Settling the open problems in Kleinberg-Oren time-inconsistent planning models

This article shows an extended work of [Kleinberg and Oren 2014]. It gives more properties of the graph time-inconsistency model raised in [Kleinberg and Oren 2014] by solving three open problems proposed in [Kleinberg and Oren 2014]. Generally speaking, it gives a tight upper bound for the ratio of actual cost due to time-inconsistency to minimum theoretic cost, and shows the hardness of motivating agent. In the end of this article, it also shows some directions of further work based on this model or its extended version.