Battle Royale vol. 1 is discussed in this post.
Vol. 2 opens with 5 students dead, two used as examples before the game actually starts. Shuuya and Noriko are idealists who hope to find a way off the island without killing anyone. Over the course of these volumes the major players are sorted out - those who would rather not play the game and those who choose to play either through amorality or weakness. Back-story continues to be added. By the end of vol. 3, 25 of the original 42 remain alive.
Observation: the students are supposed to be classmates in the 9th grade. Some are drawn as if they might actually be 9th graders while others appear to be in their mid-twenties. This adds another layer of weirdness about this series. I was in the 9th grade in 1960 and it would have been unlikely that one of my female classmates would be running a prostitution ring. Still, some of these characters are more advanced than a lot of the college students I see daily.
If you can distance yourself from the ultraviolence, Battle Royale makes for compelling reading. The story line is complex and the back-stories add another dimension to the story.
Battle Royale, vol. 2 on Amazon
Battle Royale, vol. 3 on Amazon