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

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  • Xiaochi Wu

    (Shandong University, Weihai)

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 $$\mathbb {R}^n$$ 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.

Suggested Citation

  • Xiaochi Wu, 2021. "Differential Games with Incomplete Information and with Signal Revealing: The Symmetric Case," Dynamic Games and Applications, Springer, vol. 11(4), pages 863-891, December.
    • Handle: RePEc:spr:dyngam:v:11:y:2021:i:4:d:10.1007_s13235-021-00376-1
    DOI: 10.1007/s13235-021-00376-1
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    References listed on IDEAS

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    1. Miquel Oliu-Barton, 2015. "Differential Games with Asymmetric and Correlated Information," Dynamic Games and Applications, Springer, vol. 5(3), pages 378-396, September.
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    5. Chloe Jimenez & Marc Quincampoix & Yuhong Xu, 2016. "Differential Games with Incomplete Information on a Continuum of Initial Positions and without Isaacs Condition," Dynamic Games and Applications, Springer, vol. 6(1), pages 82-96, March.
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    7. repec:dau:papers:123456789/6046 is not listed on IDEAS
    8. Rainer Buckdahn & Marc Quincampoix & Catherine Rainer & Yuhong Xu, 2016. "Differential games with asymmetric information and without Isaacs’ condition," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(4), pages 795-816, November.
    9. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
    10. FORGES, Françoise, 1982. "Infinitely repeated games of incomplete information: symmetric case with random signals," LIDAM Reprints CORE 503, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Xiaochi Wu, 2022. "Existence of value for a differential game with asymmetric information and signal revealing," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 213-247, March.

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