Deterministic time-inconsistent optimal control problems — an essentially cooperative approach
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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.
Keywordstime-inconsistency pre-committed optimal control time-consistent equilibrium control multi-level hierarchical differential games
2000 MR Subject Classification49L20 49N10 49N70 91A23
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