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A linear-quadratic partially observed Stackelberg stochastic differential game with application

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  • Zheng, Yueyang
  • Shi, Jingtao

Abstract

This paper is concerned with a linear-quadratic partially observed Stackelberg stochastic differential game with correlated state and observation noises, where the control set is not necessarily convex. Both the leader and the follower have their own observation equations, and the information filtration available to the leader is contained in that available to the follower. Necessary and sufficient conditions of the Stackelberg equilibrium points are derived. In the follower’s problem, the state estimation feedback of optimal control can be represented by a forward-backward stochastic differential filtering equation and some Riccati equation. In the leader’s problem, via the innovation process, the state estimation feedback of optimal control is represented by a stochastic differential filtering equation, a semi-martingale process and three high-dimensional Riccati equations. As an application, a dynamic advertising problem with asymmetric information is studied, and the effectiveness and reasonability of the theoretical result are illustrated by numerical simulations.

Suggested Citation

  • Zheng, Yueyang & Shi, Jingtao, 2022. "A linear-quadratic partially observed Stackelberg stochastic differential game with application," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    • Handle: RePEc:eee:apmaco:v:420:y:2022:i:c:s0096300321009024
    DOI: 10.1016/j.amc.2021.126819
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    References listed on IDEAS

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    1. Chen, Lv & Shen, Yang, 2018. "On A New Paradigm Of Optimal Reinsurance: A Stochastic Stackelberg Differential Game Between An Insurer And A Reinsurer," ASTIN Bulletin, Cambridge University Press, vol. 48(2), pages 905-960, May.
    2. Jorgensen, Steffen & Taboubi, Sihem & Zaccour, Georges, 2003. "Retail promotions with negative brand image effects: Is cooperation possible?," European Journal of Operational Research, Elsevier, vol. 150(2), pages 395-405, October.
    3. Øksendal, Bernt & Sandal, Leif & Ubøe, Jan, 2013. "Stochastic Stackelberg equilibria with applications to time-dependent newsvendor models," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1284-1299.
    4. Jingtao Shi, 2018. "Stochastic Leader-Follower Differential Game with Asymmetric Information," Chapters, in: Danijela Tuljak-Suban (ed.), Game Theory - Applications in Logistics and Economy, IntechOpen.
    5. S. Jørgensen & S. Taboubi & G. Zaccour, 2001. "Cooperative Advertising in a Marketing Channel," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 145-158, July.
    6. Xiong, Jie, 2008. "An Introduction to Stochastic Filtering Theory," OUP Catalogue, Oxford University Press, number 9780199219704, Decembrie.
    7. S. Jørgensen & G. Zaccour, 1999. "Equilibrium Pricing and Advertising Strategies in a Marketing Channel," Journal of Optimization Theory and Applications, Springer, vol. 102(1), pages 111-125, July.
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    Cited by:

    1. Li Chen & Peipei Zhou & Hua Xiao, 2023. "Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential Equations," Mathematics, MDPI, vol. 11(13), pages 1-18, June.

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