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
Pages3222-3227
Number of pages6
Volume18
EditionPART 1
DOIs
StatePublished - 2011
Event18th IFAC World Congress - Milano, Italy
Duration: Aug 28 2011Sep 2 2011

Other

Other18th IFAC World Congress
CountryItaly
CityMilano
Period8/28/119/2/11

Fingerprint

Vlasov equation
Fokker Planck equation
Game theory
Cost functions

Keywords

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

ASJC Scopus subject areas

  • Control and Systems Engineering

Cite this

Hamidou, T., Zhu, Q., & Başar, T. (2011). Risk-sensitive mean-field stochastic differential games. In Proceedings of the 18th IFAC World Congress (PART 1 ed., Vol. 18, pp. 3222-3227) https://doi.org/10.3182/20110828-6-IT-1002.02247

Risk-sensitive mean-field stochastic differential games. / Hamidou, Tembine; Zhu, Quanyan; Başar, Tamer.

Proceedings of the 18th IFAC World Congress. Vol. 18 PART 1. ed. 2011. p. 3222-3227.

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

Hamidou, T, Zhu, Q & Başar, T 2011, Risk-sensitive mean-field stochastic differential games. in Proceedings of the 18th IFAC World Congress. PART 1 edn, vol. 18, pp. 3222-3227, 18th IFAC World Congress, Milano, Italy, 8/28/11. https://doi.org/10.3182/20110828-6-IT-1002.02247
Hamidou T, Zhu Q, Başar T. Risk-sensitive mean-field stochastic differential games. In Proceedings of the 18th IFAC World Congress. PART 1 ed. Vol. 18. 2011. p. 3222-3227 https://doi.org/10.3182/20110828-6-IT-1002.02247
Hamidou, Tembine ; Zhu, Quanyan ; Başar, Tamer. / Risk-sensitive mean-field stochastic differential games. Proceedings of the 18th IFAC World Congress. Vol. 18 PART 1. ed. 2011. pp. 3222-3227
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