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Linear–Quadratic Time-Inconsistent Mean Field Games

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  • A. Bensoussan
  • K. Sung
  • S. Yam

Abstract

In this paper, we study a class of time-inconsistent analogs (in the sense of Hu et al. (Time-inconsistent stochastic linear–quadratic control. Preprint, 2012 ) which is originated from the mean-variance portfolio selection problem with state-dependent risk aversion in the context of financial economics) of the standard Linear–Quadratic Mean Field Games considered in Huang et al. (Commun. Inf. Syst. 6(3):221–252, 2006 ) and Bensoussan et al. (Linear–quadratic mean field games. http://www.sta.cuhk.edu.hk/scpy , submitted, 2012 ). For the one-dimensional case, we first establish the unique time-consistent optimal strategy under an arbitrary guiding path, with which we further obtain the unique time-consistent mean-field equilibrium strategy under a mild convexity condition. Second, for the dimension greater than one, by applying the adjoint equation approach, we formulate a sufficient condition under which the unique existence of both, time-consistent optimal strategy under a given guiding path and time-consistent equilibrium strategy, can be guaranteed. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • A. Bensoussan & K. Sung & S. Yam, 2013. "Linear–Quadratic Time-Inconsistent Mean Field Games," Dynamic Games and Applications, Springer, vol. 3(4), pages 537-552, December.
    • Handle: RePEc:spr:dyngam:v:3:y:2013:i:4:p:537-552
    DOI: 10.1007/s13235-013-0090-y
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    References listed on IDEAS

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    1. Hamidou Tembine & Quanyan Zhu & Tamer Basar, 2011. "Risk-sensitive mean field stochastic differential games," Post-Print hal-00643547, HAL.
    2. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    3. Olivier Guéant & Pierre Louis Lions & Jean-Michel Lasry, 2011. "Mean Field Games and Applications," Post-Print hal-01393103, HAL.
    4. Bezalel Peleg & Menahem E. Yaari, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 391-401.
    5. repec:dau:papers:123456789/11473 is not listed on IDEAS
    6. Wei, J. & Wong, K.C. & Yam, S.C.P. & Yung, S.P., 2013. "Markowitz’s mean–variance asset–liability management with regime switching: A time-consistent approach," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 281-291.
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