Risk-sensitive mean-field stochastic differential games

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In this paper, we study a class of risk-sensitive mean-field stochastic differential games. Under regularity assumptions, we use results from standard risk-sensitive differential game theory to show that the mean-field value of the exponentiated cost functional coincides with the value function of a Hamilton-Jacobi-Bellman-Fleming (HJBF) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker-Planck-Kolmogorov equations and HJBF equations.

Original languageEnglish (US)
Title of host publicationProceedings of the 18th IFAC World Congress
PublisherIFAC Secretariat
Number of pages6
Edition1 PART 1
ISBN (Print)9783902661937
StatePublished - Jan 1 2011

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
Number1 PART 1
ISSN (Print)1474-6670


  • Mean-field analysis
  • Risk-sensitive games
  • Stochastic differential games

ASJC Scopus subject areas

  • Control and Systems Engineering

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    Tembine, H., Zhu, Q., & Başar, T. (2011). Risk-sensitive mean-field stochastic differential games. In Proceedings of the 18th IFAC World Congress (1 PART 1 ed., pp. 3222-3227). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 44, No. 1 PART 1). IFAC Secretariat. https://doi.org/10.3182/20110828-6-IT-1002.02247