"Who incited you into doing it?" This is grammatically correct, but is not often used in this way. If you were asking someone face to face, it would be more common to hear, "who made you do it?", or simply "Who caused this?" "Who solicited you into doing it?" "Who made you do it?" or "Who caused this?" would still both be more commonly used than your example here. In fact, "incited" and "solicited" or used most often in reference to things and not a singular, specific person. For example, it is common to hear on the news that something "incited violence" or "incited public riots," or that a person "solicited the help of a friend or associate." In these cases, a thing, like "violence" or "a riot", is being "incited" and a thing like "help" is being solicited rather than the person offering the help. "Who goaded you into doing it?" This is correct and usable, but not very common in day to day speech because it uses the word image of a "goad," which is a sharp stick or instrument used to prod and herd cattle. It is a usable phrase that you might hear, but it isn't necessarily common. "Who is the instigator?" This is correct. It is perhaps a little more common to hear "instigate" used as a verb: "John Doe instigated the murder." However, it is correct to call "a person who instigates" something an "instigator." I hope this helps.