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Solutions to Equilibrium HJB Equations for Time-Inconsistent Deterministic Linear Quadratic Control: Characterization and Uniqueness

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  • Yunfei Peng
  • Wei Wei

Abstract

In this paper we study a class of HJB equations which solve for equilibria for general time-inconsistent deterministic linear quadratic control problems within the intra-personal game theoretic framework, where the inconsistency arises from non-exponential discount functions. We characterize the solutions to the HJB equations using a class of Riccati equations with integral terms. By studying the uniqueness of solutions to the integro-differential Riccati equations, we prove the uniqueness of solutions to the equilibrium HJB equations.

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  • 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, revised May 2025.
    • Handle: RePEc:arx:papers:2308.13850
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    References listed on IDEAS

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    1. David Laibson, 1997. "Golden Eggs and Hyperbolic Discounting," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 443-478.
    2. Yu-Jui Huang & Zhou Zhou, 2021. "Strong and Weak Equilibria for Time-Inconsistent Stochastic Control in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 428-451, May.
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    Cited by:

    1. 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.

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