Risk-sensitive mean field stochastic differential games

Hamidou Tembine, Quanyan Zhu and Tamer Basar
Additional contact information
Hamidou Tembine: E3S - Supélec Sciences des Systèmes - Ecole Supérieure d'Electricité - SUPELEC (FRANCE)
Quanyan Zhu: CSL - Coordinated Science Laboratory - University of Illinois System
Tamer Basar: CSL - Coordinated Science Laboratory - University of Illinois System

Post-Print from HAL

Abstract: In this paper, we study a class of risk-sensitive mean-field stochastic di fferential games. Under regularity assumptions, we use results from standard risk-sensitive di fferential 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-fi eld equilibria are characterized in terms of backward-forward macroscopic McKean-Vlasov equations, Fokker- Planck-Kolmogorov equations and HJBF equations.

Date: 2011-08-28
References: Add references at CitEc
Citations: View citations in EconPapers (10)

Published in 18th IFAC World Congress, Aug 2011, Milano, Italy. pp.3222-3227, ⟨10.3182/20110828-6-IT-1002.02247⟩

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:hal:journl:hal-00643547

DOI: 10.3182/20110828-6-IT-1002.02247

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().