In the city of the future, a young man takes on a series of mind-bending, gladiatorial games to win back the woman he loves. If he dies, she suffers; but to survive, he?ll have to break the city?s only rule.

I really like this idea. I think it would benefit though if you change the way it’s written, only slighty.

A logline is about making the story as clear as possible. To do this I suggest writing it as a series of causes and events. So with this logline I would re-word it like so:

In a city of the future, when the woman he loves is taken by (whoever) a young man must take on a series of mind bending, gladiatorial games to win her back or risk losing her forever.”

Obviously rather than the ‘risk loseing her forever’ bit, i would make the stakes a little clearer.

And i dont think that you need the ‘breaking the city’s one rule’ line. This just makes the logline more confusing and makes it read more like a tagline.