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Closed-loop and open-loop equilibrium of a class time-inconsistent linear-quadratic differential games

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  • Wei Ji

    (Guiyang University)

Abstract

In this study, we concern with a class linear quadratic (LQ, for short) N-person differential games with time inconsistency, where the time inconsistency arises from non-exponential discount function. The notions of closed-loop and open-loop equilibrium strategy are introduced. We establish the equivalent relationship between time-inconsistent differential game problems, forward-backward type differential equations, and Riccati type differential equations in the framework of closed-loop and open-loop equilibrium, respectively. We provide an example of time-inconsistent differential games from which we find a time-consistent equilibrium strategy.

Suggested Citation

  • Wei Ji, 2024. "Closed-loop and open-loop equilibrium of a class time-inconsistent linear-quadratic differential games," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 635-651, June.
    • Handle: RePEc:spr:jogath:v:53:y:2024:i:2:d:10.1007_s00182-024-00895-2
    DOI: 10.1007/s00182-024-00895-2
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    References listed on IDEAS

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    3. Yunfei Peng & Wei Wei, 2023. "Solutions to Equilibrium HJB Equations for Time-Inconsistent Deterministic Linear Quadratic Control: Characterization and Uniqueness," Papers 2308.13850, arXiv.org.
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    6. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2017. "Time-Inconsistent Stochastic Linear--Quadratic Control: Characterization and Uniqueness of Equilibrium," Post-Print hal-01139343, HAL.
    7. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-491, June.
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