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Stackelberg Stochastic Differential Games in Feedback Information Pattern with Applications

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  • Qi Huang

    (Shandong University)

  • Jingtao Shi

    (Shandong University)

Abstract

This paper is concerned with both nonzero-sum and zero-sum Stackelberg stochastic differential games on a finite horizon in feedback information pattern, where the control variables enter into the diffusion term. For the nonzero-sum case, a system of parabolic partial differential equations is obtained to give the verification theorem of the feedback Stackelberg equilibrium. As an example, a linear-quadratic nonzero-sum feedback Stackelberg stochastic differential game is investigated, where the diffusion term is also control-dependent. Coupled Riccati equations are introduced to express the feedback Stackelberg equilibrium, and sufficient conditions for the existence of their solutions are obtained. For the zero-sum case, a verification theorem that contains only one Hamilton–Jacobi–Bellman equation is given. In addition, the solvability of the Riccati equation, which is derived from the linear-quadratic zero-sum case with the leader’s control appearing in the diffusion term, is further discussed, and a sufficient and necessary condition for the existence and uniqueness of the solution is given.

Suggested Citation

  • Qi Huang & Jingtao Shi, 2024. "Stackelberg Stochastic Differential Games in Feedback Information Pattern with Applications," Dynamic Games and Applications, Springer, vol. 14(5), pages 1191-1224, November.
    • Handle: RePEc:spr:dyngam:v:14:y:2024:i:5:d:10.1007_s13235-023-00549-0
    DOI: 10.1007/s13235-023-00549-0
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    References listed on IDEAS

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    1. Zheng, Yueyang & Shi, Jingtao, 2022. "A linear-quadratic partially observed Stackelberg stochastic differential game with application," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    2. Yueyang Zheng & Jingtao Shi, 2020. "A Stackelberg Game of Backward Stochastic Differential Equations with Applications," Dynamic Games and Applications, Springer, vol. 10(4), pages 968-992, December.
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    4. Martín-Herrán, Guiomar & Rubio, Santiago J., 2021. "On coincidence of feedback and global Stackelberg equilibria in a class of differential games," European Journal of Operational Research, Elsevier, vol. 293(2), pages 761-772.
    5. Kydland, Finn, 1977. "Equilibrium solutions in dynamic dominant-player models," Journal of Economic Theory, Elsevier, vol. 15(2), pages 307-324, August.
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