Differential Games with Incomplete Information and with Signal Revealing: The Symmetric Case

Dynamic Games and Applications (2021)Cite this article

Abstract

In this paper, we investigate the existence of value for a two-person zero-sum differential game with symmetric incomplete information and with signal revealing. Before the game begins, the initial state of the dynamic is chosen randomly among a finite number of points in \(\mathbb {R}^n\), while both players have only a probabilistic knowledge of the chosen initial state. During the game, if the system reaches a fixed closed target set K, the current state of the system at the hitting time is revealed to both players. We prove in this paper that this game has a value and its value function is the unique bounded continuous viscosity solution of a suitable Hamilton–Jacobi–Isaacs equation.

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Funding

This study was supported by China Postdoctoral Science Foundation (Grant No. 2020M672037).

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Affiliations

  1. School of Mathematics and Statistics, Shandong University, Weihai, 180, Wenhua Xilu, Weihai, 264209, People’s Republic of China

    Xiaochi Wu

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  1. Xiaochi Wu
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Correspondence to Xiaochi Wu.

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Wu, X. Differential Games with Incomplete Information and with Signal Revealing: The Symmetric Case. Dyn Games Appl (2021). https://doi.org/10.1007/s13235-021-00376-1

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Keywords

  • Differential games
  • Incomplete information
  • Hamilton–Jacobi–Isaacs equation
  • Signal

JEL Classification

  • 91A05
  • 91A10
  • 91A23