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Maximum Principle for General Partial Information Nonzero Sum Stochastic Differential Games and Applications

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  • Tianyang Nie

    (Shandong University)

  • Falei Wang

    (Shandong University)

  • Zhiyong Yu

    (Shandong University)

Abstract

We study a general kind of partial information nonzero sum two-player stochastic differential games, where the state variable is governed by a stochastic differential equation and the control domain of each player can be non-convex. Moreover, the control variables of both players can enter the diffusion coefficients of the state equation. We establish Pontryagin’s maximum principle for open-loop Nash equilibria of the game. Then, a verification theorem is obtained for Nash equilibria when the control domain is convex. Finally, the theoretical results are applied to studying a linear-quadratic game.

Suggested Citation

  • Tianyang Nie & Falei Wang & Zhiyong Yu, 2022. "Maximum Principle for General Partial Information Nonzero Sum Stochastic Differential Games and Applications," Dynamic Games and Applications, Springer, vol. 12(2), pages 608-631, June.
    • Handle: RePEc:spr:dyngam:v:12:y:2022:i:2:d:10.1007_s13235-021-00402-2
    DOI: 10.1007/s13235-021-00402-2
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    References listed on IDEAS

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    1. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704.
    2. Ahuja, Saran & Ren, Weiluo & Yang, Tzu-Wei, 2019. "Forward–backward stochastic differential equations with monotone functionals and mean field games with common noise," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 3859-3892.
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