Linear–Quadratic Time-Inconsistent Mean Field Games

A. Bensoussan (), K. Sung () and S. Yam ()

Dynamic Games and Applications, 2013, vol. 3, issue 4, 537-552

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

Keywords: Mean field games; Time-inconsistent stochastic control problems; Adjoint equations; Linear–quadratic type; Banach fixed point theorem (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (23)

Downloads: (external link)
http://hdl.handle.net/10.1007/s13235-013-0090-y (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:dyngam:v:3:y:2013:i:4:p:537-552

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/13235

DOI: 10.1007/s13235-013-0090-y

Access Statistics for this article

Dynamic Games and Applications is currently edited by Georges Zaccour

More articles in Dynamic Games and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().