Who said anything about sacrificing profit? Last I read Sony could trim price a little and still make profit on the console and of course there's games/Plus and other revenue on top of that.They're not going to sacrifice profit, especially when you consider Playstation is Sonys only division that's making them money at the moment. Sony just lost 1bn dude. Whether the X1 gains any ground is irrevelent to Sonys bottom line.
No company focuses on one metric. You need profit, sure, but also volume of sales and ideally a price point to generate certain revenues.
Sony will balance profit and sales vs the value of remaining dominant. Longer term losing momentum against XB1 could easily cost more than some small price trims to stay ahead.
To be honest it's a bit moot. On current trends I don't see £20 being enough to upset the apple cart to the extent Sony would respond. I'm just noting there would be a tipping point in sales trends where they would respond. That's a given just as they cut PS3 price even though it hurt them because they needed more volume than profit at that point.