Deterministic time-inconsistent optimal control problems - an essentially cooperative approach
Abbreviated Journal Title
Acta Math. Appl. Sin.-Engl. Ser.
time-inconsistency; pre-committed optimal control; time-consistent; equilibrium control; multi-level hierarchical differential games; PREFERENCES; ECONOMIES; Mathematics, Applied
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.
Acta Mathematicae Applicatae Sinica-English Series
"Deterministic time-inconsistent optimal control problems - an essentially cooperative approach" (2012). Faculty Bibliography 2010s. 3536.