Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 835-850 |
| Number of pages | 16 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 59 |
| Issue number | 4 |
| DOIs | |
| State | Published - Apr 2014 |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01Acknowledgements: 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.
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering