Risk-sensitive mean-field stochastic differential games

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

Abstract

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
Pages3222-3227
Number of pages6
Edition1 PART 1
ISBN (Print)9783902661937
DOIs
StatePublished - 2011

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
Number1 PART 1
Volume44
ISSN (Print)1474-6670

Keywords

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

ASJC Scopus subject areas

  • Control and Systems Engineering

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