New Multiplayer Theory

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So late last night while designing a cool multiplayer physics-based game (one that hopefully I'll actually finish, as opposed to every other time), I was wondering how best to deal with internet gameplay issues such as lost packets and lag. All of a sudden, I was hit with an epiphany. Unless someone else has already come up with this that I'm not aware of, I believe I invented this new technique, and would henceforth like it to be named after me. :)

Anyway, I was wondering... does it actually matter who "wins" an online game? Would it be awful if, say, two people won? Continuing this thought, would it be bad in any way if everyone thought they had won an online game, rather than the traditional one-winner-only idea? What if no one won? The reason for these questions is thus: what if each player's computer receives input (keyboard, mouse, joystick, etc.) from every other player, and the game is computed individually on each player's computer? But here's the catch: when lag creates a problem (i.e. one player sees themselves get hit by a bullet, another sees a miss), instead of trying to fix the problem, you simply let it go? Everyone who sees a player die has him die, and for all computers where he lives, he's still alive. If the player on his own machine dies, and some machines see he's still alive, then on those machines, he either becomes a computer opponent, or dies as soon as possible (i.e. Computers calculate it so he tries to get hit with bullets, etc.). In this way, every player could see himself become the "last player standing," and there's really no downsides, except for the fact that talking smack might be interesting when everyone thinks they've won.

Tell me if you guys understood that, and tell me what you think.