Destiny uses a mix of p2p connections and dedicated servers.
Everyone holds dedicated servers on a holy grail when really they are not anything special. Dedicated servers have never been proven to be more or less effective than p2p connections.
Really it's all about net code, bungie is known for writing damn good (although laggy) net code. Dedicated servers wouldn't fix any problems.
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Only your inventory is on the bungie server thats why when you do something on the app or there site it changes in game everything else is port 2 port
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You sir, are technologically impaired.