahim El, Magnoudéwa Paka +1
Earth and Planetary Sciences · Engineering · Medicine · #Aquatic and Environmental Studies #FOS: Mathematics #Guidance and Control Systems #Mathematical and Theoretical Epidemiology and Ecology Models #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2407.20913

openalex publication_date 2024/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Itô 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.

Related

• Stochastic differential switching game in infinite horizon
• Controller-and-Stopper Stochastic Differential Games with Regime Switching
• A probabilistic verification theorem for the finite horizon two-player zero-sum optimal switching game in continuous time
• Viscosity solutions for mean field optimal switching with a two-time-scale Markov chain
• A Finite Horizon Optimal Multiple Switching Problem