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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

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  • 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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