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

T. Basar

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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 languageUndefined
    Pages (from-to)539-556
    JournalJournal of optimization theory and applications
    Volume33
    Issue number4
    DOIs
    Publication statusPublished - 1981

    Keywords

    • saddle-point solutions
    • Stochastic differential games
    • IR-85803
    • linear-quadratic games
    • conjugate-point conditions
    • information structures

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