Disclaimer: I don't work for GOG or have any insider information. Based on what I have read on other platforms, the developer generally sets the price, though GOG will likely provide a suggested price based on what their data shows will make everyone money. As far as I know GOG cannot discount the game without the developer's permission. As for how they convince the developer to sell their games at a discount, I would assume they have data showing it increases sales numbers (or at the very least copies sold.)
With regards to sales vs. permanently cheaper games, I would recommend reading up on what happened when
J.C. Penny attempted this (tl;dr it ended very, very badly.) Basically, a customer perceives a $20 item being discounted to $5 as a better value than if the item is always $5, even if $5 is the reasonable cost for that item.
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