Deterministic time-inconsistent optimal control problems - an essentially cooperative approach

    Authors

    J. M. Yong

    Comments

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    Abbreviated Journal Title

    Acta Math. Appl. Sin.-Engl. Ser.

    Keywords

    time-inconsistency; pre-committed optimal control; time-consistent; equilibrium control; multi-level hierarchical differential games; PREFERENCES; ECONOMIES; Mathematics, Applied

    Abstract

    A general deterministic time-inconsistent optimal control problem is formulated for ordinary differential equations. To find a time-consistent equilibrium value function and the corresponding time-consistent equilibrium control, a non-cooperative N-person differential game (but essentially cooperative in some sense) is introduced. Under certain conditions, it is proved that the open-loop Nash equilibrium value function of the N-person differential game converges to a time-consistent equilibrium value function of the original problem, which is the value function of a time-consistent optimal control problem. Moreover, it is proved that any optimal control of the time-consistent limit problem is a time-consistent equilibrium control of the original problem.

    Journal Title

    Acta Mathematicae Applicatae Sinica-English Series

    Volume

    28

    Issue/Number

    1

    Publication Date

    1-1-2012

    Document Type

    Article

    Language

    English

    First Page

    1

    Last Page

    30

    WOS Identifier

    WOS:000298041700001

    ISSN

    0168-9673

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