Later, underdog wants a more significant concession, but has had no success with previous threats of violence and so considers what other bargaining chips they have. Superpower negotiates, and a mutually-acceptable compromise is reached.

Well what I had in mind is that the superpower could attempt to negotiate a compromise right from the start. And to show that it's willing to compromise (not only in words), it might make the small concession first. Get the "moral high-ground", so to speak.

Now this might not work depending on who they're dealing with. But I doubt that "Muslims" in general are a group that can't be influenced in such a way. It almost certainly isn't going to be good enough for the types of people who threaten violence and follow-up on it, but they themselves could be influenced by other Muslims.

I could be expecting people to be more reasonable and rational than they actually are, so I might be wrong on how this will play out, I guess. Any (historical) real-world examples (or counter-examples)?