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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2024-12-01
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| author | Yongxin Liu Hui Min |
| author_facet | Yongxin Liu Hui Min |
| author_sort | Yongxin Liu |
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| description | 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. |
| format | Article |
| id | doaj-art-9cb96653d3354b2eafe5d099a7891af6 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-9cb96653d3354b2eafe5d099a7891af62024-12-27T14:38:11ZengMDPI AGMathematics2227-73902024-12-011224397610.3390/math12243976Two-Player Nonzero-Sum Stochastic Differential Games with Switching ControlsYongxin Liu0Hui Min1School of Statistics and Data Science, Nanjing Audit University, Nanjing 211815, ChinaSchool of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing 100124, ChinaIn 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.https://www.mdpi.com/2227-7390/12/24/3976stochastic differential gameswitching controlverification theoremvariational inequalitysufficient condition |
| spellingShingle | Yongxin Liu Hui Min Two-Player Nonzero-Sum Stochastic Differential Games with Switching Controls Mathematics stochastic differential game switching control verification theorem variational inequality sufficient condition |
| title | Two-Player Nonzero-Sum Stochastic Differential Games with Switching Controls |
| title_full | Two-Player Nonzero-Sum Stochastic Differential Games with Switching Controls |
| title_fullStr | Two-Player Nonzero-Sum Stochastic Differential Games with Switching Controls |
| title_full_unstemmed | Two-Player Nonzero-Sum Stochastic Differential Games with Switching Controls |
| title_short | Two-Player Nonzero-Sum Stochastic Differential Games with Switching Controls |
| title_sort | two player nonzero sum stochastic differential games with switching controls |
| topic | stochastic differential game switching control verification theorem variational inequality sufficient condition |
| url | https://www.mdpi.com/2227-7390/12/24/3976 |
| work_keys_str_mv | AT yongxinliu twoplayernonzerosumstochasticdifferentialgameswithswitchingcontrols AT huimin twoplayernonzerosumstochasticdifferentialgameswithswitchingcontrols |