Last step to the throne: The conflict between rulers and their successors

I model the dynamic between ruler and successor. The ruler cultivates a successor for a smooth power transition but fears being ousted by him, while the successor fears being removed by the ruler. The successor accumulates power while not threatening the ruler, and he prolongs their relationship by maintaining a low profile. The ruler gradually becomes more intolerant of the successor's growing power but, as his life nears its end, has less incentive to replace the successor. Thus conflict is most probable in the middle of their relationship; moreover, a predetermined succession order could increase its likelihood by restricting the ruler's choice. In the multi-candidate case, the strong candidate has some advantage but conflict is more likely to occur.