TY - JOUR
T1 - Nash equilibria of risk-sensitive nonlinear stochastic differential games
AU - Başar, T.
N1 - Funding Information:
1This paper is dedicated to Y. C. Ho of Harvard University on the occasion of his 65th birthday. This research was supported in part by Department of Energy Grant DEFG-02-97-ER-13939. 2Fredric G. and Elizabeth H. Nearing Professor, Decision and Control Laboratory, Coordinated Science Laboratory and Department of Electrical and Computer Engineering, University of Illinois, Urbana, Illinois.
PY - 1999/3
Y1 - 1999/3
N2 - This paper considers a class of risk-sensitive stochastic nonzero-sum differential games with parametrized nonlinear dynamics and parametrized cost functions. The parametrization is such that, if all or some of the parameters are set equal to some nominal values, then the differential game either becomes equivalent to a risk-sensitive stochastic control (RSSC) problem or decouples into several independent RSSC problems, which in turn are equivalent to a class of stochastic zero-sum differential games. This framework allows us to study the sensitivity of the Nash equilibrium (NE) of the original stochastic game to changes in the values of these parameters, and to relate the NE (generally difficult to compute and to establish existence and uniqueness, at least directly) to solutions of RSSC problems, which are relatively easier to obtain. It also allows us to quantify the sensitivity of solutions to RSSC problems (and thereby nonlinear H∞-control problems) to unmodeled subsystem dynamics controlled by multiple players.
AB - This paper considers a class of risk-sensitive stochastic nonzero-sum differential games with parametrized nonlinear dynamics and parametrized cost functions. The parametrization is such that, if all or some of the parameters are set equal to some nominal values, then the differential game either becomes equivalent to a risk-sensitive stochastic control (RSSC) problem or decouples into several independent RSSC problems, which in turn are equivalent to a class of stochastic zero-sum differential games. This framework allows us to study the sensitivity of the Nash equilibrium (NE) of the original stochastic game to changes in the values of these parameters, and to relate the NE (generally difficult to compute and to establish existence and uniqueness, at least directly) to solutions of RSSC problems, which are relatively easier to obtain. It also allows us to quantify the sensitivity of solutions to RSSC problems (and thereby nonlinear H∞-control problems) to unmodeled subsystem dynamics controlled by multiple players.
KW - Nonlinear H-control
KW - Nonzero-sum differential games
KW - Perturbation methods
KW - Risk-sensitive stochastic control
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U2 - 10.1023/A:1022678204735
DO - 10.1023/A:1022678204735
M3 - Article
AN - SCOPUS:0033095698
SN - 0022-3239
VL - 100
SP - 479
EP - 498
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 3
ER -