@inproceedings{d83770c6630f4c9f9cecf76f21818aa6,

title = "Risk-sensitive mean-field stochastic differential games",

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.",

keywords = "Mean-field analysis, Risk-sensitive games, Stochastic differential games",

author = "Hamidou Tembine and Quanyan Zhu and Tamer Ba{\c s}ar",

note = "Funding Information: in part by Grant AFOSR MURI FA",

year = "2011",

doi = "10.3182/20110828-6-IT-1002.02247",

language = "English (US)",

isbn = "9783902661937",

series = "IFAC Proceedings Volumes (IFAC-PapersOnline)",

publisher = "IFAC Secretariat",

number = "1 PART 1",

pages = "3222--3227",

booktitle = "Proceedings of the 18th IFAC World Congress",

edition = "1 PART 1",

}