Zero sum two-player differential game under three regimes
Abstract
This paper investigates a two player zero-sum stochastic differential game characterized by three distinct regimes, reflecting the regime switching dynamics within the system. We aim to derive an explicit solution for a number of configurations of the switching system by means of the viscosity solutions approach. In particular, we analyze the associated Hamilton-Jacobi-Bellman-Isaacs equations and examine how the interactions between the different regimes affect the structure of the value function. The proposed framework provides a systematic approach to characterize the optimal strategies of the two players and to obtain explicit representations of the value function un der suitable assumptions. We also illustrate how to derive the value functions in case we know the qualitative structure of switching regions.
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BibTeX
@misc{asri2026zero,
title = {{Zero sum two-player differential game under three regimes}},
author = {Brahim El Asri and Magnoudéwa Paka},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04100},
eprint = {2609.04100},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04100},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Zero sum two-player differential game under three regimes
AU - Brahim El Asri
AU - Magnoudéwa Paka
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04100
UR - https://arxiv.org/abs/2609.04100
AB - This paper investigates a two player zero-sum stochastic differential game characterized by three distinct regimes, reflecting the regime switching dynamics within the system. We aim to derive an explicit solution for a number of configurations of the switching system by means of the viscosity solutions approach. In particular, we analyze the associated Hamilton-Jacobi-Bellman-Isaacs equations and examine how the interactions between the different regimes affect the structure of the value function. The proposed framework provides a systematic approach to characterize the optimal strategies of the two players and to obtain explicit representations of the value function un der suitable assumptions. We also illustrate how to derive the value functions in case we know the qualitative structure of switching regions.
ER -