Reasons for Mukuro taking part in the Killing Game under her real Identity and Talent
- Junko is playing a long game here; having erased all of Mukuro's memories that are related to the worst actions that she took on Junko's behalf, so as to have Mukuro able to work alongside the other students in a more convincing manner, then restore these memories towards the game's end (if Mukuro ends up surviving that long). The aim of this is to drive Mukuro into a Heroic BSoD at what she did in the past and also cause the remaining survivors to fall into Despair, as they realize that one of their trusted allies was really one of the ones who destroyed the world...
- Mukuro is only pretending to stand against her sister here and acting on the side of those forced to take part in the Killing Game, so as to maximize the despair for them; when she reveals her true colours. But, over the course of this whole situation, Mukuro will slowly end up Becoming the Mask; with her realizing that her sister doesn't care for her wellbeing (along with enjoying being part of the group) and she ends up turning against Junko for real!
- At some point during the preparations for the start of Junko's plans to spread Despair over the entire world, Mukuro ends up having a Heel Realization (potentially when she sees how some of her younger sister's plans have personally affected Makoto or someone else that she has grown to care for [with it coming as a major shock to Mukuro just how much she's changed from how she was before] during her interactions with them, like Komaru) and she decides to break ties with her sister, undergoing a HeelFace Turn and trying to undo what she had once helped to create.
- Any one of the above ideas could be true, or maybe something else happens? However, given the way that Monokuma (and by extension, the Mastermind of the Killing Game) seems to really have it in for Mukuro in the Prologue(from the narrator's observations of the pair's interactions), I'm currently of the opinion that option Three seems to have been to most likely to have happened; even if we don't know the exact details behind this.
- One is partially confirmed by Word of God who has mentioned that, at least in part, Danganronpa IF happened prior to the prologue we saw.