Okay, I was mistaken with the half as much part. Sony cut the price first then Microsoft and then Nintendo. PS2 was on the market for over a year and was doing well. Microsoft and Nintendo's price drops were desperate attempts at keeping up with Sony, Nintendo especially since Gamecube was already $199. It was as if they felt like they couldn't compete on a level playing field.
The question posed in this topic was should Nintendo drop the price of 3DS because of Vita. No. They shouldn't and I don't believe they did BECAUSE of Vita. They're dropping the price because 3DS was selling worse than expected and the price of entry was too high. That has nothing to do with Vita and everything to do with Nintendo's hubris. Vita is going to run into the same problem, not because Sony priced the hardware too high, but because they can't price it any lower. The point of bringing up the Gamecube price drop was that Nintendo was dropping the price in response to getting their ass kicked and to try anything to draw interest in the console. 3DS has neither of those issues. It's main competition isn't even out yet and I believe more people would have bought it had the price been lower.