Time consistency is an important property of any solution of a cooperative dynamic game. If a solution satisfies this property, players do not need to revise it and break a cooperative agreement. Strong time consistency is a stricter property which is applicable to cooperative set-solutions. In the paper, we consider the core as the solution and provide conditions for its strong time consistency. When the core is not strong time consistent, we show that in some cases its elements can be realized using a strong time-consistent imputation distribution procedure. An explicit form of the procedure is proposed.
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