{"ID":2823630,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.24640","arxiv_id":"2512.24640","title":"A Differential Game with Symmetric Incomplete Information on Probabilistic Initial Condition and with Signal Revelation","abstract":"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.","short_abstract":"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 measu...","url_abs":"https://arxiv.org/abs/2512.24640","url_pdf":"https://arxiv.org/pdf/2512.24640v1","authors":"[\"Xiaochi Wu\"]","published":"2025-12-31T05:25:18Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}