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Selection of equilibria in a linear quadratic mean-field game

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  • Delarue, François
  • Foguen Tchuendom, Rinel

Abstract

In this paper, we address an instance of uniquely solvable mean-field game with a common noise whose corresponding counterpart without common noise has several equilibria. We study the selection problem for this mean-field game without common noise via three approaches.

Suggested Citation

  • Delarue, François & Foguen Tchuendom, Rinel, 2020. "Selection of equilibria in a linear quadratic mean-field game," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 1000-1040.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:2:p:1000-1040
    DOI: 10.1016/j.spa.2019.04.005
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    References listed on IDEAS

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    1. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, June.
    2. Rinel Foguen Tchuendom, 2018. "Uniqueness for Linear-Quadratic Mean Field Games with Common Noise," Dynamic Games and Applications, Springer, vol. 8(1), pages 199-210, March.
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    Cited by:

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    2. Dianetti, Jodi, 2023. "Strong Solutions to Submodular Mean Field Games with Common Noise and Related McKean-Vlasov FBSDES," Center for Mathematical Economics Working Papers 674, Center for Mathematical Economics, Bielefeld University.
    3. Dianetti, Jodi & Ferrari, Giorgio & Fischer, Markus & Nendel, Max, 2022. "A Unifying Framework for Submodular Mean Field Games," Center for Mathematical Economics Working Papers 661, Center for Mathematical Economics, Bielefeld University.
    4. Calvia, Alessandro & Federico, Salvatore & Ferrari, Giorgio & Gozzi, Fausto, 2024. "A Mean-Field Model of Optimal Investment," Center for Mathematical Economics Working Papers 690, Center for Mathematical Economics, Bielefeld University.
    5. François Delarue & Athanasios Vasileiadis, 2025. "Exploration Noise for Learning Linear-Quadratic Mean Field Games," Mathematics of Operations Research, INFORMS, vol. 50(3), pages 1762-1831, August.
    6. Sina Sanjari & Naci Saldi & Serdar Yüksel, 2023. "Optimality of Independently Randomized Symmetric Policies for Exchangeable Stochastic Teams with Infinitely Many Decision Makers," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1254-1285, August.
    7. Alessandro Calvia & Salvatore Federico & Giorgio Ferrari & Fausto Gozzi, 2024. "Existence and uniqueness results for a mean-field game of optimal investment," Papers 2404.02871, arXiv.org, revised May 2026.

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