TY - JOUR
T1 - Risk-sensitive mean-field games
AU - Tembine, Hamidou
AU - Zhu, Quanyan
AU - Başar, Tamer
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The work of the second and third authors was supported in part by the Air Force Office of Scientific Research under MURI Grant FA9550-10-1-0573. This paper was recommended by Associate Editor A. Ozdaglar.
PY - 2014/4
Y1 - 2014/4
N2 - 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 functional coincides 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. © 1963-2012 IEEE.
AB - 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 functional coincides 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. © 1963-2012 IEEE.
UR - http://hdl.handle.net/10754/563474
UR - http://ieeexplore.ieee.org/document/6656891/
UR - http://www.scopus.com/inward/record.url?scp=84897443281&partnerID=8YFLogxK
U2 - 10.1109/TAC.2013.2289711
DO - 10.1109/TAC.2013.2289711
M3 - Article
SN - 0018-9286
VL - 59
SP - 835
EP - 850
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 4
ER -