'Instigation' in the Bible

All the people and all Israel realized on that day that the killing of Abner son of Ner was not done at the king's instigation.

Now in the seventh month Ishmael the son of Nethaniah, the son of Elishama, of the royal family [of David] and one of the princes of the king, came [at the instigation of the Ammonites] with ten men to Gedaliah the son of Ahikam in Mizpah. As they were eating a meal together there in Mizpah,