In all fairness,.. developing a SAW game would be incredibly difficult. I mean who would you play AS? Who's the protagonist? Who are the antagonists? The movie franchise itself is (in large part imo at least) an exploration in moral ambiguity with extreme violence used as a catalyst to get the audience to sit still long enough to get the questions proposed to them.
You know what I'd love to see in a SAW game? Let me design the machines and devices. Let me select locations and design rooms for victims, and for people who are meant to escape. Let me base my choices over who lives and dies on character development throughout the story, cut scenes, and game narrative.
With this being a video game, you're going to need some stages of the story driven by my play, so the story isn't just taking the player for a ride. So then, once situations are set up by me playing as "Jigsaw", let me also step into the shoes of an officer, or detective, paramedic, whoever,.. trying to find or rescue victims, pursue and question suspects, etc. I think the way we play through these scenarios could dictate different branches of the story line opening up,.. giving us different Jigsaw scenarios to play through.
I'm probably over-complicating the ideas, 'cause I suck at conveying ideas in text.
Mainly I'd love to work with the engineering side of the Jigsaw persona, but that would require actual creativity, tons and tons of hard work, coding, game menus that would make DaVinci cry, and thousands of hours of genuine well informed play-testing to iron out bugs, and errant possibilities,.. all things we haven't seen in the video game industry in a long time.
Anyway, to bring my idea to a close, I'd say, keep the player unaware of who they are actually playing as. Hear me out:... If you play amorally, and just build devices that are unescapable,.. or kill people fairly randomly you'd find out at the end that you're playing as that ex-druggie chick, or maybe a new character desogned for the game whatever.. you'd find out that you're just being a serial killer and get caught at the end.
If you play a bit more morally, allowing good people who made bad choices in the story to escape (maybe with a scar or two to remind them why they were being "disciplined", you'd wind up playing as someone more like Jigsaw,.. ultimately engineering a crafty escape from custody.
Just my ideas and ramblings, probably too "over the heads" of most gamers for something like this to sell well.
$5 says it'll be a 1st or 3rd person shooter, culminating in a physical showdown with Jigsaw where he beats you with machinery parts.