Two-Player Nonzero-Sum Stochastic Differential Games with Switching Controls

Yongxin Liu and Hui Min ()
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Yongxin Liu: School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, China
Hui Min: School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, China

Mathematics, 2024, vol. 12, issue 24, 1-9

Abstract: In this paper, a two-player nonzero-sum stochastic differential game problem is studied with both players using switching controls . A verification theorem associated with a set of variational inequalities is established as a sufficient criterion for Nash equilibrium, in which the equilibrium switching strategies for the two players, indicating when and where it is optimal to switch, are characterized in terms of the so-called switching regions and continuation regions . The verification theorem is proved in a piecewise way along the sequence of total decision times of the two players. Then, some detailed explanations are also provided to illustrate the idea why the conditions are imposed in the verification theorem.

Keywords: stochastic differential game; switching control; verification theorem; variational inequality; sufficient condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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