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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 & 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.
    2. 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.
    3. 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.
    4. 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.

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