John Harper's AGON has some friendly-competitive stuff between players. At least in the first edition it did, I assume it's still there in second edition. Can confirm that first ed was an awful lot of fun. (Second ed published by Evil Hat; looks like first ed was self-published.)
Robin Laws's RUNE was explicitly players-vs-GM. I never played it, so I don't know how well it works in practice, but it was an interesting read twenty-odd years ago. (Published by Atlas Games; long out of print, but the free PDF jumpstart might be enough to get you going. Rune product line website.)
I feel like if you're not playing Amber Diceless competitively you're doing it wrong. Every game I've run or played in has been deeply intriguey and backstabby among the PCs, even when they're nominally working towards a common goal. Happy to talk more about that if you'd like. (Published by Phage Games; long out of print in hard copy but PDFs are available on Drivethrurpg.)
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Robin Laws's RUNE was explicitly players-vs-GM. I never played it, so I don't know how well it works in practice, but it was an interesting read twenty-odd years ago. (Published by Atlas Games; long out of print, but the free PDF jumpstart might be enough to get you going. Rune product line website.)
I feel like if you're not playing Amber Diceless competitively you're doing it wrong. Every game I've run or played in has been deeply intriguey and backstabby among the PCs, even when they're nominally working towards a common goal. Happy to talk more about that if you'd like. (Published by Phage Games; long out of print in hard copy but PDFs are available on Drivethrurpg.)