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Acta Mathematicae Applicatae Sinica, English Series 2012, Vol. 28 Issue (1) :1-30    DOI: 10.1007/s10255-012-0120-3
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Deterministic Time-inconsistent Optimal Control Problems — an Essentially Cooperative Approach
Jiong-min YONG
Department of Mathematics, University of Central Florida, Orlando, FL 32816
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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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Keywordstime-inconsistency   pre-committed optimal control   time-consistent equilibrium control   multi-level hierarchical differential games     
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.  
Keywordstime-inconsistency,   pre-committed optimal control,   time-consistent equilibrium control,   multi-level hierarchical differential games     
Received: 2010-06-11;
Fund:

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

Cite this article:   
.Deterministic Time-inconsistent Optimal Control Problems — an Essentially Cooperative Approach[J]  Acta Mathematicae Applicatae Sinica, English Serie, 2012,V28(1): 1-30
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http://www.applmath.com.cn/jweb_yysxxb_en/EN/10.1007/s10255-012-0120-3      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2012/V28/I1/1
 
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