On the saddle-point solution of a class of stochastic differential games

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Abstract

This paper deals with the saddle-point solution of a class of stochastic differential games described by linear state dynamics and quadratic objective functionals. The information structure of the problem is such that both players have access to a common noisy linear measurement of the state and they are permitted to utilize only this information in constructing their controls. The saddle-point solution of such differential game problems has been discussed earlier in Ref. 1, but the conclusions arrived there are incorrect, as is explicitly shown in this paper. We extensively discuss the role of information structure on the saddle-point solution of such stochastic games (specifically within the context of an illustrative discrete-time example) and then obtain the saddle-point solution of the problem originally formulated by employing an indirect approach.

Original languageEnglish (US)
Pages (from-to)539-556
Number of pages18
JournalJournal of Optimization Theory and Applications
Volume33
Issue number4
DOIs
StatePublished - Apr 1 1981

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Keywords

  • Stochastic differential games
  • conjugate-point conditions
  • information structures
  • linear-quadratic games
  • saddle-point solutions

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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