Variations on the theme of the witsenhausen counterexample

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publicationProceedings of the 47th IEEE Conference on Decision and Control, CDC 2008
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)9781424431243
StatePublished - 2008
Event47th IEEE Conference on Decision and Control, CDC 2008 - Cancun, Mexico
Duration: Dec 9 2008Dec 11 2008

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Other47th IEEE Conference on Decision and Control, CDC 2008

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization


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