This is not an easy question to answer. There are three possible ways to look at it.
First, some would say that Caesar is responsible for his death, because he took too much power for himself. For example, he was dictator for life, which was never done. It did appear that he was breaking the traditions of the Republic. Did he want to be king? Some may have thought so. In this sense, some might say that Caesar should have known better.
Second, other would say that in the end Caesar was assassinated. So, it could not have been his fault at all. More importantly, these would say that many people in the Republic took too much power. For example, Marius was consul seven times! Sulla and Pompey also were power hungry. So, some might argue that Caesar was just doing what they did. Shakespeare seems to take this angle.
Still other would take a middle approach by saying that both Caesar and the conspirator were at fault. I think this is the closest to the truth.