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Infinite Horizon Differential Games with Asymmetric Information

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  • Xiaochi Wu

    (Université de Bretagne Occidentale)

Abstract

This article is concerned with the existence of a value for a zero-sum differential game with an asymmetric information on initial state with an infinite horizon running cost. Before the game begins, an initial state is chosen randomly from a finite set and each player receives a private signal generated by the chosen initial state. The main result is that the game has a value with random non-anticipative strategies with delay and that its value function can be characterized as the unique bounded continuous viscosity solution of a suitable Hamilton–Jacobi–Isaacs equation.

Suggested Citation

  • Xiaochi Wu, 2019. "Infinite Horizon Differential Games with Asymmetric Information," Dynamic Games and Applications, Springer, vol. 9(3), pages 858-880, September.
    • Handle: RePEc:spr:dyngam:v:9:y:2019:i:3:d:10.1007_s13235-018-0272-8
    DOI: 10.1007/s13235-018-0272-8
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    References listed on IDEAS

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    6. Pierre Cardaliaguet & Catherine Rainer, 2012. "Games with Incomplete Information in Continuous Time and for Continuous Types," Dynamic Games and Applications, Springer, vol. 2(2), pages 206-227, June.
    7. 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.
    8. Bernard de Meyer, 1996. "Repeated games, Duality, and the Central Limit Theorem," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00259714, HAL.
    9. Bernard de Meyer, 1996. "Repeated games, Duality, and the Central Limit Theorem," Post-Print hal-00259714, HAL.
    10. 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.
    11. Ma, Jinpeng, 1995. "An infinitely repeated rental model with incomplete information," Economics Letters, Elsevier, vol. 49(3), pages 261-266, September.
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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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