Abigail's parents were killed. She receives no affection from Parris other than material needs. She finally does find affection from John Proctor. When she and the other girls conspire to make up the story about witchcraft, she and the girls are trying to stay out of trouble, but this could also be another of Abigail's attempts to get attention (good or bad) and/or affection from someone. Keep in mind that she lives in a Puritan village, a very religious place where affection is strictly regulated and passion is reserved for devotion to God. Consequently, she seeks affection in any way she can.
That being said, she can not be totally excused from the hysteria she helped create. The question is how does she exert power over the other girls. One answer is that because she feels so alone, she will do whatever it takes to get attention. The girls fall victim to Abby's determination and find it difficult to disagree with her because she seems so confident. Abby is also successful in getting the girls to go along with her lies because the whole town is so pent up with religious fanaticism that they are easily scared into believing the presence of witches. Even Mary Warren, who at one point challenges Abby, falls for Abby's lies. Hathorne asks Mary, "How could you think you saw them unless you saw them?"
I-I cannot tell how, but I did. I-I heard the other girls screaming, and you, Your Honor, you seemed to believe them, and I- It were only sport in the beginning, sir, but then the whole world cried spirits, spirits, and I-I promise you, Mr. Danforth, I only thought I saw them, but I did not. (Act 3, Scene 3)
Abby is desperate enough to try anything to get out of trouble and/or to get attention. This makes her quite determined. Since most of the people in town are so fanatically rigid with their spiritual beliefs, they are ready to believe anyone. Abby is determined, repents, and puts on a convincing show.
I want the light of God. I want the sweet love of Jesus! I danced for the Devil; I saw him; I wrote in his book; I go back to Jesus; I kiss His hand. I saw Sarah Good with the Devil! I saw Goody Osburn with the Devil! I saw Bridget Bishop with the Devil! (Act 1, Scene 3)
Following this speech, Betty rises from bed and starts accusing people as well. Abby wants to be believed and the town's fanatics are ready to believe her because they are so pent up with religious fanaticism and fear.