Yes they both can exist...but not with a peer 2 peer service.
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I mean it could. But, depending on the game mode and the time of day, you might have to wait a while to find a match.
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Peer 2 peer yes, but I very rarely have any issues with games that have dedicated servers. Doom for example, dedicated servers and I match as quickly or quicker than Destiny with players all over the world. Zero lag.
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I mean dedicated servers would solve all these issues tbh. But I doubt that's gonna happen until destiny 2 at the very least.