Two-Player Nonzero-Sum Stochastic Differential Games with Switching Controls
In this paper, a two-player nonzero-sum stochastic differential game problem is studied with both players using <i>switching controls</i>. A verification theorem associated with a set of variational inequalities is established as a <i>sufficient criterion</i> for Nash equilib...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/12/24/3976 |
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| Summary: | In this paper, a two-player nonzero-sum stochastic differential game problem is studied with both players using <i>switching controls</i>. A verification theorem associated with a set of variational inequalities is established as a <i>sufficient criterion</i> for Nash equilibrium, in which the equilibrium switching strategies for the two players, indicating <i>when</i> and <i>where</i> it is optimal to switch, are characterized in terms of the so-called <i>switching regions</i> and <i>continuation regions</i>. The verification theorem is proved in a <i>piecewise</i> 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. |
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| ISSN: | 2227-7390 |