Risk-Sensitive Mean-Field Games

by H. Tembine, Q. Zhu, T. Basar
Refereed Journals Year: 2014


H. Tembine, Q. Zhu, T. Basar, Risk-Sensitive Mean-Field Games, IEEE Transactions on Automatic Control, volume 59, Issue 4, April 2014.


In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functionalcoincides with the value function satisfying a Hamilton-Jacobi-Bellman (HJB) 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 HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean-Vlasov dynamics.




Risk-Sensitive Mean field games Risk-Seeking Risk-Averse