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

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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.

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Correspondence to Jiong-min Yong.

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This work is supported in part by the NSF grant DMS-1007514.

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Yong, Jm. Deterministic time-inconsistent optimal control problems — an essentially cooperative approach. Acta Math. Appl. Sin. Engl. Ser. 28, 1–30 (2012). https://doi.org/10.1007/s10255-012-0120-3

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  • DOI: https://doi.org/10.1007/s10255-012-0120-3

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