TY - GEN
T1 - Variations on the theme of the witsenhausen counterexample
AU - Başar, Tamer
PY - 2008
Y1 - 2008
N2 - This is a semi-tutorial paper that places Witsenhausen's celebrated 1968 counterexample within a broad class of dynamic decision problems with nonclassical information, which includes stochastic linear-quadratic Gaussian (LQG) teams as well as LQG zero-sum stochastic games. For a fixed (nonclassical) information structure, there are instances (depending on the structure of the objective function) when linear policies are optimal and other instances (including Witsenhausen's counterexample) when the optimal policies are nonlinear. The paper discusses these instances, optimality as well as saddle-point property (in the case of zero-sum games) of linear policies, and implications of these results for general multi-stage decision problems with specific information structures. It also discusses possible extensions to nonzero-sum stochastic dynamic games where the solution concept is Nash equilibrium.
AB - This is a semi-tutorial paper that places Witsenhausen's celebrated 1968 counterexample within a broad class of dynamic decision problems with nonclassical information, which includes stochastic linear-quadratic Gaussian (LQG) teams as well as LQG zero-sum stochastic games. For a fixed (nonclassical) information structure, there are instances (depending on the structure of the objective function) when linear policies are optimal and other instances (including Witsenhausen's counterexample) when the optimal policies are nonlinear. The paper discusses these instances, optimality as well as saddle-point property (in the case of zero-sum games) of linear policies, and implications of these results for general multi-stage decision problems with specific information structures. It also discusses possible extensions to nonzero-sum stochastic dynamic games where the solution concept is Nash equilibrium.
UR - http://www.scopus.com/inward/record.url?scp=62949192888&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=62949192888&partnerID=8YFLogxK
U2 - 10.1109/CDC.2008.4739205
DO - 10.1109/CDC.2008.4739205
M3 - Conference contribution
AN - SCOPUS:62949192888
SN - 9781424431243
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 1614
EP - 1619
BT - Proceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 47th IEEE Conference on Decision and Control, CDC 2008
Y2 - 9 December 2008 through 11 December 2008
ER -