PW owns cryptic, but cryptic are the game designers. decisions will most likely vary between PW, cryptic or a combination of the two depending on what they are. sometimes PW will provide input and ideas, give direct orders or just leave it to cryptic to decide.
no one will be able to tell you exactly who decides what, or where PW influence starts and ends.
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i would say it depends on what there trying to decide . as far as content, coding.. etc , cryptic,
as for giveaways , ZEN store offers, PR... ETC then PWE .
This. While Cryptic is wholly owned by PWE, my understanding is all game development is done solely by Cryptic. PWE makes no decisions regarding what does or does not go into the game. While they might give input, it will only be in relation to decisions already made by Cryptic, and are not actually involved directly or indirectly in any decision making.
What PWE is, is essentially a book/magazine publisher (and yes this is paraphrasing). They are responsible for Marketing. Whether directly or through BranFlakes, they are responsible for anything involved with promoting STO. Giveaway, Sales, Promotions, etc are most likely solely run by PWE.