A Differential Game with Symmetric Incomplete Information on Probabilistic Initial Condition and with Signal Revelation
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909978950893568 |
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| author | Wu, Xiaochi |
| author_facet | Wu, Xiaochi |
| contents | In this paper, we investigate the existence and characterization of the value for a two-player zero-sum differential game with symmetric incomplete information on a continuum of initial positions and with signal revelation. Before the game starts, the initial position is chosen randomly according to a probability measure with compact support, and neither player is informed of the chosen initial position. However, they observe a public signal revealing the current state as soon as the trajectory of the dynamics hits a target set. We prove that, under a suitable notion of signal-dependent strategies, the value of the game exists, and the extended value function of the game is the unique viscosity solution of an associated Hamilton-Jacobi-Isaacs equation that satisfies a boundary condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24640 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Differential Game with Symmetric Incomplete Information on Probabilistic Initial Condition and with Signal Revelation Wu, Xiaochi Optimization and Control 49N30, 49N70, 91A05, 91A10, 91A23 In this paper, we investigate the existence and characterization of the value for a two-player zero-sum differential game with symmetric incomplete information on a continuum of initial positions and with signal revelation. Before the game starts, the initial position is chosen randomly according to a probability measure with compact support, and neither player is informed of the chosen initial position. However, they observe a public signal revealing the current state as soon as the trajectory of the dynamics hits a target set. We prove that, under a suitable notion of signal-dependent strategies, the value of the game exists, and the extended value function of the game is the unique viscosity solution of an associated Hamilton-Jacobi-Isaacs equation that satisfies a boundary condition. |
| title | A Differential Game with Symmetric Incomplete Information on Probabilistic Initial Condition and with Signal Revelation |
| topic | Optimization and Control 49N30, 49N70, 91A05, 91A10, 91A23 |
| url | https://arxiv.org/abs/2512.24640 |