The Dome by Joe Smith

In a post-apocalyptic world, the last remaining humans live in a huge dome. With limited resources available, they hold deathmatch tournaments each quarter between those who have turned eighteen during that quarter. Young men and women compete in separate events. Of the 64 entering each tournament, only 16 will survive. 

Kristin, who was a professional roller brawl fighter before war broke out, had to fight in a deathmatch tournament to gain entry into the dome for her and her infant daughter. Now, eighteen years later, her daughter has to fight in a quarterly deathmatch tournament. She competes not only with the other 63 young women, but she also fights the hunters who hunt the losers of each event during their tournament. One of these hunters is a nineteen-year-old woman who used to be her best friend when they were growing up.

This book contains scenes with brutal fights between women, some in sports like Roller Brawl (a mix between roller derby and MMA) and Combat Race (a mixture between athletics and street fights), others in deathmatch tournaments where women fight for survival.