Journal
AUTOMATICA
Volume 145, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.automatica.2022.110439
Keywords
Stochastic differential game; Markov chain; Impulse control; Verification theorem; Variational inequalities
Funding
- National Natural Science Foundation of China [11801072, 61873325, 11831010, 11971267]
- Natural Science Foundation of Jiangsu Province, China [BK20180354]
- Fundamental Research Funds for the Central Universities, China [2242021R41175]
- Southern University of Science and Technology, China [Y01286120]
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This paper investigates a two-player nonzero-sum stochastic differential game, where both players utilize impulse controls and the state process evolves as a regime switching diffusion. A verification theorem is established based on a system of variational inequalities, serving as a sufficient criterion for optimality. Nash equilibrium strategies for the two players, indicating the optimal timing and method of intervention, are presented in terms of the obstacle parts of the variational inequalities.
This paper is concerned with a two-player nonzero-sum stochastic differential game, where both players use impulse controls and the state process evolves as a regime switching diffusion. Based on a system of variational inequalities, a verification theorem as a sufficient criterion for optimality is established. Nash equilibrium strategies for the two players, indicating when and how it is optimal to intervene, are given in terms of the obstacle parts of the variational inequalities.(c) 2022 Elsevier Ltd. All rights reserved.
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