Construction of Internal Time Consistent Optimality Principle

Many real conflicting situations occur on a given time interval and can be described by dynamic cooperative games. Most important properties in dynamic cooperation are time consistency and internal time consistency. This properties allow to preserve players cooperation during the whole time period.
In this paper we investigate possibilities of construction of new optimality principles with properties of time consistency and internal time consistency in case of dynamic hierarchical game.
As a basic model consider multistage cooperative game $G$ with hierarchical $n+1$ player game $\Gamma$, played on each stage. We choose core as a solution concept in each stage game, with the use of characteristic function defined in multistage game as sum of stage characteristic functions. The corresponding optimality principle is defined and internal time consistent. Example of a game with such optimality principle is also considered.