KAUST DepartmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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AbstractIn 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.
SponsorsThe 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.