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Time-Inconsistent LQ Games for Large-Population Systems and Applications

Author

Listed:
  • Haiyang Wang

    (Shandong Normal University)

  • Ruimin Xu

    (Qilu University of Technology (Shandong Academy of Sciences))

Abstract

In this paper, we formulate a time-inconsistent linear-quadratic (LQ) mean-field game problem for large-population systems. By the Nash certainty equivalence methodology, we construct an auxiliary problem consisting of time-inconsistent LQ control problems for every agent, respectively. An equilibrium, instead of optimal solution, is presented explicitly in the form of linear feedback for each agent in this auxiliary problem. Inspired by the framework of tackling time-inconsistency for control problems, we generalize the definition of $$\epsilon $$ ϵ -Nash equilibrium for large-population games to the time-inconsistent case. Then, the set of linear feedback controls obtained above can be proved to be an $$\epsilon $$ ϵ -Nash equilibrium for our original problem. Moreover, we solve a resource investment problem and provide a numerical simulation to illustrate the application of our theoretic results.

Suggested Citation

  • Haiyang Wang & Ruimin Xu, 2023. "Time-Inconsistent LQ Games for Large-Population Systems and Applications," Journal of Optimization Theory and Applications, Springer, vol. 197(3), pages 1249-1268, June.
    • Handle: RePEc:spr:joptap:v:197:y:2023:i:3:d:10.1007_s10957-023-02223-2
    DOI: 10.1007/s10957-023-02223-2
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    References listed on IDEAS

    as
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    4. Zhongyang Sun & Xianping Guo, 2019. "Equilibrium for a Time-Inconsistent Stochastic Linear–Quadratic Control System with Jumps and Its Application to the Mean-Variance Problem," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 383-410, May.
    5. Ying Hu & Hanqing Jin & Xun Yu Zhou, 2017. "Time-Inconsistent Stochastic Linear--Quadratic Control: Characterization and Uniqueness of Equilibrium," Post-Print hal-01139343, HAL.
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