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I'd probably split it even if it was set up à la the prisoner's dilemma and we both loose if we both choose to steal. I think most people would steal so I'd have low chances of winning in the first place. If I share then someone gets something and that's not so bad. Good karma, or whatnot. I might even get lucky and find someone who'd choose to split and then I'm $500 richer.
Anybody in the UK heard of the show Goldenballs? ( lol )
Not sure if it's still on but that's what this show was about (at the end).
They win money throughout the game and at the end you get to either split or steal.
I'd probably split though, I'm nice like that. If they chose steal I'd probably hunt them down after the show and murder them in there sleep :)
Unless the other person is extremely poor and needs the money then I would split...heck they can have the whole thing. They need the money more than I do.