New Multiplayer Theory

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Major problem is that things would get in an unpredictable state real quick. For example, is player -x- dead or not? If your computer thinks he is but really he's running around doing things, then those actions would have no effect either. It's little bits at first, but things would get further and further out of sync with actions not having the proper reactions, that the game would be next to unplayable in no time.

you'll have a bunch of people playing 1-player games while pretending it's not. the whole point of a network game is the interactions with others, so once that breaks / gets taken away, so does all the fun and challenge of playing a network game in the first place.

With the exception of a *very* few types of games (can't really think of any right now), I seriously doubt this could ever catch on.

Another problem: if each individual computer decides if a hit is really a hit or not, it's also trivial for people to cheat -- one of the tasks of a game server/player hosting the game is that there is a single traffic cop making sure everyones info is consistent with each other.

the 'proper' way of handling lag and such is to use prediction: if a player if running a long stretch from point X in direction Y and you don't hear from him in a short while, assume he's still running that direction unless there is something else in the way. then when you get an update with his real location you normally wouldn't be off by much and you can relocate the character to the proper spot. (as opposed to freezing him in place until you hear again, in which case the jump in location is likely to be significantly larger)