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Uniqueness for Linear-Quadratic Mean Field Games with Common Noise

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  • Rinel Foguen Tchuendom

    (University of Nice-Sophia Anitpolis)

Abstract

The purpose of this note is to show that a common noise may restore uniqueness in mean field games. To this end, we focus on a class of examples driven by linear dynamics and quadratic cost functions. Given these linear-quadratic mean field games, we prove existence and uniqueness of solutions in the presence of common noise and construct a counter-example in the absence of common noise. This illustrates the principle, already observed in dynamical systems like ODEs, that introducing an appropriate noise may restore uniqueness.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:dyngam:v:8:y:2018:i:1:d:10.1007_s13235-016-0200-8
    DOI: 10.1007/s13235-016-0200-8
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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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Alessandro Calvia & Salvatore Federico & Giorgio Ferrari & Fausto Gozzi, 2024. "A mean-field model of optimal investment," Papers 2404.02871, arXiv.org.
    6. Dianetti, Jodi & Ferrari, Giorgio & Fischer, Markus & Nendel, Max, 2019. "Submodular Mean Field Games. Existence and Approximation of Solutions," Center for Mathematical Economics Working Papers 621, Center for Mathematical Economics, Bielefeld University.

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