"Bloodsport" follows Frank Dux, an American martial artist serving in the military, who decides to leave the army to compete in a martial arts tournament in Hong Kong where fights to the death can occur.
 
This film has not aged well.  I remembered it being a lot better.
 
FUN FACT:  Frank Dux was the fight coordinator for this film. When Jean-Claude Van Damme was cast, Dux announced that Van Damme wasn't nearly in good enough shape, and put him through a 3-month training program. Van Damme, a world-championship martial artist in his own right, called it the hardest training of his life.