Gp = Gr - (Gc + Tm)
since all values are greater than 0 we know that Gp and Gr are both positive and therefore
That is assumption that you are making and may not be true. Both Gamestop and the publishers want to drive full price sales near the time of game release. If Gamestop has data showing that credit from trade-ins tends to drive high profit full price new game sales from them instead of other retailiers, they could be willing to take 0 or even a negative profit margin on used games sales to generate those high profit sales and keep the customer buying from them. No different than loss leaders from other retailers. They also see a signficant financial benefit from the money they are holding as credit which isn't taken into account in your gross oversimplification.