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Feedback Stackelberg Solutions of Infinite-Horizon Stochastic Differential Games

In: Models and Methods in Economics and Management Science

Author

Listed:
  • Alain Bensoussan

    (University of Texas at Dallas
    City University of Hong Kong
    Ajou University)

  • Shaokuan Chen

    (University of Texas at Dallas)

  • Suresh P. Sethi

    (University of Texas at Dallas)

Abstract

We present a sufficient condition for a feedback Stackelberg equilibrium of a stochastic differential game on an infinite horizon. This condition gives rise to a system of elliptic partial differential equations involving a static Stackelberg game at the level of Hamiltonian. As an example, we consider a linear quadratic problem, obtain the corresponding algebraic Riccati equation, and provide its solution in the scalar case.

Suggested Citation

  • Alain Bensoussan & Shaokuan Chen & Suresh P. Sethi, 2014. "Feedback Stackelberg Solutions of Infinite-Horizon Stochastic Differential Games," International Series in Operations Research & Management Science, in: Fouad El Ouardighi & Konstantin Kogan (ed.), Models and Methods in Economics and Management Science, edition 127, pages 3-15, Springer.
    • Handle: RePEc:spr:isochp:978-3-319-00669-7_1
    DOI: 10.1007/978-3-319-00669-7_1
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    Cited by:

    1. Lu, Fuxiao & Tang, Wansheng & Liu, Guowei & Zhang, Jianxiong, 2019. "Cooperative advertising: A way escaping from the prisoner’s dilemma in a supply chain with sticky price," Omega, Elsevier, vol. 86(C), pages 87-106.
    2. Chutani, Anshuman & Sethi, Suresh P., 2018. "Dynamic cooperative advertising under manufacturer and retailer level competition," European Journal of Operational Research, Elsevier, vol. 268(2), pages 635-652.
    3. Alberto Bressan & Yilun Jiang, 2020. "Self-consistent Feedback Stackelberg Equilibria for Infinite Horizon Stochastic Games," Dynamic Games and Applications, Springer, vol. 10(2), pages 328-360, June.
    4. Song, Jian & Chutani, Anshuman & Dolgui, Alexandre & Liang, Liang, 2021. "Dynamic innovation and pricing decisions in a supply-Chain," Omega, Elsevier, vol. 103(C).
    5. Ren'e Aid & Sara Biagini, 2021. "Optimal dynamic regulation of carbon emissions market: A variational approach," Papers 2102.12423, arXiv.org.

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